News of the sitting president perdures as the media's unremitting obsession, as always, but a body can't swing a spraying polecat these days without also hitting some commentary about past presidents and the history of the presidency. For example, C-Span recently televised a lecture by the talented Establishment historian Michael Beschloss on America's imperial magistracy, with special attention to the accomplishments and character of Father Abraham. Beschloss — author and editor of several books on American presidents — was speaking at the Lincoln Forum in Gettysburg several days after the presidential election, and during the Q&A, he indulged in a little presidential ranking. (Guess who came out on top.) It's a game that writers on the public scene, whether laymen or registered members of the clerisy, find almost irresistible. I'm surprised I haven't given in to it before this. But now I've seen it played once too often by a worshipper of the presidency.
I would be hard pressed to come up with a ranking of the best presidents, and it would be pretty thin gruel in any case. Pointless, too, since the worst have had immeasurably more influence in shaping our history than the "best," whoever they may be. Therefore, what you have here is Strakon's list of the worst U.S. presidents — a round dozen of them, in homage to Suetonius, historian of the twelve Caesars.
But before I start the list I've got to get a few stipulations and qualifications out of the way. (That's how you know this is a Strakon column.) First, in building the list, I'm taking into account not only the calculated, deliberate, and direct actions of the president himself but also events occurring during his term that his people — or sponsors — helped steer. I don't want to be accused of blaming the puppet for actions of the puppet-master.
Second, I admit it may seem odd that no president of the past quarter of a century makes the list. If I were a historian I could fall back on some excuse such as, "It's too early to consider them. We don't have enough perspective." But honestly, at the risk of disappointing haters of Bush of Arabia, I don't think they qualify. They're up against some mighty stiff competition, for one thing. And however wicked and dastardly they were per se, they came along too late to wreck the Republic.
Take Clinton, for instance. He helped to further degrade the populace, but he was propelled into office by an irrevocably degraded populace to begin with. And he did much to shatter the icon of the presidency in the eyes of the non-degraded remnant of believers — which actually wins him a better ranking than president No. 12, who refurbished that icon. If I were going to add a thirteenth president, I'd probably put Reagan on there, largely on account of all his empty wind and deficit spending. I hope that helps.
Finally, when I point out that this isn't rocket science, I don't mean it's easy. I mean it's not scientific. The order of presidents in the early going — the "least of the worst" — is especially debatable and subject to reshuffling.
Kennedy makes the list primarily because of his disastrous and scary foreign-policy arc, from the Bay of Pigs to his fumbling summit with Khrushchev to the Berlin crisis to the Cuban missile crisis. Actually, it didn't end in 1962. Only 20 days before Kennedy's own assassination, his national-security apparatus was complicit in the assassination of "our ally," South Vietnamese President Diem. Oliver Stone and other Kennedyite fools think that this Cold Warrior, fierce and incompetent, would have avoided the Vietnam quagmire had he lived. Fat chance.
Kennedy qualifies for the list also because of that icon-restoring I mentioned earlier. He and the flacks around him, aided by their revolting, lying sycophants in the media, did their best — and their best was very good — to create entire generations of Kennedyite fools. And those fools were also fools for the glittering, heroic, sacred Arthurian presidency itself. On the domestic side, Kennedy didn't get much evil accomplished, owing to his lack of skill in governing and negotiating, but he did put some big bad trains on the rails — notably the first and worst of the major civil-rights acts — that his more skillful successor was able to send roaring down the tracks.
One of the reasons I've listed Jefferson is the dismaying gap between his rhetoric as a revolutionary and his performance once in the White House. If that strikes anyone as unrealistic, I'd ask them to consider whether it's my expectations that are unrealistic — or those of limited-government republicans. Promoting the Embargo, permitting the nascent public debt to survive, and starting the National Road look like small potatoes to us now, sinking as we are under the weight of the fullblown leviathan, but those acts of Jefferson, only the third occupant of the magistracy, helped set the tone and establish the framework of that very leviathan. The same is true of his sending the U.S. Navy to police the Barbary Coast — a terrible precedent that came terribly early in our history. Americans now have the idea that they can freely wander the world and, if they get in trouble, aircraft carriers must rush to their rescue, financed by taxpayers with the good sense to stay at home. And those carriers do rush to the rescue all too frequently when the people, or corporations, getting in trouble are politically connected.
So much for small potatoes, so-called. Jefferson's Louisiana Purchase was one big honking potato by anyone's measure. He said his principal aim in cutting the deal with Napoleon was to exclude the great European empires from the backyard of the Republic, and while I'm not about to call Mr. Jefferson a liar, I will point out that the purchase also enormously increased the area of the so-called public lands. That was land over which the Central Government asserted not only political sovereignty but also — in a style we moderns must recognize as totalitarian — actual ownership.
Jeffersonians are usually considered foes of bank privilege, but the government's sale of "public" lands to settlers established a class of unjustly privileged creditors and a class of unjustly expropriated debtors in the West, as cashless settlers took mortgages from banks to purchase land they shouldn't have had to pay for at all and wound up either foreclosed upon or dependent on the banks for life. Meanwhile, Jefferson was using revenue from public-land sales to finance the National Road. It's a good thing Alexander Hamilton never became president; Jefferson as president was quite enough of a Hamiltonian himself.
Mentioning Hamilton reminds me of his tardy executioner, Aaron Burr. In standing sentinel over his new Louisiana Territory, Jefferson seemed to be less worried about encroachments by European empires than about his old running mate's purported scheme to set up an independent commonwealth in the Western wilderness. In 1807, Jefferson haled Burr into court on a charge of treason. That was two years before the birth of another man who, when he occupied the White House, defined secession as treason. He occupies a place on this list also.
Boring, boring, boring, I know. He appears on all the leftists' lists of the worst, and that alone gave him a shot at staying off my list. But he's got to be on it somewhere. Nixon was the second Great Society president. He inherited Great Society socialism from his predecessor, and if he did anything important to overthrow it instead of enlarge it, my memory fails, and I am prepared to be educated. EPA, OSHA, Consumer Product Safety Commission, gasoline socialism, affirmative action, wage-price controls, "We're all Keynesians now" — Nixon was the very model of the Republican socialist.
Nixon and his people ended the draft and the Vietnam War, but they pre-emptively forfeited whatever credit they were owed from that when, upon taking office in January 1969, they drafted the next American boy and permitted the next bomb to be dropped in the stupid, unjust, and murderous foreign war they were inheriting. Nixon was not only the second Great Society president but also the second Vietnam president. If he hadn't carried out some important presidential-icon-besmirching of his own in the Watergate affair, I'd assign him a worse rank.
To Part two of this series.


I know I have kept you waiting on the edge of your seats and screens (LOL) so you could hear about my crazy stories. But it will have to wait. I knew April would be crazy. Really crazy. But really I didn't think it would be this crazy.
I leave tomorrow to Nashville, TN for Scrap ETC event. I can't wait to spend time on my own no worries about work (although, I'm still on-call, I'm always on call) or anything else. I get to scrap. Take classes with my friends Erin, Laurie and Veronica. I also get to meet and hang out with Deb from Scraptalk. This should be so much fun. On top of all this, we get to take classes and learn from eachother. Plus we get to go shopping on Wednesday at LSS in the area.
On Sunday, I will also take a class from Debbie Schuh. I'm really excited about this. I have been a stalker of her blog since I learned about her work in CKU-A San Jose '06. I love that her work always has neat ways to do altered stuff.
Then Monday and Tuesday of next week, I'll be in Memphis, TN visiting the king. And next Wednesday I'll fly back. And I promise, I will try to give you all an update when I return. I'm not taking a laptop this time. But I will have my cellphone with me. If anyone wants to chat, give me a ring.
I'm really tired, I have been up since 2am and couldn't go back to sleep. Work has been crazy. I only have 4 days before I leave again for another week and some days. So I got tons of catching up. I swear, I'll try to update with all my stories from my trip. But for now, I'm trying to get back to my old self and not being so much jet lagged.
P.S. Patty and Lisa, I waited until everyone would be out of the picture so I could take the photos. I really like the postcard look of photos. But got tons of photos with people in them.
What a beautiful city! I really enjoyed this little medieval town. I'm really tired and need to get to bed early as I have flight early very early tomorrow.
But here are some pics to keep you all up to date.
I have some stories about today but will leave those for another time.
Well I have been very busy. My business meetings went well and all was done on Friday. But I really didn't have any time to sightsee. On Saturday, I was lucky enough to visit Lourdes. Being Catholic it was a very moving experience, it brought me to tears for no reason. Lourdes is where the Virgin Mary made an apparition to Bernadette back in 1858.
The journey begins with me waking up at 430am to get ready to catch a taxi at 530am so I can catch the 609am train to Lourdes. I arrive at the train station with enough time but the machine will not accept my credit card (not a single one, even though it said it would accept VISA). I went to almost every single machine (about 15) and tried it. It kept saying "CARTE NON GEREE" which I didn't know what it meant. I figured it meant that the card was not good. Check for my self, I need a french pocket dictionary along with my phrase book. I looked it up now that I'm online and it means card not managed. I'm guessing that it means they can't accept cards that aren't French banks or something like that. I had used it the previous day, so I know it works in France. I miss my train and I know not to get on it without a ticket or I would be fined. I was about to go and ask the information desk when I see that that the ticket agent booth lights turn on, they open at 7am and the next train is at 715am, so I wait by the door so I can be sure to get my ticket before the train leaves. With my little French I manage to get a ticket and I'm on my way. I get to sit with three guys but they all speak French so they little I can understand is are on their bikes and they are riding around but I wasn't sure where, they had maps of the area. One of the guys reminded me of the actor who plays Harry Potter. They get off 2 exits before Lourdes. More on them later.
Here are some pics from Lourdes. It is a beatiful town, rich in history and also very picturesque.
After an all day of walking around the sights, I returned and who do I see at the train station. Yeah, the three French guys and they start talking to me and asking me for my ticket as they are now the new "conductors" They are pretty funny and we end up on the same car, but this time we get to each have our own seats so that we can take a nap. I was exhausted by this time and finally slept. When I got back to my hotel, I slept for 12 hours. Something I had not done in over 3 weeks. I met up for lunch with one of my coworkers who works here in Toulouse, actually is 45 minutes away. Travis, his wife Stacy and their son Liam went with me to see around a little of the town and got to go to this beautiful church.
We then went on to see the gateway that is where Travis works and we get telemetry for our satellites. After dropping his family off he took me to the Space Museum in Toulouse, I had tons of fun and got to walk around different things, including the mock up of the MIR station and also the new module that was just shipped to the international space station a couple of weeks ago, it's name is Colombus.
They also have information on Globalstar, which was pretty cool to come all this way and find information on it. Turns out that in that space museum, anything that has been made here in Toulouse and it's related to space it will be shown. The payload of our satellites were made, and that's why it's shown here.
It's 1am and I'm off to bed, I have to wake up early to make my 750am train.
18 hours later I arrived at the hotel and unpacked. Took a little nap and off to dinner. Then back to the hotel and crashed (not really), I haven't been able to sleep as much as I wanted. I'm sure tonight will be a hard crash. It's 710am and I have to get ready to go to work. I will update later.
I'm sure I'm forgetting something. But I'm all packed and ready to go to France. I'll miss everyone. I will send updates from Toulouse.


Note: lists are subjective and are not meant to be an objective assessment of the quality or value of any particular movie. This list is undeniably personal and it reflects my own thematic preferences. I consider "best" to be some kind of combination of technical achievement, enjoyment of viewing and a variety of other factors. It's also contextual: ask me a month from now and I might provide you with a very different looking list. Additionally, it was difficult for me to leave some movies off the list which I actually adore (Aliens, Predator) but which I intuitively don't think constitute horror enough to be featured on a list such as this one. Understand all of this before replying or commenting with an outraged "how could you leave X off of the list!?" or "I can't believe you ranked X higher than Y!!!"


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Porsche India launches new 718 Cayman and Boxster
Porsche India launches new 718 Cayman and Boxster-Pavan Shetty, Director Porsche India and Deesch Papke, CEO of Porsche Middle East and Africa FZE.
German sports car major, Porsche launched their new 718 Cayman and 718 Boxster in India for Rs 81.63 lakh and Rs 85.53 lakh respectively. The new 718 series coupe and roadster derive their rich heritage from the victorious race cars in Porsche's stable, such as the 718 RSK which won multiple races in the 1950's and 1960's.
Both sports cars feature a mid engine and are small yet powerful machines. Powered by a 2.0 litre, turbocharged, four cylinder, flat engine these cars prove to be more powerful and faster than their predecessors. The engine is capable of putting out 300hp and turning 380Nm of torque, propelling these machines to 100kmph from standstill in a mere 4.7 seconds and achieving top speed at 275kmph.
The engine has been mated to a 6-speed manual transmission and both cars also get the option of auto start/ stop to improve efficiency while the vehicle is coasting. Both the Coupe and roadster are capable of delivering a fuel efficiency of 14.49kmpl which is an improvement of 13pc over the previous models.
The entire exterior design of both models have been replaced except for the boot lid, windscreen and roof structure. They get larger cooling intakes, bi-xenon headlamps and integrated LED DRLs. Both models now get a wider stance and now get a distinct persona thanks to re-designed headlamps, an accentuated strip in the rear, 3D LED technology in the headlamps and four-point brake lights.
The interiors of the cars get exquisite leather upholstery and technology like Porsche's latest gen Communication Management, touch screen infotainment system which can also operated through voice control. The vehicle also gets a Sport Response button for models which have been equipped with PDK. increasing engine response direct for a period of 20 seconds.
Present at the launch were Pavan Shetty, Director Porsche India and Deesch Papke, CEO of Porsche Middle East and Africa FZE.
Tags Porsche Porsche India Porsche 718 Cayman Porsche 718 Boxter 718 RSK

redpajama_set_name: RedPajamaCommonCrawl


The man who brought the Tour de France to Scarborough, who was on £243,000 a year, "made errors of judgement regarding his expenses".
An investigation was mounted by the Sunday Times, which presented the tourism body with evidence of bullying and erroneous expenses claims.
The resignation followed years of concerns about Verity's bullying behaviour towards staff and his expenses claims, described by several staff members as "lavish".
It is understood that among the expenses Verity attempted to claim were some relating to the funeral of his sister, who died in January last year.
Welcome to Yorkshire ordered its own investigation into the allegations and concluded that Verity "made errors of judgment at a very difficult time for him and his family".
Verity, 54, has agreed to reimburse Welcome to Yorkshire for monies owed. The amount is understood to be a five-figure sum.


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Iraqi politicians 'break deadlock'
Rival blocs set to form new government in deal that would allow al-Maliki to remain prime minister.
Al-Maliki's party said it would form a government even if other blocs chose to boycott the parliamentary session [AFP]
Iraqi politicians appear to have broken an eight-month political impasse by agreeing to take part in a new government headed by Nouri al-Maliki, the incumbent prime minister.
Officials said on Wednesday that the Sunni-backed Iraqiya coalition that had been opposing the prime minister decided to join his government.
Iraqiya joins the Kurdish alliance in supporting al-Maliki following months of contentious negotiations.
"Finally, fortunately, it's done. It's finished. All the groups are in it,'' Mahmoud Othman, a Kurdish politician who took part in the nearly seven hours of negotiations, said.
Ali al-Dabbagh, a government spokesman and member of al-Maliki's State of Law coalition, said Iraqiya had decided after extensive talks to accept the parliament speaker's job and cede al-Maliki the prime minister's job.
An official with Iraqiya, who asked not to be identified, confirmed that the coalition had agreed to take the parliament speaker's position in a deal that would see al-Maliki stay on for another four years.
Iraqiya will decide on a nominee from the party for speaker of parliament at a meeting on Thursday, which will be just the second parliamentary meet since an inconclusive election on March 7.
Iraq has been without a government since the vote, which gave Iraqiya two more seats than al-Maliki's bloc. Neither had enough for a majority in parliament, forcing the factions to negotiate a government.
Repeated rejection
Over the past months, Iraqiya had repeatedly rejected another al-Maliki term and demanded the right to form the government as the top vote winner in the election.
Politicians from al-Maliki's National Alliance said they would proceed with government formation as
long as they had a political majority - even if other blocs chose to boycott Thursday's parliamentary session.
"We do not imagine a government that does not represent all Iraq's factions ... But the government does not and will not stop, God forbid, if a list stays behind," Ibrahim al-Jaafari, a senior member of the National Alliance, said.
"We don't expect major surprises in this deal," Rawya Rageh, Al Jazeera's correspondent in Baghdad, said.
She said al-Maliki would likely remain prime minister and Jalal Talabani, a Kurd, would retain the presidency.
Rageh also said the deal could include a new strategic council intended to serve as a check on the prime minister's power.
Iraqiya would take the speaker's post, the foreign ministry and a role with possibly expanded authority over defence issues, the economy and foreign affairs.
Parliament met briefly in June, but politicians said they needed more time to decide who would hold the highest offices.
Last month, Iraq's high court ordered parliament to resume its sessions, putting pressure on politicians to expedite a deal.
The long deadlock has fuelled tension - even as sectarian violence that came after the 2003 US-led invasion has been receding - while US forces prepare to withdraw in 2011.
A series of attacks on Christian targets across Baghdad on Wednesday stirred renewed fear in the minority community.
The bomb and mortar blasts occurred just 10 days after a bloody siege at a Catholic cathedral in the capital that killed 52 people.


Now the point of comedy is not just looking funny, it's use of language. We have at our disposal a great language... and the imaginative, creative use of that language can be at the service of humour.
Freedom of expression is not absolute. Countries have laws that define the framework for exercising this right and which, for instance, condemn racist language.
A lot of the websites built through the 1990s used Perl. The first webmaster of Sun Microsystems coined a wonderful phrase. He said Perl is the duck tape of the Internet - it's this language that people would write all these scripts that make things just work.
We breathed the air of freedom without knowing the language or any person.
Any friendship or relationship is about a language.
Under the Assads, Kurds were forbidden from learning their own language at school, or even from speaking it in the military. The result is a generation of Syrian Kurds, many now in late middle age, who can't write their own language.
Language is memory and metaphor.
You know, we have main English language parties, federalist parties, and traditionally the ones to watch would be the Conservatives, who form the government, and then the Liberals.
The best way in the world to deceive believers is to cloak a message in religious language and declare that it conveys some new insight from God.
Once in my childhood I had been eager to learn Irish; I thought to get leave to take lessons from an old Scripture-reader who spent a part of his time in the parish of Killinane, teaching such scholars as he could find to read their own language in the hope that they might turn to the only book then being printed in Irish, the Bible.
But maybe music was not intended to satisfy the curious definiteness of man. Maybe it is better to hope that music may always be transcendental language in the most extravagant sense.


Jim Motavalli (the former editor of E), gets inside the green car revolution in his latest book High Voltage: The Fast Track to Plug In the Auto Industry (Rodale). Even if you aren't a car enthusiast, his enthusiasm for the recent surge in electric and plug-in hybrid options on showroom floors, mixed with auto history, first-hand driving experiences and interviews with the industry's key players, makes for an entertaining read. He leads with a breakdown of the different electric models: battery electric (cars that offer no gas backup like the Nissan Leaf and Ford Focus); plug-in hybrids (cars like the Chevy Volt, that do have a backup gas-powered engine); hybrids (like the Toyota Prius, which mixes gas and electric drivetrains); and fuel-cell cars (electrics in which fuel cells replace battery packs). These electric cars represent a major breakthrough for the planet, finally pointing the industry in an oil-free direction. But speed, Motavalli is quick to acknowledge, is key. The Tesla Roadster—and subsequent Tesla models—he credits with providing a rocket ship-like takeoff. It's a car made for acceleration—which makes it as fun to drive as it is responsible to own.
The success of electric and hybrid cars largely depends on the success of their batteries. In fact, Motavalli writes, "battery companies have become the rock stars of the EV business." Not only are consumers paying more for electric cars thanks to the batteries, but carmakers are in many cases losing money. While battery technology is moving forward, no one will provide a firm estimate of when costs will come down, and the dominant model—the lithium-ion—is likely to remain dominant for the next decade. Other challenges include the lack of charging stations to support widespread electric vehicles, or as Motavalli notes, the more innovative battery swapping sites. He writes: "Suppose you could just drive into something resembling a gas station without attendants and have robots switch your battery pack for a fresh, charged one in just minutes?" The technology already exists, and he's seen it in action. Motavalli's behind-the-scenes perspective gives readers real insight into the possibilities offered by electric cars which clearly will no longer be relegated to a niche market.


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KCK Public Schools begins forums on proposal for cameras in classrooms
KANSAS CITY, Kan. — Tonight, teachers and other staff members of Kansas City, Kansas, Public Schools will be able to provide feedback on a proposal from the district to install cameras in classrooms.
The school board first reviewed a $6.8 million proposal in October. It called for installing about 1,600 cameras in the classrooms of schools throughout the district. Before making a final decision on whether to move forward with the proposal, the district promised to gather feedback. Here are the details on the forums:
Wednesday, Dec. 7, 2022:
4 to 6 p.m.
District headquarters, 2010 North 59th St.
Meeting for staff members only
Saturday, Dec. 17, 2022:
10 a.m. to 12 p.m.
Meeting is open to the public
Saturday, Dec.17, 2022:
Virtual meeting, more details to come
The district's proposal says cameras will allow teachers to stream or record their lessons, giving students across the district equal access to high-quality instruction. Due to a nationwide teacher shortage, the district has relied on long-term substitute teachers in many cases.
Recording lessons will also allow students to keep up with work when they're absent and give teachers an opportunity to review their work.
The summary from October's board meeting does not mention the words "safety" or "security" as reasons to install cameras, but when KSHB 41 News spoke with parents of students, they immediately thought of security as a reason for cameras in classrooms. They also brought up invasion of privacy concerns.
"I think there is a very fine line of invasion of privacy, but at the same time security protection for the children. So long as there is some sort of structure and program system put in properly, all parents can meet in the middle," said Antonio Taylor, father to a kindergarten student.
Another parent wondered how students may feel about the cameras.
"I would think there would be a little bit of a privacy issue and some of the kids may not be as comfortable with it," added another kindergarten parent, Dan Thompson. "As far as security, I like that a lot."
Independent facilitators will attend each forum. Participants will be able to learn more about the proposal, ask questions and submit feedback.


text:
Touchy, touchy!
German economist apologizes for Jewish comparison
BERLIN, Germany (AP) — A leading German economist apologized Monday for drawing a much-criticized parallel between corporate managers today and the Nazi-era persecution of Jews that followed the 1929 financial crisis.
Hans-Werner Sinn, the head of the Munich-based Ifo institute, was quoted as telling the daily Tagesspiegel in an interview about the global economic meltdown that "in every crisis, people look for culprits, for someone to blame."
"No one wanted to believe in an anonymous systemic error in the world economic crisis of 1929 either," he added, according to the report. "Back then it hit the Jews in Germany; today, it's the managers."
Recent weeks have seen widespread condemnation of perceived failings by financial experts prior to today's financial crisis.
In contrast, the 1929 crisis was followed by the rise to power in 1933 of the Nazis, who set in motion a systematic persecution of Jews that culminated with the death of 6 million Jews in the Holocaust.
Sinn drew strong criticism from the government and the opposition, from Germany's Central Council of Jews and from the Simon Wiesenthal Center. He issued an apology a few hours after the interview hit newsstands.
"We should note the contemporary hatemongers who, once more, libel 'Jewish finance' for the contemporary financial crisis," Samuels wrote.
www.sfgate.com/cgi-bin/article.cgi?f=/n/a/2008/10/27/international/i061506D24.DTL
By GEIR MOULSON, Associated Press Writer
← Author of fabricated Holocaust memoir wins legal fight
Orwellian Alert! British Crackdown Threatens Us All →


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REPORT: The impact of Christians leaving Middle East
April 18, 2016 By World Watch Monitor Iraq, Islamic State, Migrants, Refugees, Syria
Refugee camp next to St. Elia Church in Erbil, Iraq.
Open Doors International
War and persecution has led to a haemorrhaging of Christians from the Middle East, particularly from Syria and Iraq. A new report highlights what the region stands to lose should Christians continue to leave.
The report, compiled by a trio of Christian charities and a university, argues that Christians are an essential part of Middle Eastern history and culture, and that they continue to contribute powerfully to society, particularly in the fields of education, medicine, science and engineering.
For Syria and Iraq to lose Christians altogether, the report says, would not only damage the fabric of the society, but negatively impact upon the two countries' economies.
"In the Middle East, the Church is under severe pressure and Christians face increasing marginalization, though their presence in the region dates back two millennia," it says. "Many are choosing to leave in a desire to ensure a more certain future for their families, but others remain committed to their countries and their homes. Nonetheless, Christians in Syria and Iraq continue to contribute to their societies in a variety of ways, including education, culture and arts, social affairs, politics, economics, humanitarian assistance and religious activities."
Before 2011, Syrian Christians comprised around 8-10% of a 22 million population, notes the report, though 40-50% of those Christians have since left. Meanwhile, there were approximately 1.5 million Christians in Iraq before 2003, but estimates now range from 200,000 to 500,000.
"Approximately 30-35 million Christians worldwide are members of Middle Eastern church families, but only 15 million of these reside in the Middle East," it adds. "While there is a high level of emigration, there are also many Christians committed to staying in their countries."
One common concern about the long-term effects of conflict in Syria is that the current diversity of Syria will be lost.
Why are they leaving?
International Christian organisations have been trying to "source the support needed to stem a growing sense of hopelessness", it says, but "increased poverty is one of many factors encouraging emigration".
Increased marginalisation is another factor. "In many countries Christians face increasing marginalisation, and perhaps nowhere is this strain felt as strongly as in Syria and Iraq," the report states. "Whoever has the ability to leave is leaving. The Christians have a greater sense of insecurity because they cannot integrate into the changing scenery. Other community members could integrate into the new social scene, but not the Christians.
"Christians who emigrate are at an advantage for integration compared to other minorities … because they are mostly being resettled into communities where Christianity is the dominant faith, and also because of strong diaspora communities already in place, ready to receive them. So it may be that they will be less likely to return to Syria than Muslims when and if the conflict ends."
The report says that Christians in Syria and Iraq have "generally enjoyed freedom of worship", but that the current crisis this has changed.
"In the current changing political landscape, the few Christians who still live in areas under the control of the so-called Islamic State or other Islamic groups often have to agree to pay a jizya tax, an Islamic religious tax imposed on non-Muslims, and face a variety of other restrictions to church buildings and to engaging in religious activities," it says. "In these areas, many Christians have fled or are fleeing; those who remain have become extremely vulnerable, with their churches, homes, businesses and very lives at times targeted."
In Iraq, the report says Christians have an "ancient history" and have been free to practise their faith and rites, but that "in some less stable regions … Christian communities are frequently the target of extremist Islamist attacks, including a number of instances of deadly church bombings since 2003 and brutal treatment by the so-called Islamic State."
What impact?
A school for Syrian refugees in Lebanon. Christian schools in Syria and Iraq are 'widely acclaimed as the best and most desirable educational institutions', says the report.
"One common concern about the long-term effects of conflict in Syria is that the current diversity of Syria will be lost," says the report.
"Christians add a diversity of perspectives to public discourse and thus help encourage critical thinking in society. Without Christians … there would be little space in Iraq for intellectual curiosity and critique … Perhaps most distinguishes Christians in Iraq is their high average level of education."
The report adds that many Muslims in the Middle East "appreciate Christians as encouraging secular and liberal thinking, and [say] that the high representation of Christians in the arts and intellectual circles may be attributed to the relatively liberal education enjoyed by many Christians. Many fear, therefore, that the loss of a Christian influence in Syria could open a greater space for extremism.
"There is a strong tendency among many rebel factions toward Islamisation and the building of a predominantly Sunni Muslim society, but many Syrians, including members of the Muslim majority, do not want this."
"Christians can be found in most if not all economic sectors … [they] have a reputation for quality work, and attracted investment into Syria during the decade before the current crisis," says the report, although it adds that "their economic influence is not as visible as it once was".
It says "areas that were managed by Christians were better managed, they knew better how to use the resources and provide services."
Meanwhile, "Christian schools are widely acclaimed as the best and most desirable educational institutions," it says.
The report, Hope for the Middle East, was compiled by Open Doors, Middle East Concern, Served and the University of East London.
Persecution Watch countries: Beyond the Top 50
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Christians matter least in Pakistani politics


An executive from America was walking along the beach in a small coastal Mexican village, taking a much needed vacation. It was his first in more than 10 years. He noticed a small boat with just one fisherman pulling up to shore. Inside the small boat were several large fish. The executive complimented the fisherman on the quality of his fish and asked how long it took to catch them.
"But what do you do with the rest of your time?" the executive asked.
"And after that?" the fisherman asked.


What's amazing to me is how people want to believe in eternal torment.
Sciotamicks, do you like the idea of ET? You defend it with great gusto.
Lets try to look at this objectively. Obviously people draw conclusions from the bible. Some see UR plain as day. Others see ET plain as day. Now obviously certain verses can be used to support either case. But on deeper investigation only one view can be right.
Now IMHO the verses that plainly support UR are about 90% while ET is maybe 10%, and then on close examination of the ET verses they are actually very weak and can only mean ET due to mistranslation or misinterpretation.
So given the above, why do people try to cling to ET? Why not investigate the UR side and see if it holds weight? Its like ET gives them some power or some reason to live or something.
To support ET, you have to believe silly views that suggest sin will have its own place to exist forever, when this obviously contradicts the stated mission of Jesus. So for example, sciotamicks would rather believe that sin lives on forever than believe that Jesus actually takes away all sin of the world. Why?
Its mind-boggling. People want to believe in eternal torment. They seem to like the idea. Even in the face of overwhelming evidence (the 90% plain UR verses), they prefer to cling to the 10% that could be misinterpreted as ET.
When you want to believe in eternal torment, you will see it in every verse you read, even when its not there.
When I believed in eternal torment for 30 years, I believed it because I thought it was the truth. Sometimes I wanted to believe in it, but most of the time I didn't want to believe in it. But I didn't know there was any other possibility.
When I learned of UR, it blew me away. I didn't think it could be true because no one had told me about it in 30 years. But I studied it and I quickly found ET to be wanting; basically ET is based on a few mistranslated and misinterpreted verses. UR is the superior view in that it takes into account God's love, God's character, and can align with 100% of all verses. ET can only align with all verses by either changing them or outright ignoring them.
People, ask yourself why you prefer to believe in eternal torment?
Who here really believes this? Its what the bible says.
Yet most believers in ET (except maybe hyper-calvinists) don't truly believe salvation is a complete work of God.
People will suggest that you have to choose to believe of your own free will, or you have to have your own faith. But these ideas are not found in scripture. Sure people choose to believe, but only after God has revealed Himself to them.
Scripture is clear faith comes from God, belief is granted from God, God leads people to repent, and God is the one who is actually dragging people to Christ.
Yet people like this idea that they do their own "tiny" part to be saved. It is simply pride - that way it is your fault if you end up in "hell", and that way it is to your credit if you make it to heaven.
Now if you continue to say we are twisting your words then it is evident that you are backtracking and have closed your mind to the issue altogether. Three people have now understood your statement and yet you say we are misunderstanding it. If this was me, I would apologize and restate my point more clearly... you seem to think it is our fault that you are not being clear.
Unbelievable......that's all I can say....unbelievable.
Christian Universalists don't need the "but" when speaking of our faith in Jesus.
I don't believe I have ever read where any one has denied that, "Salvation is a complete work of God."
Your pondering about others thoughts and what they believe is so wrong..... this is what you believe and projecting upon other's.
I have never read of anyone stating that they "don't truly believe salvation is a complete work of God".
This once again is what you believe and projecting of what others think, believe.
Yes, God's grace reveals to the sinner their sin, through the Holy Spirit, leading and revealing to them why Christ died on the cross!! Then the Father's grace gives that individual the faith the choice to agree with God about their sin (unbelief) and make that choice to repent, turn away from sin and in exchange give to them the faith to believe in His beautiful gift of salvation, eternal life with Him, through Jesus Christ, forever and ever !!!
Yes, this is true and once again I have never read anyone denying it is not the work of God who draws men/women by His Holy Spirit, to Himself and revealing to them their sin, (unbelief) and that the remedy to this destruction of the life of sin is through the cross of Jesus Christ, the Lamb of God, the ultimate sacrifice, whom shed His blood for the world and its sin. His grace granting them the choice to exchange for their life of sin, a life of forgiveness through Jesus Christ, the faith to freely choose to live a life in His righteousness for those who do agree with the Father the darkness of the life of sin in their hearts.
What a wonderful revelation of His grace to be able to repent of sin. Thank you, Father for your grace given through Your faith to be able to choose and to turn from the darkness, to the light of Jesus Christ, that You, Father reveal to the heart!!! Hallelujah !!!!
Boy, one really has such an imagination of what others are thinking and doing !!
Sciotamicks doesn't seem to believe salvation is a complete work of God.
If what sciotamicks was saying were true, we could all boast about being saved.
All will/are made righteous through Christ - through God's judgments, therefore all will be saved.
Sorry Latte'chic, it may be a generalization but I see it time and time again on this forum.
People claim salvation is a complete work of God, but then also claim we have to do something of ourself to be saved.
Sorry, if we have to do something of ourselves to be saved, then it is not a complete work of God. If we have to do something of ourselves to be saved, then we can boast about it! It is so subtle, but you even do it yourself above. You claim salvation is a complete work of God, in that He only gives us a choice to be saved. So then its not really a complete work of God is it? Because according to you the real determining factor of who gets saved is ourselves, not God.
Its called doublespeak, or talking out of both sides of your mouth.
Now don't confuse this with what God works in us to do. Certainly we will do things (like believe and have faith and be made righteous) and will do good works when we are saved. But this is a result of God working in us and God ultimately saving us.
Now, legoman, didn't you claim to have once believe in ET? And then you claim God showed you universalism to be the truth, right?
Now, who made that choice to evaluate the difference between ET-Universalism, to make that choice to turn from ET to universalism ? You, did !!! God didn't make you do it, your own thoughts, comparing the two and then you chose to believe in universalism, rather then ET, right?
So, who now is doublespeaking, or talking out of both sides of the mouth ?


text:
\section{Introduction}
\label{sec:intro}
Record linkage (de-deduplication or entity resolution) involves identifying duplicate
records in large, noisy databases~\cite{christen_2011}.
Traditional linkage methods that
directly link records to one another become computationally infeasible
as the number of records grows~\cite{christen_2011,winkler_2006}, and thus, it is
increasingly common for researchers to treat linkage as a
clustering task, in which latent entities are associated with one or more
noisy database records, and the inferential goal is to identify the
latent entity underlying each observed database
record~\cite{steorts15entity, steorts14smered, steorts??bayesian}.
Although there are
many probabilistic, generative models for clustering --- of which
several have been used for record linkage --- the
theoretical properties, such as performance bounds, have such not
been critically assessed.

The work of \cite{steorts15entity, steorts14smered, steorts??bayesian} attempted to deconstruct  distorted data by latent variable mixture models. The authors achieved this by clustering similar records to a hypothesized latent entity for each observed record, where their \emph{linkage structure} kept track of which latent entity belongs to the same observed records. This is modeled through a latent variable mixture model with a distortion process on the data {(sections \ref{sec:categorical} and \ref{sec:string})}. Thus, the main goal is to be able to take distorted data and uncover the underlying structure in the presence of noise. This is similar to signal processing, where a signal is received in the presence of some noise and often the goal is to understand if the underlying true (latent) signal can be recovered.
We develop performance bounds under the framework proposed by \cite{steorts15entity, steorts14smered, steorts??bayesian}.

We provide an upper bound on the Kullback-Leibler (KL) divergence between models
with different linkage structures and use it to provide a lower bound  on the minimum probability of misclassifying a latent entity. More precisely, under the categorical model of \cite{steorts14smered,steorts??bayesian} and string model of \cite{steorts15entity}, we find the minimum probability of getting a latent entity incorrect.
We make connections to Kolchin partition (KP) models \cite{pitman}, along with extending our overall KL bounds in general. Finally, we explore how our bounds perform in practice and describe their user practicality.

\subsection{Prior work}
Bayesian methods and latent variable modeling have become recently popularized in record linkage models. A major advantage of Bayesian methods is their natural handling of uncertainty quantification for the resulting estimates. The first notion of understanding a distortion process for record linkage is the hit-miss-model,  which uses a binary distortion process on the data \cite{copas_1990}.  Within the Bayesian paradigm, most work has focused on specialized approaches related to linking two files \cite{gutman_2013, liseo_2011}.  These contributions, while valuable, do not easily generalize to more than two files or to de-duplication within a single file. For a review of recent development in Bayesian methods, see \cite{liseo_2013}.

The work of \cite{steorts14smered,steorts??bayesian} recently introduced a Bayesian model that simultaneously handled record linkage and de-duplication for categorical data. Their approach allowed for natural uncertainty quantification during analysis and post-processing.
Finally, \cite{sadinle_2014} recently extended the  work of \cite{steorts??bayesian} to both categorical and string valued data using a coreference matrix or a partitioning approach. In the later paper, it was shown that the coreference matrix is a special case of the linkage structure, thus, we work with the linkage structure.
Another advantage of \cite{steorts??bayesian} and similar approaches is that their linkage structure is amenable to an efficient MCMC inference algorithm.
{These models have become practically relevant as they have been shown to perform well on a variety of applications, including official statistics and medical data. In addition, extensions have been made to more general framework of models \cite{sadinle_2014, liseo_2011, zanella2016microclustering}, which is incorporated into our framework in section \ref{sec:gibbs}.}

Given the noted distortion process, deriving performance bounds seems  natural to recover the underlying structure. For example, much work has been done in information theory for subset selection in graphical model selection, signal de-noising, compressive sensing, and others.
In compressed sensing, one question recently addressed in \cite{donoho2006}, was directly measuring the part of the data from sounds and images that \emph{will not} be thrown away. We make a connection here, as in record linkage we wish to take noisy, distorted data and recover this under the KL divergence. Divergence functions by \cite{shannon1948, kullback_1951} are useful in many applications including recent statistical applications of clustering, as done in \cite{banerjee2005} for hard clustering to obtain optimal quantization by minimizing the Bregman divergence (motivated by rate distortion theory). \\

The rest of this paper proceeds as follows.
Two recent record linkage models are given in section~\ref{sec:background}; Section~\ref{sec:categorical} and section~\ref{sec:string} review these  models.
 Section~\ref{sec:properties} derives the respective performance bounds, while section \ref{sec:gibbs} extends our general result to a wider class of models. Section \ref{sec:experiments} shows performance of the bounds in practice, discusses our findings and user practicality.
  Section \ref{sec:discussion} discusses future work.

\vspace{-2mm}
\section{Bayesian Record Linkage}
\label{sec:background}
We assume two Bayesian record linkage models, one dealing with categorical data and the other dealing with both categorical and noisy string data, such as names, addresses, etc.
The first is that of \cite{steorts14smered,steorts??bayesian}, and the second is that of \cite{steorts15entity}.

\subsection{Categorical Bayesian Record Linkage}
\label{sec:categorical}

We review common notation to both models.\footnote{For a toy example of the record linkage process, see the Supplementary Material.}
{Let $\bm{X}=(X_1,\ldots,X_n)$} represent the data, with $k$ databases, indexed by~$i$.  The $i$th list has $n_i$ observed records, indexed by~$j$.  Each record corresponds to one of $N$ latent entities, indexed by $j'.$ Assume
 $N=\sum_{i=1}^k n_i$ without loss of generality.
Each record or latent entity has values on $p$~fields, indexed by~$\ell$, and are assumed  be categorical and the same across all records and entities \cite{steorts14smered,steorts??bayesian}.
$M_\ell$ denotes the number of possible categorical values for the $\ell$th field.

In both models, $X_{ij\ell}$ denotes the
observed value of the $\ell$th field for the $j$th record in the $i$th list,
and $Y_{j'\ell}$ denotes the true value of the $\ell$th field for the $j'$th latent
entity. Then $\Lambda_{ij}$ denotes the latent entity to which the
$j$th record in the $i$th list corresponds, i.e., $X_{ij\ell}$ and $Y_{j'\ell}$
represent the same entity if and only if $\Lambda_{ij}=j'$.
Then $\bm\Lambda$ denotes the $\Lambda_{ij}$ collectively.
Distortion is denoted by $z_{ij\ell}=I(X_{ij\ell}\ne Y_{\Lambda_{ij}\ell})$,
where $I(\cdot)$ denotes the indicator function.
As usual,  $I$ represents the indicator function (e.g., $I(x_{ij\ell}=m)$ is 1 when
the $\ell$th field in record $j$ in file $i$ has the value $m$),
and let $\delta_a$ denote the distribution of a point mass at $a$ (e.g., $\delta_{y_{\Lambda_{ij}\ell}}$).
The model of \cite{steorts14smered,steorts??bayesian} is:
\begin{align}
\label{model:cat}
X_{ij\ell}\mid\Lambda_{ij},Y_{\Lambda_{ij}\ell},z_{ij\ell},\bm\theta_\ell&\stackrel{\text{ind}}{\sim}
\begin{cases}
\delta_{Y_{\Lambda_{ij}\ell}}&\text{ if }z_{ij\ell}=0 \notag \\
\text{MN}(1,\bm{\theta}_\ell)&\text{ if }z_{ij\ell}=1
\end{cases}\\
z_{ij\ell}&\stackrel{\text{ind}}{\sim}\text{Bernoulli}(\beta_\ell) \notag \\
Y_{j'\ell}\mid\bm{\theta}_{\ell}&\stackrel{\text{ind}}{\sim}\text{MN}(1,\bm{\theta}_\ell) \notag \\
\bm{\theta}_\ell\stackrel{\text{ind}}{\sim}\text{Dirichlet}(\bm{\mu}_\ell) & \;\; \text{and} \;\;
\beta_\ell\stackrel{\text{ind}}{\sim}\text{Beta}(a_\ell,b_\ell) \notag  \\
\Lambda_{ij} &\stackrel{\text{ind}}{\sim}\text{Uniform}\left(1,\ldots,N\right),
\end{align}
where MN denotes the Multinomial distribution and
$a_\ell,b_\ell, \bm{\mu}_\ell$ are all known. Guidance for the hyper-parameters and a justification of the (discrete) uniform prior are given in \cite{steorts14smered,steorts15entity, steorts??bayesian}.
Model \ref{model:cat} assumes that different records are independent conditional on the deeper variables of the model.  Moreover, it assumes the same conditional independence of different fields for the same record.
Finally, observe that record linkage and de-duplication are both simply a question of whether $\Lambda_{i_1,j_1}=\Lambda_{i_2,j_2}$, where $i_1\ne i_2$ for record linkage and $i_1=i_2$ for de-duplication.

\subsection{Empirical Bayesian Record Linkage}
\label{sec:string}
The work of \cite{steorts15entity}
assumes  fields $1,\ldots,p_s$ are string-valued, while fields $p_s+1,\ldots,p_s+p_c$ are categorical, where $p_s+p_c=p$ is the total number of fields. They assume an empirical Bayesian distribution on the latent parameter. For each $\ell\in\{1,\ldots,p_s+p_c\}$, let $S_\ell$ denote the set of \emph{all} values for the $\ell$th field
that occur anywhere in the data, i.e.,
$S_\ell=\{X_{ij\ell}:1\le i\le k, 1\le j\le n_i\},$
and let $\alpha_\ell(w)$ equal the empirical frequency of value~$w$ in field~$\ell.$
Let $G_\ell$ denote the empirical distribution of the data in the $\ell$th field from all records in all databases combined.  So, if a random variable~$W$ has distribution $G_\ell$, then for every $w\in S_\ell$,
$P(W=w)=\alpha_\ell(w)$.
Hence, let $G_\ell$  be the prior for each latent entity $Y_{j'\ell}$.
The distortion process changes such that
\begin{align*}
P(X_{ij\ell}&=w\mid\Lambda_{ij},Y_{\Lambda_{ij}\ell},z_{ij\ell}) \\
&=\dfrac{\alpha_\ell(w)\,\exp[-c\,d(w,Y_{\Lambda_{ij}\ell})]}{\sum_{w\in S_\ell}\alpha_\ell(w)\,\exp[-c\,d(w,Y_{\Lambda_{ij}\ell})]},
\end{align*}
where $c > 0$ is a fixed normalizing constant corresponding to an arbitary distance metric $d(\cdot,\cdot)$.  Denote this distribution by $F_\ell(Y_{\Lambda_{ij}\ell})$.
The model becomes
\begin{align}
\label{model:string}
X_{ij\ell}\mid \Lambda_{ij},\,Y_{\Lambda_{ij}\ell},\,z_{ij\ell}\;&\stackrel{\text{ind}}{\sim}\begin{cases}\delta(Y_{\Lambda_{ij}\ell})&\text{ if }z_{ij\ell}=0\\F_\ell(Y_{\Lambda_{ij}\ell})&\text{ if }z_{ij\ell}=1, \ell\le p_s\\G_\ell&\text{ if }z_{ij\ell}=1, \ell>p_s\end{cases} \notag \\
Y_{j'\ell}\;&\stackrel{\text{ind}}{\sim}G_\ell \notag \\
z_{ij\ell}\mid\beta_{i\ell}\;&\stackrel{\text{ind}}{\sim}\text{Bernoulli}(\beta_{i\ell}) \notag\\
\beta_{i\ell}\;&\stackrel{\text{ind}}{\sim}\text{Beta}(a,b) \notag \\
\Lambda_{ij}\;&\stackrel{\text{ind}}{\sim}\text{Uniform}\left(1,\ldots,N\right),
\end{align}
where all distributions are also independent of each other; assume that $a,b, N$ are assumed known. This framework was shown to work well in applications and simulation studies, however, it was quite sensitive to the choice of the hyperparameters. This method  beat supervised methods, such as random forests when the amount of training data input into the supervised methods was $< 10\%$.

Figure~\ref{fig:graphicalProcess} contains a graphical representation of models \ref{model:cat}-\ref{model:string}.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.35\textwidth]{figures/recordLinkage_graphicalModel}
\caption{Graphical representation of models \ref{model:cat}-\ref{model:string}.}
\label{fig:graphicalProcess}
\end{center}
\end{figure}

\section{Performance Bounds of Record Linkage}
\label{sec:properties}

Recall the connection to KL divergence in the sense that for any two distributions $P$ and $Q$, the maximum power for testing $P$ versus $Q$ is $\exp\{-n D_{\text{KL}}(P || Q)\}.$ Hence, a low value of $D_{KL}$ means that we need many samples to distinguish $P$ from $Q.$ A natural question is how  does changing $\boldsymbol{Y}$ (latent entity) or $\boldsymbol{\Lambda}$ (linkage structure) change the distribution of $\bm{X}$ (observed records)? We search for both meaningful upper and lower bounds, since an upper bound will say that $P$ and $Q$ are never more than so far apart, whereas a lower bound says how easy it is to tell $P$ and $Q$ apart. Moreover, we investigate how well can we recover $\boldsymbol{Y}$ (latent entity) and $\boldsymbol{\Lambda}$ (linkage structure) from $\bm{X}$ (data).

Assuming the conditions of \cite{steorts14smered, steorts15entity},
let
 $\mathcal{P} = \left\{f(X\mid \boldsymbol{Y}, \Lambda_{ij}, \bm{\theta}, \bm{\beta}):
 \forall \Lambda_{ij} \in \{ 1, \ldots, N \}.\right\}$
We know that $X_1,X_2,\ldots,X_N$ are all independent given $(\boldsymbol{Y},\boldsymbol{\Lambda}, \bm{\theta}, \bm{\beta})$ under both $P, Q \in \mathcal{P}.$ This implies that
$D_{X_1, X_2, \ldots, X_N} (P \| Q) = \sum_i D_{X_i}(P \| Q).$
  We first provide a theorem under the model of \cite{steorts14smered}, which assumes categorical data and a hierarchical model. In Theorem~\ref{theorem:cat}, we find the minimum probability of getting a latent entity wrong. Moreover, we are able to say that with growing distortion of the data, there is no difference between two latent entities and the bound becomes infinite and non-informative in this case.
Next, under the model of \cite{steorts15entity} we provide a general theorem, which assumes both categorical and noisy text data. This theorem provides an upper bound on the KL divergence of arbitrary distributions $P$ and $Q$.

\subsection{Kullback-Leibler Divergence under Categorical Data} \label{sec:cat}
We use Fano's inequality \cite{prelov2008} to bound the probability of misclassification, as a function of the KL divergence between $P$ and $Q$, as defined in the previous section.
Assume that $\boldsymbol{\Lambda}$ and $\hat{\boldsymbol{\Lambda}}$ are two distinct linkage structures that correspond to the same latent entity $(\boldsymbol{y}).$
Let $r+1$ be the cardinality of $\mathcal{P}$, i.e.\ $r+1 = N$.

\begin{theorem}
\label{theorem:cat}
This result finds an upper bound on the KL divergence and a
 lower bound for the  probability that model \ref{model:cat} gets the linkage structure incorrect.
Let
$\gamma = \max_{\Lambda_{ij} \neq \Lambda'_{ij}}
2\sum_{ij\ell} I(Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda'_{ij}\ell}) (1-\beta_{\ell}) \ln \left \{
\dfrac{1}{
\min_m \theta_{\ell m} \beta_{\ell}} \right\}.$
 \begin{enumerate}
\item[i)] The KL divergence is bounded above by $\gamma.$ That is,
$D_X(P || Q) \leq \gamma \enskip \forall P, Q \in \mathcal{P}$.
\item[ii)] The minimum probability of getting a latent entity wrong is
$Pr( {\Lambda}_{ij} \ne \Lambda^\prime_{ij}) \geq 1 - \dfrac{ \gamma + \ln 2}{\ln r}, \enskip \forall i,j$
\end{enumerate}
\end{theorem}
That is, as the latent entities become more distinct, $\gamma$ increases. On the other hand, as the latent entities become more similar, $\gamma \rightarrow 0.$
{

\begin{rem}
Consider Theorem \ref{theorem:cat} (i). Suppose $\beta_{\ell} \rightarrow 1.$ Then $D_{\bm{X}} \geq 0.$ If instead $\beta_{\ell} \rightarrow 0,$ then $D_{\bm{X}} \geq 1.$ The lower bound is only informative when $\beta_{\ell} \rightarrow 0.$ We have more information when the latent entities are separated.
\end{rem}
\begin{proof}
To show this, we simply apply Pinsker's  inequality, where
for all $P,Q \in \mathcal{P}$:
$
D(P \| Q) \geq 2||P-Q||^2_1
\implies \notag \\
D(P \| Q) \geq I(Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell}) (1-\beta_{\ell})^2
\nonumber \implies  \notag \\
 D_{\bm{X}}(P \| Q)  \geq \sum_{ij\ell} I(Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell})  (1-\beta_{\ell})^2.
$
\end{proof}
}
\begin{proof}
We assume the model of \cite{steorts14smered,steorts??bayesian}, which assumes that data is categorical.  We assume model \ref{model:cat} holds in section \ref{sec:categorical}. We first prove (i). Consider $f(X\mid \boldsymbol{Y}, \boldsymbol{\Lambda}, \bm{\theta}, \bm{\beta}). $ Then
\begin{align}
\label{cat:like}
&Pr(X_{ij\ell} =m \mid \boldsymbol{Y}, \boldsymbol{\Lambda}, \bm{\theta}, \bm{\beta})  \\
&= 1(Y_{\Lambda_{ij}\ell} = m) (1-\beta_{\ell})
+ \theta_{\ell m} \beta_{\ell}.\notag
\end{align}
It follows from equation~\ref{cat:like} that
\begin{align*}
D_{X_{ij\ell}}(P\| Q)
&= \sum_{m=1}^{M_\ell}
I(Y_{\Lambda_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}\} \\
& \times \log\left[
\frac{I(Y_{\Lambda_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}}
{
I(Y_{\Lambda^\prime_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}
}
\right].
\end{align*}
It directly follows that
\begin{align*}
D_{\bm{X}} (P\| Q)
&=
\sum_{ij\ell m} \left\{
I(Y_{\Lambda_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}\} \right. \\
&\times \left. \log\left[
\frac{I(Y_{\Lambda_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}}
{
I(Y_{\Lambda^\prime_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}
}
\right]
\right\}.
\end{align*}
\textcolor{black}{If $Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell}$}, then
\begin{align}
\| P-Q\|_1
&= \sum_m \left | I(Y_{\Lambda_{ij}\ell} = m) (1-\beta_{\ell})
+  \theta_{\ell m} \beta_{\ell} \right. \notag \\
& \qquad \left. -I(Y_{\Lambda^\prime_{ij}\ell} = m) (1-\beta_{\ell}) -  \theta_{\ell m} \beta_{\ell}
\right |  \notag \\
&= 2(1-\beta_\ell).
\label{eqn:pq}
\end{align}
Equation \ref{eqn:pq} holds
since $P(m) = Q(m)$ unless $m = Y_{\Lambda_{ij}\ell}$ or $m = Y_{\Lambda^\prime_{ij}\ell}.$
\textcolor{black}{If $Y_{\Lambda_{ij}\ell} = Y_{\Lambda^\prime_{ij}\ell}$, then $P=Q$ and $\|P-Q\|_1 = 0$.}
The reverse Pinsker inequality of \cite{berend_2014} relates the KL
divergence to the $L_1$ norm in the following way:
$D(P \| Q) \leq \| P-Q\|_1 \ln \{ (\min Q)^{-1}\}.$ Using this, we find that \textcolor{black}{(if $Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell}$)}, then
\begin{align*}
D(P \| Q)  &\leq 2(1-\beta_{\ell}) \\
\qquad &\times \ln \left \{
\dfrac{1}{
\min_m I(Y_{\Lambda^\prime_{ij}\ell} = m) (1-\beta_{\ell}) +  \theta_{\ell m} \beta_{\ell}
}
\right\}  \\
&\leq
2(1-\beta_{\ell}) \ln \left \{
\dfrac{1}{
\min_m \theta_{\ell m} \beta_{\ell}
}
\right\}.
\end{align*}
Hence,
\begin{align*}
\max_{P,Q \in \mathcal{P}}D_{\bm{X}}(P \| Q) &\leq
\max_{\Lambda_{ij} \neq \Lambda^\prime_{ij}} 2\sum_{ij\ell} I(Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell})(1-\beta_{\ell}) \\
& \qquad \times \ln \left \{\dfrac{1}{\min_m \theta_{\ell m} \beta_{\ell}} \right\}
:=\gamma.
\end{align*}
This proves (i).
We now prove (ii). Using Fano's inequality \cite{prelov2008}, the minimum probability of getting a latent entity wrong is
$Pr( \Lambda_{ij} \ne \Lambda^\prime_{ij}) \geq 1 - \frac{ \gamma + \ln 2}{\ln r},$ where $r+1$ is the cardinality of $\mathcal{P}$, i.e.\ $r+1=N$. As the latent entities become more distinct, $\gamma$ increases. On the other hand, as the latent entities become more similar, $\gamma \rightarrow 0.$
\end{proof}

\subsection{KL Divergence Bounds for String and Categorical Data} \label{sec:str}
We now consider $P$ and $Q$ under \cite{steorts15entity} for both categorical and noisy string data. Recall that  $\beta_\ell$ tunes the amount of distortion as defined in equation \ref{model:string}.
Recall that $d(\cdot, \cdot)$ denotes any arbitrary distance metric between an observed string and a latent string as seen in equation \ref{model:string}, and $c > 0$ is a fixed normalizing constant corresponding to the distance metric $d.$

In Theorem \ref{theorem:string}, for any distinct linkage structures,  the minimum probability of getting a latent entity wrong is governed by a lower bound, which is growing at a rate $c \rightarrow \infty$ that is determined by the moment generating function of the distances between an observed string in data and a latent string.
\begin{theorem}
\label{theorem:string}
Assume data $\bm{X},$ and distributions $P,Q \in \mathcal{P}$ defined in section \ref{sec:properties}.  Assume two distinct linkage structures, denoted by $Y_{\Lambda_{ij}\ell}, Y_{\Lambda^\prime_{ij}\ell}.$
\begin{enumerate}
\item [i)] There is an upper bound on the KL divergence between any $P,Q \in \mathcal{P}$
given by $\kappa,$ that is $D_X(P||Q) \leq \kappa.$
\item [ii)] $Pr(\Lambda_{ij} \neq \Lambda^\prime_{ij}) \geq 1- \dfrac{\kappa + \ln 2}{\ln r},$
where
\begin{align*}
\kappa &= \max_{\Lambda_{ij} \neq \Lambda^\prime_{ij}}\bigg[
2 \sum_{\ell} (1-\beta_\ell) I(Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell})
  +  \\
& \qquad \sum_{\ell m}  I(Y_{\Lambda_{ij}\ell} \neq Y_{\Lambda^\prime_{ij}\ell})
 \left(
1 - e^{-c d(Y_{\Lambda_{ij}\ell}, Y_{\Lambda^\prime_{ij}\ell})}
\right) \\
&\times E[ e^{-c  d(m, Y_{\Lambda_{ij}\ell})} ] \bigg]\ln\{ (\min Q)^{-1} \}
\end{align*}
and $r+1$ is the cardinality of $\mathcal{P}$.
\end{enumerate}
\end{theorem}

The proof of Theorem \ref{theorem:string} can be found in the Supplementary Material.

\section{Kolchin Partition Models}
\label{sec:gibbs}
{
The models in sections \ref{sec:categorical} and \ref{sec:string} assume discrete uniform priors on the linkage structure.  We extend this to a more general class of models from Bayesian nonparametrics known as KP models \cite{pitman}. Special cases include the work of \cite{zanella2016microclustering, liseo_2011, sadinle_2014}. We provide notation, examples, and then provide a general theorem. }

The prior structure on $\boldsymbol{\Lambda}$ can instead be viewed on the set of labelings. Specifically, let  $z$ denote the partition of the observed records determined by $\boldsymbol{\Lambda}$, and $\mathcal{B}$  denote the set containing all the possible partitions of the $r$ observed records. Then a distribution on the sample labels $\boldsymbol{\Lambda}$ induces a distribution on $\mathcal{B}.$ That is, matches and duplicates are completely specified given the knowledge of $z$, which is invariant with respect to the labelings of the partition blocks.

\subsection{Special Cases of KP Models}
We give some special cases of KP models that extend the class of models that we consider.

\subsection{A Uniform Prior on the Label Space}

Let $z(\boldsymbol{\Lambda})$ denote the partition identified by $\boldsymbol{\Lambda}$ and let $n(z)$ denote the number of distinct entities considering all the observed records, i.e. the number of blocks of the partition. One has $$N!/(N-n(z))!=(N)_{n(z)}$$ different labelings which identify the same partition $z(\boldsymbol{\Lambda})$. Then
$$ P(z(\boldsymbol{\Lambda})=z)=\left(\frac{1}{N} \right)^r \frac{N!}{(N-n(z) )!} \quad \forall z \in \mathcal{B} .$$
Note also that $N^r=\sum_{n=0}^r (N)_{n} S(r,n)$ where $S(r,n)$ is   the Stirling number of second kind,
that is the number of possible partitions of the $r$ records into $n$ non empty sets, which implies
\begin{equation}
P(z(\boldsymbol{\Lambda})=z)=\frac{(N)_{n}}{N^r}\quad \forall z \in \mathcal{B} \label{gibbs1}
\end{equation}
where $n=n(z)$. Following \cite{pitman}, equation (\ref{gibbs1}) is a special case of a KP model.
Moreover, the distribution of the number of distinct elements $n(z)$ is given by
$P(n(z)=n)= \dfrac{(N)_{n} S(r,n)}{ N^r}.$ (A similar prior was considered in \cite{liseo_2011}).

\subsection{The Uniform Prior on the Partition Space}
\label{pyprior}
Assuming one database, \cite{sadinle_2014}  focused mainly on the partitions of the $r$ records induced by $\boldsymbol{\Lambda}$ and proposed a flat prior on the partition space, that is a prior which assigns equal probability to each different partition of the $r$ observed records. Assume that
$$p(\boldsymbol{\Lambda})=\dfrac{1}{B_r \, (N)_{n(z)}} $$
where $B_r=\sum_{n=0}^r S(r,n)$ is the $r$-th Bell number. In terms of partitions, the prior used by \cite{sadinle_2014} can be written as
$p(z(\boldsymbol{\Lambda})=z)=\frac{1}{B_r}$ and
$p(n(z)=n)=\frac{S(r,n)} {B_r}$.
This prior is also a special case of a KP model.

Moreover, the discrete uniform priors of \cite{steorts14smered, steorts??bayesian, steorts15entity} can also be represented easily as KP models. We refer to \cite{steorts??bayesian} for details.

We now provide a general theorem, which gives a relationship regarding priors (or partitions or blocks) of KP models to our KL divergence bounds. Suppose the prior on the linkage structure can be represented as a KP model \cite{pitman}. Then a wide class of priors is able to be considered and compared.
\begin{theorem}
\label{thm-gibbs}
Consider model \ref{model:cat} or \ref{model:string}. Then the error bounds behave like the corresponding bounds in Theorem \ref{theorem:cat} or \ref{theorem:string}.
\end{theorem}
\begin{proof}
The results directly follows from the proofs of Theorems \ref{theorem:cat}, \ref{theorem:string} and the representation of KP models \cite{pitman}.  Specifically, all bounds in Theorems \ref{theorem:cat} and \ref{theorem:string} depend upon the linkage structure $\boldsymbol{\Lambda}$, which in the proofs, is agnostic to its form.
 \end{proof}

\subsection{Microclustering and Record Linkage}
There has been early work in Bayesian nonparametrics to push forward record linkage. The work of \cite{miller15microclustering, zanella2016microclustering} recently pointed out that most clustering tasks assume the cluster sizes grow linearly with the number of the data points. Such examples include infinitely exchangeable clustering models, including finite mixture models, Dirichlet process (DP) mixture models, and Pitman--Yor process (PYP) mixture models. However, in record linkage, such an assumption is undesirable since linkage methods require models that yield clusters whose sizes grow sublinearly with the total number of data points (records). Due to this, \cite{zanella2016microclustering}  defined the microclustering property as well as a new model exhibiting such growth, where their models outperformed or performed as well as the PYP and DP in terms of standard record linkage evaluation metrics on data for official statistics, medical data, and human rights data. Furthermore, the authors proved that one of their models satisfies the microclustering property under very weak assumptions. We refer to their paper for further details.

One insight of this paper was the fact that their class of microclustering models considered can always be written as
a KP model. Combining this clustering approach with the likelihood in equation \ref{model:cat} or \ref{model:string} immediately allows one to perform record linkage inference. Furthermore, Theorems \ref{theorem:cat} and \ref{theorem:string} are immediately satisfied since the prior on the linkage structure can be represented as a KP model.

\section{Simulation Study and Discussion}

\label{sec:experiments}

We consider how the bounds in Sections \ref{sec:cat} and \ref{sec:str} hold for two simulated experiments. In our experiments (\textbf{Experiment I} and \textbf{Experiment II}), synthetic categorical data are generated according to either model \ref{model:cat} or \ref{model:string} using the parameters shown in Table \ref{table:params} and \ref{table:params-str}, respectively. In order to
consider a realistic set of strings for $S$, we consider the set of 20 most popular female baby names from 2014, according to the United States Census. Then for the distance $d$, we consider the generalized Levenshtein edit distance.

We then generate both categorical and string records according to either model \ref{model:cat} or \ref{model:string}. For each experiment, we vary exactly one of the parameters to demonstrate its impact of the linkage error rate $Pr( (\hat{\Lambda}_{ij}, \boldsymbol{Y}) \ne (\Lambda_{ij}, \boldsymbol{Y}))$. We choose the other values such that the performance is neither extremely low nor extremely high. We set the distortion parameter $\beta_\ell$ to the same value for each $\ell$, i.e.\ $\beta_\ell = 0.6$ denotes a distortion probability of 0.6 for every field. $\beta_\ell = $ 0.0 to 1.0 means we started with $\beta_\ell = 0$ for all $\ell$ and swept the values until $\beta_\ell = 1$ for all $\ell$. Recall $p$ is the number of fields, and thus the maximum value of $\ell$. We also set each $\theta_{\ell m}$ to the same value, i.e.\ $\theta_{\ell m} = 0.1$ denotes $\theta_{\ell m} = 0.1$ for all $\ell$ and all $m$. This further implies each field $\ell$ takes on exactly $M_\ell = 1/\theta_{\ell m}$ values in order for $\theta_\ell$ to be a valid probability distribution.

\begin{table}
\begin{center}
  \begin{tabular}{ l c c c c}
    Experiment & $N$ & $\beta_\ell $ & $p = p_c$  & $\theta_{\ell m}$ \\ \hline
    Fig. 1(a) & 10 to 500 & 0.6 & 3 & 0.1 \\
    Fig. 1(b) & 100  & 0 to 1 & 3 & 0.1 \\
    Fig. 1(c) & 100  & 0.6 & 1 to 8& 0.25 \\
    Fig. 1(d) & 100  & 0.8  & 5& $\frac{1}{46} \text{ to } 1$
  \end{tabular}
  \caption{Categorical Experiments}
  \label{table:params}
  \end{center}
\end{table}

\begin{table}
\begin{center}
  \begin{tabular}{ l c c c c c}
    Experiment & $N$ & $\beta_\ell $ & $p = p_s$ & $c$ \\ \hline
    Fig. 2(a) & 100 to 500 & 0.6  & 1 &  1.0 \\
    Fig. 2(b) & 100  & 0.2 to 1 & 1  & 1.0 \\
    Fig. 2(c) & 100  & 0.6 & 1 to 10  & 1.0 \\
    Fig. 2(d) & 100  & 0.6 & 1 & 0 to 2
  \end{tabular}
  \caption{String Experiments}
  \label{table:params-str}
  \end{center}
\end{table}

We compare the bound in Theorem \ref{theorem:cat} to two record linkage algorithms \cite{steorts14smered, steorts??bayesian, steorts15entity}. The first is an exact sampler, which samples directly from $Pr(\Lambda_{ij} | X_{ij}, \boldsymbol{Y}, \boldsymbol{z})$. The second is a more realistic Gibbs sampler with empirically motivated priors proposed by \cite{steorts15entity}. We run the Gibbs sampler for 10,000 iterations on all experiments to ensure proper mixing. There is some difficulty in comparing $\Lambda$ to $\hat \Lambda$, as there are multiple equally correct modes due to arbitrary re-orderings of the latent individuals $\hat \boldsymbol{Y}$ and corresponding linkage structure $\hat \Lambda$. Even though the Gibbs sampler may infer the correct latent individuals $\boldsymbol{Y}$ and linkage structure, because the ordering is arbitrary, it is unlikely that $\Lambda = \hat \Lambda$. To avoid such an issue of label switching, we fix $\hat \boldsymbol{Y}$ during the sampling process.

Specifically, we compare the bound to the empirical error rate of the Gibbs sampler proposed by \cite{steorts15entity}. In order to compute the empirical probability $Pr( \hat{\Lambda}_{ij} \ne \Lambda_{ij})$, we hold $\boldsymbol{Y}$ fixed during Gibbs sampling to ensure errors in $\hat \boldsymbol{\Lambda}$ are not due to arbitrary changes in the ordering of the labels of $\boldsymbol{Y}$. In addition, we compare the linkage error rate to an exact sampler, which samples directly from $Pr(\boldsymbol{\Lambda} | X, \boldsymbol{Y}, \boldsymbol{z})$.

\paragraph{Results of Experiment I}
In Figures \ref{fig:experiments} (a)-(d) we vary the number of records $N$, distortion parameter $\beta$, number of fields $p$ and number of values each field takes $M_\ell$, respectively. The empirical results demonstrate Theorem \ref{theorem:cat} captures the dependence between the error rate and the all relevant latent parameters $\theta$, $N$ and $\beta$. Specifically, linking records becomes more difficult as $N$ increases, the distortion parameter $\beta$ increases, the number of fields $p$ decreases or the number of values each field can take $M_\ell$ decreases. The bound nicely captures the logarithmic increase in error with respect to $N$ in Figure \ref{fig:experiments} (a), which gives hope for linking records in very large databases. Other terms appear to be $\bar O(n)$ when not near extreme error values, implying low noise and a larger feature space are essential to performing high quality record linkage.

\begin{figure}
  \begin{minipage}[t]{1\textwidth}
    \hspace{-4mm}
    \includegraphics[width=0.28\textwidth]{figures/N}
    \label{fig:N}
    \hspace{-6mm}
    \includegraphics[width=0.28\textwidth]{figures/beta}

  \end{minipage}

   \vspace{-10mm}
  \begin{minipage}[t]{1\textwidth}
    \hspace{-4mm}
 \includegraphics[width=0.28\textwidth]{figures/theta_fields}
     \hspace{-6mm}
    \includegraphics[width=0.28\textwidth]{figures/theta_values}

  \end{minipage}

    \caption[]{Theorem \ref{theorem:string} (gold squares) holds on simulated
    categorical records

    compared to exact sampling (grey circles) and Gibbs sampler (blue diamonds).}
       \label{fig:experiments}
\end{figure}

\paragraph{Results of Experiment II}
Figures \ref{fig:experiments-eb} (a)-(d) show Theorem \ref{theorem:string} is tight to the true performances on string data when varying $N$, $\beta$, number of string fields $p_s$ and $c$, respectively. As expected, and similarly to the categorical results, linking records becomes more difficult as $N$ increases, the distortion parameter $\beta$ increases and the parameter $c$ decreases. The effects of parameter variation is less noticeable in the string experiments due to the fact that linking string fields is easier than ones that have been anonymized, i.e., categorical fields.

\begin{figure}
  \begin{minipage}[t]{1\textwidth}
    \hspace{-4mm}
    \includegraphics[width=0.28\textwidth]{figures/string_N}
    \label{fig:N}
    \hspace{-6mm}
    \includegraphics[width=0.28\textwidth]{figures/string_beta}

  \end{minipage}

   \vspace{-10mm}
  \begin{minipage}[t]{1\textwidth}
    \hspace{-4mm}
 \includegraphics[width=0.28\textwidth]{figures/string_ps}
     \hspace{-6mm}
    \includegraphics[width=0.28\textwidth]{figures/string_c}

  \end{minipage}

    \caption[]{Theorem \ref{theorem:string} (gold squares) holds on simulated
    noisy string records

    compared to exact sampling (grey circles) and Gibbs sampler (blue diamonds).}
       \label{fig:experiments-eb}
\end{figure}

The Gibbs sampler (blue diamonds) performs almost as well as the exact sampler (grey circles). In fact, due to the conditional entropy version of Fano's inequality and the fact that $H(X | Y) \leq H(X)$, any Gibbs sampler cannot perform better in expectation than an exact sampler. Thus, we believe the gap between the bound (gold squares) and the exact sampler does not necessarily indicate the existence of a better algorithm, but perhaps only some unnecessary slack due to the application of Pinsker's and then reverse Pinsker's inequalities.

\subsection{Discussion of Results}
\label{sec:discussions}
As illustrated in Theorems \ref{theorem:cat} and \ref{theorem:string}
we have derived an upper bound on the KL divergence as well as lower bounds for misclassifying a latent entity.
In Theorem~\ref{theorem:cat} (i), we showed that the latent entities become more distinct when $\gamma$ is increasing. This is in contrast to when $\gamma$ gets closer to 0, since then the latent entities become more similar. In Theorem~\ref{theorem:cat} (ii), we showed that as the distortion parameter $\beta_\ell \rightarrow 1,$ then the upper bound $\gamma$ is infinite. In practice, as illustrated in \cite{steorts14smered}, the latent entities are difficult to distinguish when the amount of distortion is more than 5\% at every field value.  Thus, this corresponds to when the bound is too loose.  On the other hand,  as $\beta_\ell \rightarrow 0,$ the latent entities become more separated.

We discuss how separated the latent entities are under choices of $\beta_\ell, \theta_\ell$ and $N$, providing guidance to the user in this setting given our simulation results. As practical guidance when the distortion is between 0 to $5\%$ at every feature value, the latents will be more separated and the bound will be be loose. On the other hand, as $\beta_\ell$ increases, the bound becomes tighter. The choice of $\beta_\ell$ can be made using subjective information about the underlying data and tuned using the hyper-parameters $a,b$. (See \cite{steorts14smered, steorts15entity} for choosing such values). On the other hand, we can see that for more realistic values of the distortion parameter in Figure \ref{fig:experiments} (a), (b), and (d) , the bound is quite loose when the distortion parameter $\beta_\ell$ is large. Thus, a loose bound here is warranted due to the amount of noise or model-misspecification being placed into the model as well as the fact that all of the fields being used are categorical. Such results match the intuition given in \cite{steorts14smered}.

In Theorem~\ref{theorem:string} (ii), we derived a lower bound where the minimum probability of getting a latent entity wrong is controlled by $c,$ which is determined by the moment generating function of the distances between an observed string and a latent string. This bound has the same type of form as the bound in Theorem~\ref{theorem:cat}, however, since we now have string-valued data, we see that the minimum probability of getting a latent entity wrong is dominated by the string-valued variables and specifically, the distances functions used and the constants used. In comparison to \cite{steorts15entity}, this completely matches up with the sensitivity that was seen to the choice of the distance functions as well as the choice of $c$ as this will completely dominate the posterior, and hence, the ability to tell latent entities apart under this posterior.

{In practice, the driving force of the tightness of the bound is $c$, the steepness parameter of the string distribution in equation 2. As $c$ increases, it is less likely for a string-valued record's features to be distorted to values that are far from that of their latent feature values. This is verified in Figure \ref{fig:experiments-eb}(c), where linkage error decreases as $c$ increases. The work of \cite{steorts15entity} gave practical choices for $c$, which were [0,2].
Similarly, we can speak to the tightness of $d$, which relies on the distortion parameter $\beta_\ell$ not being too small in practice, as verified in Figure \ref{fig:experiments-eb}(b). In terms of the bounds found in Theorem 1 and 2, the empirical Gibbs sampler has tight bounds in almost all situations, except when the number of features is large, $N$ is too small, or $\beta_\ell$ is too small (and similarly for $\theta_\ell$). This coincides with exactly what we would expect in practice from the real experiments of \cite{steorts15entity}.

For all applications in both categorical and string data, we expect the bounds to be as loose in practice (corresponding to easier record linkage), when the distortion parameter is small ($0-4$) and when the the number of fields is large ($p \geq 5$) or the number of values that each field can take, $M_\ell$, increases (this will be application specific). Finally, the bounds should be tighter, corresponding to more difficult record linkage, as the total number of records N increases (see Figure \ref{fig:experiments}). These parameter values match almost exactly with two real data experiments (corresponding ranges of  parameters) as well as a simulation study from \cite{steorts14smered, steorts??bayesian}.

}

\section{Future Directions}
\label{sec:discussion}
First, we have derived general
performance bounds for record linkage, making connections to KP models and other related Bayesian models. More specifically, we have drawn connections to a wide class of models from Bayesian record linkage. Second, our bound for the categorical Bayesian record linkage model is easily interpretable and matches the intuition of the generative model. Third, our bound for the categorical and noisy string model, takes a similar form to that of the categorical model. We are also able to interpret  this bound in a way that aligns with the interpretations \cite{steorts15entity, steorts14smered, steorts??bayesian} as well as show the practicality of our bounds to the aforementioned papers. More specifically, our bounds are empirically loose for categorical data, which is not unexpected since there is little information available to match on. This contrasts the empirical tight bounds for both categorical and noisy string data. As illustrated in our experiments, with just one string variable, our bounds become much tighter, and as the number of strings increases, the bound becomes more tighter when compared to exact and Gibbs sampling.

In addition, there has been early work in Bayesian nonparametrics to push forward record linkage. The work of \cite{miller15microclustering} pointed out that most clustering tasks assume cluster sizes grow linearly with the size of the database. Such examples include infinitely exchangeable clustering models, including finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models, which all  make this linear growth assumption. However, in record linkage such an assumption is  undesirable since linkage methods require models that yield clusters whose sizes grow sublinearly with the total number of data points. This observation led the authors to define the microclustering property as well as a new model exhibiting such growth. Our work has been able to provide bounds for the aforementioned work since the prior consider is a KP model.
In future work it would be helpful to try and draw connections between those proposed in  \cite{miller15microclustering} and \cite{steorts15entity, steorts14smered, steorts??bayesian} in order to generalize such bounds and provide tighter bounds using conditional entropy or other sophisticated bounding methods.

\subsubsection*{Acknowledgments}
We thank David Choi, David Dunson, David Banks, and the reviewers for improving the ideas that led to publication of this paper.  This work was supported in
part by NSF grants SES-1534412 and SES-1131897, DARPA FA8750-12-2-0324 and FA8750-14-2-0244.
\looseness=-1

\clearpage
\newpage

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


text:
Keeping safe in town
Nominate someone!
Planning applications - deadline 7-Mar-08
New Medical Centre for Boscombe?
Drinking in Boscombe?
Planning application - deadline 7-Mar-08
What do you think of Boscombe Precinct?
Planning applications - deadline 24-feb-08
I had an absolutely fantastic time on Saturday night, we went to 60,0000000 postcards, then the consortium then the camel bar. We me a lot of lovely people who were caring and were looking out for each other, I felt very safe in the tow centre where we stayed / moved between clubs - not at all unsafe. On our way home we walked past Subway and the I-bar in Holdenhurst rd, the police had taped a large area off, this was at about 6.30 am. I was so sad to read the next day that we had actually passed the sites of both of the murders that happened that night on the way home, - others clearly did not find Bournemouth the warm, friendly place that we did. I have thought about how safe it is to go out quite a bit, and how I will feel when my own children start to go out into Bournemouth. I don't think I will try to stop them - its part of growing up, but I hope they will understand how easily a person can be seriously injured or killed. I think that TV and Film can convince us that people can survive all sorts of violent attacks and still get back up for more, but that's not real... the two deaths last weekend were apparently the result of what would have been fairly minor tussles, many of which happen every weekend, and any of which could end tragically ...
Launching: The Neighbourhood Management Awards 2008
Community Champions, Community Group of the Year,
Young Achiever, Business in the Community,
Partnership Working and Cultural Diversity
Neighbourhood Management in Boscombe West and Springbourne are looking to recognise and reward those people, partners, businesses and groups who have helped to make this area a better place for its residents.
These people, groups, businesses and organisations will have played a significant part in delivering services, activities, support, advice and/ or helping others.
If you know of, or are any of the following, please look at the attached Entry Form to make your nomination.
Selfless service by an individual (over 18) to a voluntary body or to the community in the NM Area
Voluntary or community group that has improved the quality of life for residents in the NM Area
Outstanding contribution made by a young person or group of young people aged 11 to 18
Outstanding business contribution to the well-being of the community
Celebrating Partnership Working in the NM Area
Bringing Cultural Diversity to the NM Area
CLOSING DATE 31ST MARCH 2008
7-2008-20968-K
4 Cecil Road
Crown clean one False Acacia. Crown lift one Red Oak. Crown lift one Sweet Chestnut and prune back from building.
Mr M DeKment
deadline for comment: none published by Council
full details on the Council website
7-2008-9978-G
627/629 Christchurch Road (the one/two units immediately to the left of WHSmith)
Erection of a 1/3 storey block comprising ground floor shop and 8 flats on upper levels with bin and cycle stores
Kemble Estates Ltd
deadline for comment: 07/03/2008
7-2008-6936-C
40 Knole Road
Erection of a three storey block of 9 flats with bin and cycle stores and formation of vehicular access and parking spaces.
Posted by Ben at 19:18 Labels: planning boscombe
Consultation has started to look into the possibility of a new medical centre in Palmerston Rd. Boscombe West has some of the poorest health in the South - residents statistically living ten years fewer than other parts of Bournemouth. Bournemouth and Poole PCT have recognised the need for targeted services in our area and are looking into using the old hospital stores next to the watertower to provide new resources. I will be representing the views of residents to the PCT over the next few weeks and I am keen to hear your opinion. What services would you like to see provided? Are there any services which are not traditionally medical which would help to improve health in the area?
Another inportant decision for Boscombe - do we need a 'cumilative impact zone'?
With the many changes in licencing over the past few years there has been a lot of concern about the impact of numerous licensed premisis in some parts of Bournemouth and resulting antisocial behaviour. When businesses apply for a license to sell alcohol, (Bars, off licenses, Rstaurants, Hotels etc) the licensing act requres that the license is granted unless there is an objection.
Sometimes when an area is seriously affected by antiscocial behaviour it is possible to make that area a cumilative impact zone. This means that there is the a presumption that the license will not be granted, and the onus is then on the business to justify that they will not contribute to the problems in the area. Bournemouth centre has a zone currently and there is a consultation document available at the moment which puts forward Boscombe as an area which could have a cumalitive impact zone.
I hope that residents will feedback to the council on this see the document here
Here are some thoughts to go along with!
Drink related antisocial beaviour is high in the Boscombe area
Good quality & well run bars could create a vibrant night-time economy, increasing the number of people around in the evening, making the area feel safer and more family/tourist friendly.
Drink related anti-social behavior may be different to the town centre as it is more related to street drinkers than those leaving clubs.
7-2008-2117-H
Alterations and conversion of ground floor shop to flat
European Equities plc
The pedestrian area in the centre of Boscombe was created when the Sovereign Cntre was built around 17 years ago. Over the last few years the area has not been maintained so well, some of the paving has bee replaced with tarmac and the gullys have a tendancy to fall in from time to time (this happened to me once as I wheeled my bike over one of them!).
The possibility of doing something about the precinct area has been raised, and I am very keen to hear what people think about this and give me feedback.
Here are some of my thoughts so far....
The last 18 months has seen at least three good quality cafe's opening in the area which have changed the feel of the area, including popular outside tables.
Footfall in Boscombe is up, bucking local and national trends
Boscombe is one of the best flat shopping area's supported by a popular shopmobility scheme.
The design of the two ends of the precinct make it very difficult to access shops beyond that area. Obstructions include pedestrian guard rails and multiple sets of traffic lights - could better design resolve this issue an encourage shoppers into the area's outside the precinct?
Visitors to the Opera house have reportedly been put off by the walk to awkward rd carpark, could this be resolved by negotiations with Aldi to use their carpark in the evenings?
I look forward to hearing some views on this!
7-2008-546-L
476-478 Christchurch Road
(opposite St John's Church)
Erection of a bin store
Brooklyn Management
7-2008-1268-M
(the Boscombe branch of Nationwide Building Society)
Erection of a fence and gates


text:
This time we really are all doomed, famous doomsayer prof says
Continued survival of humanity starting to get embarrassing for Ehrlich
Lewis Page
Mon 22 Jun 2015 // 11:52 UTC
Opinion A professor famous for predicting the imminent demise of the human race at regular intervals since the 1970s has predicted the imminent demise of the human race.
Paul Ehrlich, who is the Bing Professor of Population Studies at the Stanford Woods Institute for the Environment, says it's definitely on this time. In a tinned statement issued on Friday, the arm-waving prof lays it on the line:
There is no longer any doubt: We are entering a mass extinction that threatens humanity's existence ... the window of opportunity is rapidly closing ...
"[The study] shows without any significant doubt that we are now entering the sixth great mass extinction event," Ehrlich said ...
"If it is allowed to continue, life would take many millions of years to recover, and our species itself would likely disappear early on," said lead author Gerardo Ceballos.
The idea is that humanity is causing lots of species of animals, plants etc to become extinct and this will develop into a runaway death snowball in which we ourselves will disappear - for example, because crops are no longer being fertilised by bees, or similar.
The doom scenario is laid out in a paper by Ehrlich, Ceballos and their colleagues in the journal Science Advances. You can read it for free.
If we do all die off reasonably soon in a runaway biodiversity loss doom event, it will be good news for Professor Ehrlich's credibility. Though he originally trained as an entomologist (specialising in butterflies) he is probably best known for co-writing the 1968 book Population Bomb, which in early editions stated that basically everyone in India would inevitably starve to death due to overpopulation in the 1970s and the same fate would overtake the USA in the 1980s.
In fact, as it worked out both Indians and Americans nowadays eat noticeably more food than they used to, and despite a pretty serious global population increase this is also true of humanity in general.
Undeterred by that little whoopsie, Professor Ehrlich went on to massively big up the theory of "nuclear winter", which suggests that the planet's climate would be irrevocably wrecked should a nuclear war occur, wiping out the entire human race without exceptions. Ehrlich's answer to this supposed problem was that the Western powers should get rid of their nuclear weapons.
The nuclear winter theory was fortunately never tested, but it is widely seen nowadays as scientifically questionable and it's commonly suggested that it was constructed as a result of the campaign for disarmament, rather than the other way around. The great physicist Freeman Dyson wrote of nuclear winter:
As a scientist, I judge the nuclear winter theory to be sloppy piece of work, full of gaps and unjustified assumptions. As a human being, I hope fervently that it is right ... since I am a scientist dedicated to truth, I will criticize nuclear winter theory as harshly as I would criticize any other half-baked scientific theory.
So Ehrlich is pretty much zero for two, so far. If humanity fails to die out on cue this time (it seems pretty clear that we're not going to adopt the instant and draconian limits on economic activity that Ehrlich sees as the only way to prevent the extinction death snowball) the prof's chances of ever being taken seriously - already pretty poor at this point, to be honest - will plunge to zero. ®
So you want to replace workers with AI? Watch out for retraining fees, they're a killer
Comment Who said workforce development was just for humans?
AI + ML29 Jan 2023 | 5
Chrome bug bedevils file storage in the cloud
'I'm sorry, Dave. I can't do that'
Devops29 Jan 2023 |
Apple sued for promising privacy, failing at it
What's allowed for Cupertino is verboten for everyone else
Personal Tech28 Jan 2023 | 17
Simplifying digital sovereignty in a multi-cloud world
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Man seized in Morocco is now presumably sleepless in Seattle
Cyber-crime28 Jan 2023 | 4
Microsoft squashes Windows 11, Server 2022 bugs with preview patches
Remote Desktop, domain controllers giving you gyp? Gamble on these fixes
OSes28 Jan 2023 | 4
California toys with digital vehicle titles on private DMV blockchain
Because this is necessary, definitely can't go wrong
On-Prem28 Jan 2023 | 24
If you want to keep the miscreants out, put the updates in, Redmond says
Patches28 Jan 2023 | 3
Uncle Sam slaps $10m bounty on Hive while Russia ban-hammers FBI, CIA
New meaning to sweetening the pot
You there, boffins and tech giants, take this $50m and figure out better chips
Yes, the Chinese will never think of doing something like this, muhaha
Systems27 Jan 2023 | 7
AI cannot be credited as authors in papers, top academic journals rule
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Science27 Jan 2023 | 23
Three seconds of audio could end up costing Fox $500,000
And that, kids, is why we don't play the Emergency Alert System tone on TV
Bootnotes27 Jan 2023 | 93