text:
package com.tanchaoyin.diandian.utils;

import android.graphics.drawable.GradientDrawable;
import android.widget.TextView;

import com.tanchaoyin.diandian.api.gank.GankType;

/**
 * Created by TanChaoyin on 2016/3/18.
 */
public class GanKDataTagUtil {

    /**
     * @param dataTagTV dataTagTV
     * @param url       url
     */
    public static void setTag(int type,TextView dataTagTV, String url) {
        String key = UrlMatch.processUrl(url);
        GradientDrawable drawable = (GradientDrawable) dataTagTV.getBackground();
        if (UrlMatch.url2Content.containsKey(key)) {
            drawable.setColor(UrlMatch.url2Color.get(key));
            dataTagTV.setText(UrlMatch.url2Content.get(key));
        } else {
            if (type == GankType.video) {
                drawable.setColor(UrlMatch.OTHER_VIDEO_COLOR);
                dataTagTV.setText(UrlMatch.OTHER_VIDEO_CONTENT);
            } else {
                // github 的要特殊处理
                if (url.contains(UrlMatch.GITHUB_PREFIX)) {
                    drawable.setColor(UrlMatch.url2Color.get(UrlMatch.GITHUB_PREFIX));
                    dataTagTV.setText(UrlMatch.url2Content.get(UrlMatch.GITHUB_PREFIX));
                } else {
                    drawable.setColor(UrlMatch.OTHER_BLOG_COLOR);
                    dataTagTV.setText(UrlMatch.OTHER_BLOG_CONTENT);
                }
            }
        }
    }
}

redpajama_set_name: RedPajamaGithub


That's a good idea... please tell me if that works out ok...!
I will. I'm not sure when I'm going back yet.
Oh that's understandable. We stayed with some people who had some huge dogs that wanted to play apparently so they jumped up and basically put their front paws on my shoulders o_o that was a little crazy and I did not appreciate it.
like yeah no duh I'm not going to let you either. So I told her "I didnt really give you permission to touch me." and she eventually stopped.
But a dog can totally be trained like that. Service dogs for example, before they pass their test they have to be able to walk through a busy public place and completely ignore any food or people— even if the people try to distract it.
I think it would be the Kill Order... maybe partially because the movies didn't cover any of that information? Idk. I just found it interesting knowing what happened to cause them to make the maze since the first book starts literally in the maze.
Random question but would you rather be a service dog or solely a family pet dog?
Ah, that makes sense... Wait, was The Kill Order the book with the scene of the lightbulb and little Thomas being given to WICKED?
Try not to feel too lonely if you're single; enjoy this day if you're part of a couple...!
Or redefine what Valentine's Day means...?
Apparently, the forums that we know will be "ended" (for lack of a better word) soon...?
Can we continue talking on the new thing (something called "Home Base"...?)...?
If so, I'll keep an eye out for a thread/message (I don't fully understand how it works... XD) from you...?


Mr Burrell was not detained by the police on the day of his death for policing matters. Officers went to Mary Seacole House on the 30th March 2011, the NHS premises where he was held under the Mental Health Act, at the request of NHS staff because they could not control him, as well as concerns about threats to NHS staff and self-harm. The officers placed him under restraint and then took him with NHS staff to the Queen Elizabeth Hospital for treatment and he was then taken to the Caffra ward in the Oleaster Unit and placed in seclusion.
These movements were under the observation of NHS staff. The misconduct proceedings arise from the force used by officers to detain Mr Burrell to allow medical examinations, to free him from restraints and their version of events concerning a face or head covering on Mr Burrell.
The material placed around his face / head was put there by NHS staff to protect people from spitting.
NHS staff entered the seclusion room after monitoring him through a window. He died after attempts to resuscitate him failed.
Quite rightly this case was subject to an independent investigation by the then Independent Police Complaints Commission (IPCC) as death had arisen following police contact. Dorset Police criminally investigated NHS staff. The case was inherited by the new Independent Office for Police Conduct (IOPC).
The NHS review of this case concluded in September 2011, five months after Mr Burrell died.
The IPCC investigation, coronial proceedings, criminal trial and misconduct hearing took almost eight years.
The Gross Misconduct hearing was chaired by a Temporary Deputy Chief Constable and an Assistant Chief Constable from independent forces and a lay member.
I set out these facts because there are some important issues they raise.
It is vital for public trust that matters involving the death of people after contact with the police is independently and rigorously examined.
It is not acceptable that the investigation and proceedings took nearly eight years.
The panel noted the inability for witnesses to have independent recollection after the time that had elapsed and raised concerns over some aspects of the investigation. This extended period of investigation, criminal and misconduct proceedings has had a profound impact on Mr Burrell's family. It left four officers, and their families, in a professional and personal hiatus for a large part of their police career. It has created a prolonged period of distrust between West Midlands Police and parts of the community. This has been at extensive cost to the public.
NHS staff and police officers have been treated differently. Mr Burrell was an NHS patient and died while under NHS care and treatment. The extended investigation into officers has focussed attention on actions of the police alone which I feel does not reflect the facts. This was not a case of the police arresting someone, it was the police restraining someone at the NHS's request while they were under their medical supervision.
The case met a standard for the CPS to decide criminal proceedings ought to be brought on the truthfulness of the accounts officers gave. The same position was reached in bringing misconduct proceedings although matters of use of force were examined in the misconduct case too. A jury reached a verdict in the criminal trial applying the criminal standard. In the gross misconduct hearing an independent panel hearing all the evidence made a decision on a balance of probabilities. Our legal and professional process mean we should respect both. A DCC and an ACC from outside West Midlands and a lay member devoted considerable time to hearing the case. I commend the effort that they made to do this and the fact they agreed to undertake this role. I respect their decision and also the officer's right to appeal the finding which will follow the due process.
It is important to be clear that the officer was dismissed because the panel concluded his account of the face covering on Mr Burrell was not truthful. No findings were upheld concerning the use of force.
In looking across these events I find myself very sad.
Mr Burrell should not have died and I am sorry this happened.
His family has suffered greatly. I feel officers and their families have suffered intolerable personal pressure. The time this has taken has damaged local police community relations. No one can walk away from this case feeling they have won anything.
It has been a tragedy.
We have to do much better than this in the future. I have confidence in the new IOPC and its local and national leadership. We need robust external scrutiny by a fit for purpose body and I believe they are that. I intend to discuss this case with them to ask we reflect from all sides on how this case has been managed. I want us to ensure cases such as this where other agencies are involved are dealt with consistently.
I shall meet and listen to all the officers involved in this case. I have offered to meet Mr Burrell's family.
We have a stronger approach to managing incidents in mental health premises. I regret the fact officers were deployed as they were that day in 2011 and feel we exercise stronger control on these matters now. The NHS has to be capable of managing its patients. Police restraint in a mental health hospital should not be needed. Today we issue officers spit guards and body cameras which would have improved the response and investigation of this case.
Many see these matters after eight years as not yet resolved. Sadly I agree this is not yet complete. I do however believe that the relationship between police and the community needs to come back together. Eight years will have soon passed and we need to look forward and build confidence in policing.
I would ask everyone to carefully respect the context of how people see this case and how they seek to raise their grievances or air their views. For staff that also means acting within the code of ethics and professional conduct in how personal views are expressed, both on and off duty, and for everyone else the law. I ask us all, at a basic human level, to consider the ordeal Mr Burrell's family, these officers and their families have and are going through.
Back to work… 2019 here we go!


[Urgent Warning] Government COVERING UP pain device deaths?!
It's a MASSIVE government cover-up that left THOUSANDS of people in agony… and hundreds of people dead.
You or someone you love may have been harmed.
For years we were promised that spinal implants were the next big thing in pain relief.
They were going to block even the worst pain – and help desperate people who'd been suffering for years.
Now we're learning that these tiny devices left a trail of death and destruction in their wake… and the Feds haven't lifted a finger to stop it.
If you have a spinal implant… or are even CONSIDERING one… this is one story you can't afford to miss.
If you're like many seniors who are crippled with pain, you've probably tried just about everything.
So it's no wonder that some people get desperate enough to have a device surgically implanted in their spinal cords to block pain signals from reaching their brains.
But a new exposé reveals the terrifying truth: More than 500 people with spinal-cord stimulators have died.
FDA officials admit that they've known about the deaths… and they haven't done SQUAT.
In fact, these government clowns are STILL insisting the devices are safe.
But the numbers tell another story.
Approximately 60,000 spinal-cord stimulators are implanted in patients every year.
In the last 10 years, 80,000 injuries have been reported to the FDA.
That's a 13% failure rate. And everybody knows that the REAL number is much higher – because most problems are never reported to the FDA.
Spinal-cord stimulators rank THIRD in terms of medical devices that cause injuries.
But when you consider how many MORE metal hip replacements (which are #1) and insulin pumps (#2) are out there, the abject FAILURE of spinal-cord stimulators is INSANELY disproportionate.
And what these electrical stimulators can do while they're implanted on your spinal cord is a nightmare.
Victims and whistleblowers alike tell stories of patients getting shocked and burned… sustaining IRREVERSIBLE damage… and suffering PERMANENT DISABILITY.
Somehow, device makers have found a way to make chronic pain even LESS livable.
If you're experiencing pain that won't go away with drugs or other mainstream therapies, don't agree to a surgical implant. ANY surgery comes with an entire set of its own risks – from the anesthesia to infections of the incision site, an allergic reaction (and rejection of the device), and the post-op painkillers.
As a first step, explore your options with a certified medical acupuncturist. Acupuncture has been proven to relieve pain in emergency situations just as well as morphine.
If this ancient "needle therapy" doesn't work for you, there are a number of external, non-invasive devices that work on a similar principle.
But you can adjust them… or remove them altogether… if you experience any discomfort.
You can try one out at your chiropractor's office, or you can buy one to use at home.
Look for a "microcurrent" stimulator called TENS or MENS.


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[from Scope and Content] BOND by Robert Wingfield, jun., of Upton, gent. to William Fitzwilliam, of Milton, esq. to abide by an award of Sir Walter Myldmay to settle actions between them now depending in the Queen's Bench.
This page was last modified on 10 March 2007, at 04:50.


On your own or attached? Either way, you may be thinking about your money this weekend – whether you're wining and dining your partner, or going out for drinks with your friends.
A recent survey from Confused.com revealed singletons spend less than those in a relationship. In fact, being in a relationship costs £2,340 more a year compared to being single.
Whether you agree with this or not, there are ways to save if you're solo or coupled up.
Here are two simple ways to save when single, and two ways you and your partner can consider.
Only adult in your household? Bingo! You can get 25% off your council tax bill. Find out more about council tax exemptions.
Who's responsible for what? Where should that spare twenty quid go? These are questions you should work through together as a couple. However, when you're single, it is easier to budget for the things you want. Budgeting is a great way to save money by pinpointing those money leaks and finding out where you can get those extra pennies.
If you live with your partner, it can make it easier to split the costs of running a household. If you go down this route, a joint account can be convenient. However, you should be aware that having a both your names on a bill, account or loancan affect your credit rating. With any decisions on joint ventures, remember honesty is key for a harmonious relationship – both with your money and your partner.
Joint accounts – the right decision for you?
A lot of things these days can be expensive, such as getting a house or a car. If you're saving with someone else towards a house deposit, for example, it can happen faster. What would you and your partner like to save up for? Both of you putting money aside also means your money goes further to spend elsewhere.
Do you have any thoughts of your own on how to save?
Does your partner have a secret stash of cash?
What a useless article. The second piece of advice for singletons is actually for couples, and the first item on saving in a couple doesn't save anything at all.
1)Age: younger people are more likely to be living as singles.
2)Socio-economic background: people in couples, especially married couples, are more likely to earn more. So while they might be spending more, they are still spending a lower % of their income.
Stop breathing, and then you won't spend one penny.
The stats look a bit dodgy to me. Single people (must you refer to them as "singletons?") only save 25% on their council tax bill, where as couples save 50% on all household bills, mortgage, rent, etc. Supermarket shopping is also cheaper as you can take advantage of the "family packs" or buy one-get one free offers on food knowing that with two people, all of the food can be consumed before it goes stale, and you're not forced to eat a dozen bananas in three days. Couples also save money on holidays, as they don't have to pay the single person supplement. And couples are not stigmatised by society for being lonely, desperate, something wrong with them, etc. Finally, saving up for a mortgage deposit as a single person is almost impossible. At least with couples you have half a chance of doing it.
Spend a lot of time reading different banks/building society interest on savings.
Look out for the "whoops" bargains at supermarkets, Asda did it first.
Look out for Subway and Mcdonald's discount vouchers - on line, in the local paper etc.
Shop late at shops, supermarkets, veg markets, particularly Saturday for good discounts.
Do one big weekly shop, rather than popping in several times a week: you spend more.
Drink before you go out to the pub, spend less in the pub.
Always buy alcohol on offer when offer in the shops.
Don't be proud, for the discering shopper that are some really good clothes in the charity shops.
Take out cash at the start of the week, then you won't chip and pin and be more aware of the frittering.
Seek out cheaper dry cleaners/shoe menders/restaurants etc.


called Parents for Quality Education.
trade stocks and bonds internationally.
was bombed in the first place.
up on the seventh and eighth of June.
effect for the past few years.
supposed to be taught Counselor Mrs.
the make-up days or failure is possible.
on Thursday, June 3, 1993.


The heart as the center of life, as a symbol of emotions, such as sound, as the organ that we share with many living beings … The competitor will offer its own interpretation of the element that has for centuries been a source of inspiration in art, avoiding the repetition of stereotyped forms.
Entries cannot be sent by post. Entries arriving after 20th of June dates may not be judged. The jury will pre-select 20 works that has to be delivered to the Ca' Pisani Design Hotel by the 30th of July. Finally, 12 or more winners will be selected.
Entrants are responsible for the delivery of their work to (and back) the Ca' Pisani Design Hotel.
The best designs are selected according to contest theme, form, functional and emotional aspects; the wearable jewelry are considered for their degree of innovation, aesthetic qualities, functionality in addition to ergonomics and quality of workmanship. Both luxury and daily-usage designs can be submitted. A section is also reserved to jewelry that can also be considered "wearable technologies".
If you have already entered your piece in another competition, you may also enter it in the Venice Jewelry Design Selection. You will need to let us know by the date of the first round of judging (July 15, 2016) if the piece won in another competition. If it did, we will remove it from the judging.
The international committee read more..
The exhibition at the Ca' Pisani Design Hotel is covered by an assurance for the maximum value of € 1000 for pieces. Entrants selected has to insurance there works for the delivery.
June 20, 2016: A digital file of your piece, which can be in the form of a drawing, rendering or photograph.
July 15, 2016: First round of judging is held.
July 19, 2016: The 20 finalists are notified and have to send there objects to Ca' Pisani Design Hotel by the July 30.
August 1-30, 2016: Final round of judging is held to choose the 12 selected.
September 6, 2016: The 12 finalists are notified.
After 15th of October 2016: All finalist and winning pieces will be returned to designers.
All entries must be collected from Venice Design Week untill the 20th of June.
For the entries pre-selected sent to Venice will be available from the 15th of October to be picked-up or returned to the address given by Special Delivery after the 20th of October. Optional: postal deliveries are recorded separately and Items valued under € 1,000 will be charged € 140 for postage, packing and insurance, payable, in advance, by bank transfer to: Venice Design Week or selected partner. For items above this, additional costs of postage, packing and insurance will be added.
There will also be guided tours during the VDW.
Technical partner: OONA gallery, OHMYBLUE, architetti Da Rin Perego, D33 sas.


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text:
Let - Deacon Road, London, NW2 - £1,550 pcm Tenancy Info
NEWLY REFURBISHED
Close to Transport Links
Wooden Flooring Throughout
Situated on the ground floor of a converted mid terrace house, just a short walk from Willesden High Rd.
The property comprises two bedrooms, a front facing reception, large and fully equipped kitchen, modern bathroom and sole use of a low maintenance rear garden.
The entire property has been kept to the very highest standard, and as such is presented in wonderful condition.
Benefits include modern, yet neutral decor throughout, a modern bathroom and a fully equipped kitchen.
This lovely flat can be provided as FULLY FURNISHED or UNFURNISHED and is available immediately for occupation.
The property is situated just 0.1 miles from Dollis Hill tube station and equidistant to a selection of bus routes emanating from Willesden Green bus garage.
Willesden is an area in North West London which forms part of the London Borough of Brent. It is situated 5 miles (8 km) northwest of Charing Cross. It was historically a parish in the county of Middlesex that was incorporated as the Municipal Borough of Willesden in 1933 and has formed part of Greater London since 1965.
The area is mostly in the NW10 postcode district, but partly also falls on the NW2 postcode district. Dollis Hill is also sometimes referred as being part of Willesden.
In 1965 the Municipal Borough of Willesden was abolished and it became part of the London Borough of Brent in Greater London.
Willesden Green Station (Jubilee line Zone 2)
The railways were instrumental in developing Willesden from a quiet village to a vibrant part of London. Willesden Green Station was opened in 1879 by the Metropolitan Railway and has a grand 1920s facade. The Metropolitan connected Willesden to Central London, Harrow, Uxbridge, Rickmansworth and Aylesbury. The Metropolitan no longer stops regularly at the station.
By road, Willesden is connected to many places as the A41 road/A5 road runs close by in nearby Kilburn/Cricklewood. The North Circular Road, the inner orbital road of London, is nearby running through Neasden.
A large bus garage was built in 1902 and thus many bus routes start or run through the town.
London Buses serving Willesden are:
6 Willesden Aldwych
52 Willesden Victoria Station
98 Willesden Russell Square
N98 Stanmore Russell Square
206 Kilburn Park Wembley Park
226 Golders Green Ealing Broadway
260 White City Golders Green
266 Hammersmith Brent Cross
297 Willesden Ealing Broadway
302 Mill Hill Broadway Kensal Rise
460 Willesden North Finchley
EPC for Deacon Road, London, NW2

redpajama_set_name: RedPajamaCommonCrawl


Does anybody here have this??? Sorry i am doin gmy stress thing again but before i went on the pill my periods were sooooo heavy and very very painful. Now we are going to start trying all sorts have been running through my head and last night I read in the Zita West book about Fibroids - wished I had not - and all the stuff sounds just like me.
Now i could be stressing for no reason at all as i am sure you have seen by now i am a huge worrier but I was wondering if anybody else had this at all?
I know well I am just freaking myself out I think, I read something and freak out i have it ;-( will see if i get my AF this week if not have to go back to him anyway as that will have been the second one I have missed in a row.
God i need to chill out.
I have 2 fibroids (one is the size of a strawberry) and had no side-effects from them at all.
Fortunately, they are growing up into me rather than down into the uterus - so wont make any problems for the baby (I'm 14wks pg).
At my last scan they measured them and they have gone down in size - which is apparently natural during pregnancy.
If I were you, I'd arrange to have a scan at your local hospital if you're v.worried. Usually they don't cause too many problems unless they are very large or if they are in the lower part of the uterus.
I dont want to upset you, but lets try not s. I had heavy bleeding and didnt notice, bloating and pains during my periods. I also had 3 miscarriages.....until hub and i decided to go for fertility tests and wham! I had 3 fibroids, one as big as the head of a new baby, one size of an average orange and another strawberry size. Apparently, they have made my womb dia home and will struggle with any invaders( pregnancy). I never went pass 10 weeks. Sooo, I had all of them REMOVED tru surgery in December 07, and was back to normal in 2 weeks. I have just finished going tru my ICSI programme wia they had my eggs collected and fertilised with my hubbys sperm. 8 eggs were collected, and 3 were very good and 2 will be put back into me on saturday and 2 weeks later do a pregnancy test and then wham bam!!!!
Fibroids are Myomas and they grow where there is blood. It is benign and depends on where it is located.
My advice is to get checked and not to waste precious time, which i did (4years) and now I am 38, but have a 9 year old son. If i had checked earlier, i would have had all the treatment years back and possibly have another child or children now.
Sorry, dont need to frighten you, but if i had a choice i will reverse the hand of the clock to wia i couldve had myself checked on the first possibility.
Feel free to ask me any Qs, i have gone tru it and i will keep you posted in 2 weeks time for my pregnancy result.
wow Dly thank you very much for getting back to me, I feel bad talking about this or even worrying about it as i am not even sure this is something that I have. A friend of mien has it and is now trying for a baby.
I do get heavy periods or at least i did when i was off the pill. iuse to have no pain at all but use to faint due to losing os much blood. Then the pains started cramps and back ache where the worst.
Since the pill i have not haad any of that but am always bloated. Though in saying that i due I think suffer from IBS so I am wondering if it is just that.
I thought you had to have 3 mc's first before they would test you for things like this?? I am due my af today or tomorrow and then we were going to think about trying this month.
Do you think i should still do that??
Ok fab I will start trying and see what happens if I worry about this anymore I might have a word with him. Sadly my doctor is not very helpful at all. Whenever i go about anything i don;t feel i get his full attention and he normaly passes all pains as growing pains which do my head in .
Today I have told myself to stop ove thinking everything as you can see this is what i do a lot LOL and to just sit back and let life do it;s thing. i can't do anything till AF shows her face if she does as all and if she does not then I will be asking for a scan to make sure all is well.
Thanks girls for talking to me abou this.


Whenever we have compromised our authenticity and truth, the first symptom is usually a feeling of emptiness within. And to live in a world of make-believe and to insist on living in a fantasy, we gradually lose touch with who we really are. I did that once in a connection with someone – a very confusing relationship. Like many other people do, because a strong connection was felt, a misinterpretation was experienced.
I was fooling myself and in denial, failing to honor and respect my own truth. Finally, like in all cases such as these, circumstances evolved to the breaking point wherein I had to become completely honest with myself—and with many addictive types of situations, more than once before I could finally break the chains of my own illusion.
Today the I-CHING Kua 54 brings a cosmic communiqué about relationships. The paragraph above was about a one-on-one partnership; however this guidance applies to more than a personal or love relationship—we could relate this to business partnerships, a company, organization, family or any other type of group.
In any of those scenarios it is possible to enter unknowingly at first into a situation wherein our own spirit becomes compromised due to eventual inequality or subordination that comes about through a desire to be in a role or to be in a certain position.
Sometimes it takes a while before we realize we have become a pawn in someone else's game or have fallen from grace due to susceptibility to flattery or manipulated through unrealistic promises.
What comes to mind is the word "discernment" as it relates to knowing who to trust and who not to trust and perhaps naiveté or gullibility. Some folks can get themselves very confused and in big trouble by believing others, taking everything at face value.
Gosh, what comes to mind next is the whole scenario of the Anthony family—you know about that right? The Florida legal case involving the death of little Caylee Anthony. What we could see happening in some of the family members involved is what is referred to as "silver-tongued devil's". What does that mean? People who will say anything to manipulate and coerce and other folks who take those silver-tongued individuals at face value.
I think one of the greatest lessons for those who are born with a consciousness that is too innocent and naïve is to develop a level of sophistication that incorporates the concept that some people can be really good liars. And some will lie about things that it isn't even necessary to lie about. And further that people will manipulate the truth for their own agenda. If we have not grown up around folks like these, it is very easy to be taken in—we just cannot conceive of that type of manipulative dishonesty!
It's confusing. And when confronted with it we will say to ourselves, "That's what they said, why would they lie?" Mostly because we wouldn't, we believe that other people are like we are. They're not always.
Ho! And that's the real wake up call, isn't it? When we find out, in undeniable terms, that all along we have been a pawn in someone else's game, it is an awakening of sorts.
BUT there are no real victims and then we have to ask ourselves how it happened and what our own role was in the scenario and then we can get honest about it.
Was it our own low self-esteem issue that got us caught in the illusion? Were we failing to respect our self and our intuition?
When these things happen, as we look back we can clearly see how we were lying to ourselves or denying the obvious. We might ask ourselves, "How could I have been so blind"?
One of the most painful things in life is facing the truth that we've sold ourselves short—or perhaps for a while exchanged our very own soul by entering into agreements that weren't good for us in the first place.
The bottom line message is that we need to allow ourselves to feel it and take responsibility for our part in it—this is the first step in release and reclaiming our soul. And feeling those emotions of self-betrayal (even though initially it feels like the other (s) betrayed us) can be horribly painful. It's like I blogged about yesterday… bringing light into those dark places!
I've got to say from my personal experience, that I thought I'd cleared the energy (of that one relationship situation) many times; but, apparently I didn't go deep enough. It was back when Uranus was exiting my 7th house and my transiting SN was hitting all the 12th house planets that the final catharsis occurred. It was pretty dramatic and probably involved clearing more than one lifetime's worth of issues. Sleepless nights and many tears were involved but after all the review and re-examination in a new light (it took some time), I learned quite a lot and felt so much clearer about so many things. I know that sounds vague, but I am sparing you the details.
When we wake up to the realization that there is a fatal flaw in what we thought was going to be a perfect situation, we sometimes want to go back to sleep again and not look at reality—meaning that we put those rose-colored glasses back on and make excuses to cover up what we know deep down is true but simply can't face—sometimes we don't see it but everyone else does but we think it is they who are confused (not us).
We can so easily ignore the whispering of our own intuition when we become attached to a desired outcome—that happens so easily. The thing is to love yourself out of it and the first thing is forgiveness, knowing you did the best you could at the time.
In my case, it was an instance of misinterpreting the signals of 'strong connection' to another soul as something that it wasn't. It was karmic connection that needed to be released in this lifetime.


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If I mess up, you may not like it, but in all likelihood you will either eventually forget my transgression or actually forgive me. After all, we all mess up from time to time, and our capacity for empathy and forgiveness is remarkable – except when it comes to forgiving ourselves.
In a similar light, you and I could both make the same mistake and you might forgive me, but you would be much harder on yourself. Why is that? What is that condemning voice and where does it come from?
Sometimes however, the ego plays the role of the little devil, urging you to leave your better judgment and play with fire, to take risks that defy your better judgement. This mostly happens around your need to feel loved. Afterwards we say to ourselves, "What the hell was I thinking?" In any case, the attraction to the honey pot is just too sweet, and as I said, nine times out of ten you end up regretting it.
After such a mistake the ego takes on the role of avenging angel, seeking to make you feel badly, with the goal of insuring that you won't make that mistake again. Unfortunately about all that does is make you feel badly about yourself, I'm not sure how much it really effects our decision making.
So, are there things from your past that you haven't forgiven yourself for? What to do? How do you let go of this well intended, avenging angel?
What I am going suggest is that you do an end run on your ego. When you get to the "other side" you will realize that the need you were trying to salve was false and that you can let go of it.
1.The first step is to recall the difficult situation you have been unable to forgive yourself for.
2. The second step is to connect with the essence of nature and breathe into it. (Your logical mind may interrupt at this point, but you will instinctively know what to do.) Note: being in nature will help, but just looking out at it will do.
3. The third step is to breathe your breath and the breath of Nature into the situation.
You should feel a shift. This should help the situation immensely. You will still remember what happened, but the charge on it should dissipate considerably.
You can use this technique for anything you are hanging on to that no longer serves you. Using the breathe of nature cleanses and feeds your wound, while at the same time bringing peace and wholeness. And your attention to your breath focuses your consciousness on something that is always positive – breathing life into you. Breath is Love. Love is Breath.


text:
Penguin Cafe - Birmingham Royal Ballet - Review
Home > London > Performing Arts | Theatre | Theatre Reviews
by Alison Brinkworth (subscribe)
Freelance journalist in Birmingham with a passion for the dynamic theatre, art, food and fashion scene in Britain's 'Second City'.
Dance triple bill shines with science and penguins
Every so often, Birmingham Royal Ballet(BRB) puts on a show that features a trio of short dances, rather than one long production.
The advantage of seeing these triple bills is that they not only give the audience a chance to sample more alternative types of dance than the most popular pieces, but also give the ballet company an opportunity to push the boundaries a little further with more experimental performances.
Dazzling choreography to show the speed of light in BRB's triple bill
This time around, the latest BRB tour includes three very contrasting dances - E=mc squared; Tombeaux and Still Life at the Penguin Cafe.
Catching the first night at Birmingham Hippodrome, the variety of content in this production means that there will be something to suit most tastes, whether its classical ballet, modern dance or a routine mixed with a dose of cheeky fun.
The award-winning trio were picked as they are among the most innovative of works by famed BRB choreographer David Bintley from over the past 25 years, but they still feel as fresh and vibrant as when first performed.
The opening dance, E=mc squared, is the most striking in terms of pushing boundaries. Based on Einstein's scientific formula, it cleverly breaks down each part of the world's most famous equation into a series of dances typifying the meaning.
So, first of all there is E for Energy, when the stage becomes a whirl of frenetic activity. Bodies everywhere, syncopating in constant movement; dancers who almost appear to be speed skating; and just a few strands of light shining across them all on a completely black stage.
A scene from E=MC squared. Part of a trio of delights offered in the latest Birmingham Royal Ballet tour.
Feeling almost tired from all the movement, there's time to catch your breath as the scene moves on to M for Mass, focussing on the slower, weightier elements. Ballerinas are lifted up delicately with gravity bringing them down far more gracefully and visually than what Einstein could ever have imagined. Their motion is almost like peaks and troughs on a scientific wave machine.
At this point, there is an interruption to the "equation of dance" with probably the most avant garde section of the night. This brief piece from The Manhattan Project features a dancer dressed as a geisha, all in white with a red fan in front of a glowing red background. While her movements are gentle the accompanying soundtrack is a constant deep drilling bass. It's striking and will stay with you long after you leave the auditorium.
Back to the science and C squared (the C for Celeritas meaning speed) is adapted to signify the speed of light. Rows of spotlights flood the stage as the dancers bounce so happily to the delightful score that it is almost addictive.
The wonderful choreography is so spot on that is like watching light bouncing off a mirror and the leads in this, Maureya Lebowitz and Mathias Dingman are delightfully cute (and springy).
Tombeaux is the second of the trio and much more classical in style.
This was extremely personal to Bintley. He created this work in 1993 and while on the surface it seems to be about a funeral, in reality it symbolises the choreographer's thoughts on the death of British ballet as he wanted it to be and is a product of all his frustrations.
Sombre scenes in Tombeaux
That bitterness is quite clear to see in this extremely dark and melancholy section, but ballerina Nao Sakuma brings joy through her exceptional dancing to William Walton's Variations on a Theme.
After the sombre mood of Tombeaux, a finale of the most vibrant production in this trio is a perfect pick me up.
Still Life at the Penguin Cafe is an enthralling, eye-catching section of the show featuring dancing penguins, zebras, and even a particularly soulful Brazilian Wooly Monkey.
From the moment the light-footed penguin waiters skedaddle on to stage to the breezy, optimistic tunes of Simon Jeffes, I defy anyone to not succumb to this routine.
There are obvious likenesses to the penguins who danced with Julie Andrews' Mary Poppins in the famous children's film, but these penguins are actually the creature's descendants, The Great Auk, which are now extinct.
A dancing penguin from Still Life at the Penguin Cafe
There's also a sassy Utah Longhorn Ram in chic 1930s dress, who does a 'Fred and Ginger' type turn of the dancefloor with a dashing Iain Mackay, looking debonair in full coat and tails. It's Strictly Come Dancing meets animal hospital, but in the best kind of way.
Meanwhile, the female zebras wonderfully pose like fashion models as they graze on an African meadow.
Despite the light-heartedness of it all, there is, as always with Bintley's work, a more complex undercurrent, which in this case is the issue of extinction. There's plenty of fun, but be warned, the final scene left me with a lump in my throat.
The Penguin Cafe triple bill will also be performed at:
Sadler's Wells Theatre, London - October 15-16, 2013
Theatre Royal Plymouth - October 29-30, 2013
The performance is 2h 45mins long including two 25mins intervals. Tickets cost from £13.
Sadler's Wells Theatre, London - www.sadlerswells.com or call 08444 124 300.
Theatre Royal Plymouth, Plymouth -www.theatreroyal.com
or call 01752 267222.
subscribe to Alison Brinkworth's articles
Why? See world class ballet
When: Sadler's Wells Theatre, London - October 15-16 and Theatre Royal Plymouth - October 29-30
Website: www.brb.org.uk
Where: Sadler's Wells Theatre, London and Theatre Royal, Plymouth
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text:
\section{Introduction}

Different approaches to integrating, analysing and acting upon clinical information leads to wide, unwarranted variation in medical practice across regions and institutions \citep{McKinlay2007, Westert2018}.
Algorithms designed to support the clinical decision-making process can help overcome this issue, with successful examples in oncology prognosis \citep{Beck2011, Esteva2017}, retinopathy detection \citep{Gulshan2016} and radiotherapy planning \citep{Valdes2017}. Still, these support systems focus on effectively replacing physicians with autonomous agents, trained to optimise patient outcomes or diagnosis accuracy. With limited design concern for end-users, these algorithms lack interpretability, leading to mistrust from the medical community \citep{Lai2020, RoyalSociety2017}.

Instead, our work aims to better describe and \emph{understand the decision-making process} by observing physician behaviour, in a form of epistemology. These transparent models of behaviour can clearly synthesise domain expertise from current practice and could thus form the building blocks of future decision support systems \citep{Li2015}, designed in partnership with clinicians for more reliable validation, better trust, and widespread acceptance. In addition, such policy models will enable quantitative comparisons of different strategies of care, and may in turn lead to novel guidelines and educational materials to combat variability of practice.

The associated machine learning challenge, therefore, is to {explain how physicians choose clinical actions}, given new patient observations and their prior medical history -- and thus describe an interpretable decision-making policy. Modelling clinical diagnostic and treatment policies is particularly challenging, with observational data involving confounding factors and unknown evolution dynamics, which we wish to then translate into a transparent representation of decision-making. State-of-the-art solutions for uncovering demonstrated policies, such as inverse reinforcement learning \citep{Ng2000} or imitation learning \citep{Bain1996, Piot2014, Ho2016}, fall short of interpretability -- mainly proposing black-box models as behaviour representations.

\begin{figure}\vspace{-0.5em}
         \centering
         \includegraphics[width=0.75\textwidth]{Figs/Fig1_demo.pdf}

    \caption{\textbf{Schematic representation of behavioural policies as trees, adapting over time.}
    \label{fig:intro}
\end{figure}

In contrast, transparent policy parametrisations based on visual decision boundaries \citep{Huyuk2021}, high-level programming syntax \citep{Verma2018} or outcome preferences \citep{Yau2020} can explain learned behaviour, at the cost of restrictive modelling constraints and obscure dynamics. Among possible interpretable representations, \emph{decision trees} offer the flexibility to capture high-dimensional environments and, as we demonstrate, can model time-series through recurrence. In addition, decision trees are highly familiar to the medical community, with many clinical guidelines having this form \citep{Chou2007, McCreery1991, Burch2012}. Cognitive research suggests human decision-making does follow a hierarchical, branching process \citep{Zylberberg2017}, making these models straightforward to understand. As a result, our algorithm \textbf{Policy Extraction through decision Trees (\textsc{Poetree})} represents clinical policies as decision trees, evolving over time with patient information -- as illustrated in Figure \ref{fig:intro}.

\paragraph{Contributions}

The main contributions of this work are as follows: (i) A novel framework for policy learning  in the form of incrementally grown, probabilistic decision trees, which adapt their complexity to the task at hand. (ii) An {interpretable model for representation learning} over time-series called recurrent decision trees. (iii) Illustrative analyses of our algorithm's expressive power in disambiguating policies otherwise unidentifiable with related benchmarks; integration of domain knowledge through inductive bias; and formalisation and quantification of abstract behavioural concepts (e.g. uncertain, anomalous or low-value actions) -- thus demonstrating its effectiveness in both understanding and replicating behaviour.

\section{Problem Formalism}
\label{sec:pbformalism}

Our goal is to learn an \emph{interpretable representation of a demonstrated decision-making process} to understand agent behaviour. The clinical context requires \emph{offline learning} using observational data only, as experimenting with policies would be both unethical and impractical. Finally, as previous observations and actions affect treatment choice, we are concerned with a \emph{partially-observable} decision-making environment.

We assume access to a dataset of $m$ demonstrated patient trajectories in discrete time $\mathcal{D} = \{ (z_1^i, a_1^i, \ldots, z_{\tau_i}^i, a_{\tau_i}^i) \}_{i=1}^m$, where $\tau_i$ is the length of trajectory $i$. We drop index $i$ to denote a generic draw from the population. At timestep $t$, the physician-agent observes patient features, denoted by random variable $Z_t \in \mathcal{Z}$, and chooses treatment or diagnostic action $A_t \in \mathcal{A}$, where $ \mathcal{A}$ is a finite set of actions. Let $z_t$ and $a_t$ denote realisations of these random variables. In contrast to traditional Markovian environments, the agent's reward function $R$, state space $\mathcal{S}$ and transition dynamics are all inaccessible.

Let $f$ denote a representation function, mapping the history of patient observations and actions to a representation space $\mathcal{H}$, and $h_t = f(z_1, a_1, ...z_{t-1}, a_{t-1}) = f(z_{1:t-1}, a_{1:t-1})\in \mathcal{H}$ represent the patient history prior to observing a new set of features $z_t$. Following the partially-observable  Markov Decision Process (POMDP) formalism, information in $\{h_t, z_t\}$ can be combined to form a \emph{belief} over the inaccessible patient state $s_t$. In contrast to recent policy learning work on POMDPs, which uncover mappings \emph{from belief to action space} \citep{Sun2017, Choi2011, Makino2012, Huyuk2021}, however, our aim is to highlight how newly-acquired observations $z_t$ conditions action $a_t$, to ensure decisions are based on interpretable, meaningful variables. As a result, agent behaviour \textit{must} be represented as a mapping \emph{from observation to action space}.

An adaptive \emph{decision-making policy} is a stationary mapping $\pi: \mathcal{Z} \times \mathcal{H} \times \mathcal{A} \rightarrow [0,1] $, where $\pi(a_t|z_t, h_t)$ encodes the probability of choosing action $a_t$ given patient history $h_t$ and latest observation $z_t$ -- thus $\forall t, \sum_{a_t \in \mathcal{A}} \pi( a_t | z_t, h_t) = 1$. We assume trajectories in $\mathcal{D}$ are generated by an agent following a policy $\pi_E$, such that $a_t \sim \pi_E(\cdot | z_t, h_t) $. The goal of our work is to find an \emph{interpretable} policy representation $\pi$ which matches and explains the behaviour of $\pi_E$.

\section{Interpretable policy learning with decision trees}
\label{sec:methods}

\subsection{Soft decision trees}
\label{sec:soft_decision_trees}

Motivated by the interpretability and pervasiveness of trees in the medical literature \citep{Chou2007}, Policy Extraction through decision Trees (\textsc{Poetree}) represents observed decision-making
\begin{wrapfigure}[27]{r}{0.37\textwidth
    \centerin
    \begin{subfigure}[b]{0.28\textwidth}\centering
         \includegraphics[width=\linewidth]{Figs/DT_detailed_hat.pdf}\vspace{-0.1em}
         \caption{DT policy.}\label{fig:SDT}
    \end{subfigure}

    \begin{subfigure}[b]{0.37\textwidth}\centering
         \includegraphics[width=\linewidth]{Figs/simple_DT_withoutcausal_withZ2.pdf}\vspace{-0.4em}
         \caption{RDT policy.}\label{fig:RDT}
    \end{subfigure}
    \vspace{-1.25\baselineskip}
    \caption{\textbf{\textsc{Poetree} policy structures}.}
    \label{fig:methods_RDT_detailed
\end{wrapfigure}
policies as trees. Our model architecture is inspired by soft decision trees -- structures with binary nodes, probabilistic decision boundaries and fixed leaf outputs \citep{Irsoy2012} -- for their transparency and modelling performance \citep{Frosst2017}. This supervised learning framework can be adapted for policy learning by setting input variables as $\mathbf{x} = z_t$ or as $\{h_t, z_t\}$ (for fully- or partially-observable environments), and targets as $\mathbf{y} = a_t$ \citep{Bain1996}.

\paragraph{Inner nodes} Illustrated in Figure \ref{fig:SDT}, the path followed by normalised input $\mathbf{x} \in \mathbb{R}^D$ is determined by gating functions encoding the probability of taking the rightmost branch at each non-leaf node $n$: $p_{gate}^n(\mathbf{x}) = \sigma \left( \mathbf{x}^T \mathbf{w}^n +b^n \right)$, where $\{\mathbf{w}^n\in \mathbb{R}^D$; \, $b^n\in \mathbb{R}\}_{n \in Inner}$ are trainable parameters and $\sigma$ is the sigmoid function. This design choice is motivated by its demonstrated flexibility and expressivity \citep{Silva2020}, and can be made interpretable by retaining the largest component of $\mathbf{w}^n$ to form an unidimensional axis-aligned threshold at each node, as illustrated in Figure \ref{fig:intro} and detailed in Appendix \ref{appendix:axisaligned}. Model simplification can be made more robust through L1 regularisation, encouraging sparsity in $\{\mathbf{w}^n\}_{n \in Inner}$. The path probability of each node, $P^n(\mathbf{x})$, is therefore given by the product of gating functions leading to it from the tree root.

\begin{comment}
\begin{wrapfigure}[16]{r}{0.7\textwidth}\vspace{-0.5\baselineskip}
    \centering\hspace{-1.cm}
    \begin{subfigure}[b]{0.30\textwidth}\centering
         \includegraphics[height=4.27cm]{Figs/DT_detailed.pdf}\caption{DT policy.}\label{fig:SDT}
    \end{subfigure
    \begin{subfigure}[b]{0.35\textwidth}\centering
         \includegraphics[height=4.47cm]{Figs/simple_DT_withoutcausal_withZ.pdf}\caption{RDT policy.}\label{fig:RDT}
    \end{subfigure
    \caption{\textbf{Decision tree policy structure, with different history extraction models}. Loss $\mathcal{L}$ is given by (a) $L$ and (b) $L + L_{\tilde{z}}$. }
    \label{fig:methods_RDT_detailed
\end{wrapfigure}
\end{comment}

\paragraph{Leaf nodes} In our tree architecture, leaves define a fixed probability distribution over $K$ categorical output classes. Leaf $l$ encodes relative activation values $\hat{a}_t^l = \text{softmax}({\theta}^l_a)$, where $ {\theta}^l_a \in \mathbb{R}^K$ is a learnable parameter. For ease of computation and interpretation, the output of the maximum-probability leaf $\hat{a}_t^{l_{max}}$, where $l_{max} =\argmax_l P^l(\mathbf{x})$, is taken as overall classification decision, following \citet{Frosst2017}.

\subsection{Recurrent decision trees}
\label{sec:method_unifiedRDT}

To account for previously acquired information, our algorithm must jointly extract and depend on a representation of patient history $h_t$. As in Figure \ref{fig:RDT}, RDTs take history $h_t$ and new observation $z_t$ as inputs, and output \emph{both} predicted action ${a}_t$ and subsequent history embeddings $h_{t+1}$ from decision leaves. These are computed as $h_{t+1}^l = \text{tanh}(\theta_h^l)$, where $\theta_h^l \in \mathbb{R}^M$ is an additional leaf parameter -- alternative leaf models are discussed in Appendix \ref{appendix:tree_growth}. Finally, as third leaf output with parameters $\theta_z^l \in \mathbb{R}^D$, our model also predicts \emph{patient evolution}, or observations at the next timestep $\tilde{z}_{t+1}$, effectively capturing the expected effects of a treatment on the patient trajectory as a policy explanation \citep{Yau2020}. A single tree structure is used at all timesteps: unfolded over time, our recurrent tree can be viewed as a sequence of cascaded trees \citep{Ding2021} with shared parameters $\Theta = \{ \{w^n, b^n \}_{n \in Inner}; \, \{\theta^l_a, \theta^l_h \theta^l_z \}_{l \in Leaf} \}$ and topology $\mathbb{T}$.

\pagebreak
\subsection{Tree growth and optimisation}
\label{sec:tree_growth}

\paragraph{Optimisation objective}

The policy learning objective is to recover the tree topology $\mathbb{T}$ and parameters $\Theta$ which best describe the observation-to-action mapping demonstrated by physician agents. Our loss function combines the cross-entropy between one-hot encoded target $a_t \in \{0,1\}^K$ and each leaf's action output, weighted by its respective path probability under input $\{h_t,z_t\}$:
\begin{equation}
   L(\{h_t,z_t, a_t\}; \mathbb{T}, \Theta) =  - \sum_{l\in Leaf} P^l(h_t,z_t)   \sum_{k} a_{t,k} \log \left[ \hat{a}_{t,k}^l \right] \label{eq:loss1

\end{equation}
where $\hat{a}_{t,k}^l$ is the output probability for action class $k$ in leaf $l$. Additional objectives are necessary for the multiple outputs to match their intended target: regularisation term $L_{\tilde{z}}$ is designed to learn patient evolution $\tilde{z}_{t+1}$ as expected by the acting physician. It minimises prediction error on $z_{t+1}$ and ensures the policy is consistent between timesteps by constraining predicted observations to lead to similar action choices as true ones, under the new history $h_{t+1}$
\begin{equation}
    L_{\tilde{z}}(\{h_t, z_t, z_{t+1}\}; \mathbb{T}, \Theta) = \delta_1 \: \Vert z_{t+1}-\tilde{z}_{t+1} \Vert^2 + \delta_2 \: D_{\text{KL}} \left( \pi(\cdot |h_{t+1}, z_{t+1} \Vert \pi(\cdot |h_{t+1}, \tilde{z}_{t+1} \right)
\end{equation}
where $\{\delta_1, \delta_2\}$ are tunable hyperparameters, weighting fidelity to true evolution and to demonstrated behaviour. For a set of training trajectories $\mathcal{D}$, and an overall loss $\mathcal{L} = {L} + L_{\tilde{z}}$, our policy learning optimisation objective becomes:
\begin{equation}
   \argmin_{\mathbb{T}, \Theta} \: \mathcal{L}(\mathcal{D})
\end{equation}
The probabilistic nature of our model choice makes it fully-differentiable,
allowing optimisation of parameters $\Theta$ through stochastic gradient descent and backpropagation through the structure for a fixed topology $\mathbb{T}$. Optimising with respect to $\mathbb{T}$, however, requires a more involved algorithm.

\begin{minipage}{\textwidth}
\begin{algorithm}[H]
\begin{wrapfigure}[9]{r}{0.43\textwidth}
    \vspace{-4.6em}
    \centering
    \includegraphics[width=0.47\textwidth]{Figs/Optimisation3.pdf
\end{wrapfigure}
\begin{minipage}{.55\textwidth}
\footnotesize
 \textbf{1.} Initialise $\mathbb{T}$ to inner node with two suboptimal leaves\;
  Optimise $\Theta$ via gradient descent of loss $\mathcal{L}$\;
 \While{$\exists$ suboptimal leaves in $\mathbb{T}$}{
  Split suboptimal leaf into inner node with two leaves\;
  \textbf{2a.} Locally optimise $\Theta$ via gradient descent of $\mathcal{L}$\;
  \lIf{validation performance improves}{retain split}
   \lElse{\textbf{2b.} Retain leaf as optimal}
 }
 \textbf{3.} Globally optimise $\Theta$ via gradient descent of $\mathcal{L}$\;
 Prune branches in $\mathbb{T}$ with low path probability $P^l(D_{val})$.
 \end{minipage}%
 \caption{\textbf{Tree growth optimisation}.} \label{algo:tree_opti}
\end{algorithm}%
\end{minipage}

\paragraph{Tree growth}
Following the work of \citet{Irsoy2012} and \citet{Tanno2019}, our decision tree architecture is incrementally grown and optimised during the training process, allowing the model to independently adapt its complexity to the task at hand. Algorithm \ref{algo:tree_opti} summarises the growth and optimisation procedure. Starting from an optimised shallow structure, tree growth is carried out by sequentially splitting each leaf node and locally optimising new parameters -- the split is accepted if validation performance is improved. After a final global optimisation, branches with a path probability below a certain threshold on the validation set are pruned. Further details on the tree growth procedure are given in Appendix \ref{appendix:tree_growth}.

\paragraph{Complexity} Policy training can be computationally complex due to the multiple local tree optimisations involved and significant number of parameters in comparison to other interpretable models \citep{Huyuk2021}. Still, at test time, computing tree path probabilities for a given input is inexpensive,
which is advantageous to allow fast decision support.
A detailed comparison of runtimes involved with our method and related work is proposed in Appendix \ref{appendix:poetree_implementation}.

\begin{table}[h]
\centering
\caption{\textbf{Related work.} Comparison to policy learning methods in terms of interpretability.}
\vspace{-1.7mm}
\label{tab:related_work_InterpPol}
\resizebox{\textwidth}{!}{%
\begin{tabular}{lcccc}
\toprule
\multirow{2}{*}{Related work} &  Offline & Partial & Interpretable & Modelling\\
 & Learning & Observability & Policy & Assumptions \\
\midrule
BC-IL \citep{Bain1996} & \cmark &  \textcolor{lightgray}{\xmark}  & \cmark &  \textcolor{lightgray}{--}\\
PO-BC-IL \citep{Sun2017} & \cmark &  \cmark  & \textcolor{lightgray}{\xmark} &  \textcolor{lightgray}{--}\\
Interpretable BC-IL \citep{Huyuk2021} & \cmark &  \cmark &  \cmark &  $\mathcal{S}$ known; low-dim. env.\\
DM-IL \citep{Ho2016} & \textcolor{lightgray}{\xmark} & \textcolor{lightgray}{\xmark} &  \textcolor{lightgray}{\xmark} &  \textcolor{lightgray}{--}\\
MB-IL \citep{Englert2013} & \cmark & \textcolor{lightgray}{\xmark}  & \textcolor{lightgray}{\xmark} & Simple dynamics \\
\midrule
IRL \citep{Ng2000} & \textcolor{lightgray}{\xmark} & \textcolor{lightgray}{\xmark} & \textcolor{lightgray}{\xmark} & $\pi_E$ optimal wrt. $\mathcal{R}$ \\
PO-IRL \citep{Choi2011} & \textcolor{lightgray}{\xmark} & \cmark & \textcolor{lightgray}{\xmark} & $\pi_E$ optimal wrt. $\mathcal{R}$ \\
Offline PO-IRL \citep{Makino2012} & \cmark & \cmark & \textcolor{lightgray}{\xmark} & $\pi_E$ optimal wrt. $\mathcal{R}$ \\
Interpretable RL \citep{Silva2020} & \textcolor{lightgray}{\xmark} & \textcolor{lightgray}{\xmark} & \cmark &  $\mathcal{R}$ known\\
\midrule
\textsc{Poetree} \textbf{(Ours)} & \cmark & \cmark & \cmark &  \textcolor{lightgray}{--}\\
\bottomrule
\end{tabular}}
\end{table}

\section{Related Work}
\label{sec:relatedwork}
In this section, we compare related work on interpretable policy learning, and contrast them in terms of key desiderata outlined in Section \ref{sec:pbformalism}. Table \ref{tab:related_work_InterpPol} summarises our findings

\paragraph{Policy learning}
While sequential decision-making problems are traditionally addressed through reinforcement learning, this framework is inapplicable to our policy learning goal due to the unavailability of a reward signal $R$. Instead, we focus on the inverse task of replicating the demonstrated behaviour of an agent, known as \emph{imitation learning} (IL), which assumes no access to $R$. Common approaches include behavioural cloning (BC) where this task is reduced to supervised learning, mapping states to actions \citep{Bain1996, Piot2014,chan2020interpretable}; and distribution-matching (DM) methods, where state-action distributions between demonstrator and learned policies are matched through adversarial learning \citep{Ho2016,Jeon2018,Kostrikov2019a}. \emph{Apprenticeship learning} (AL) aims to reach or surpass expert performance on a given task -- a closely related but distinct problem.
The state-of-the-art solution is inverse reinforcement learning (IRL), which recovers $R$ from demonstration trajectories \citep{Ng2000, Abbeel2004, Ziebart2008}; followed by a forward reinforcement learning algorithm to obtain the policy.

\paragraph{Towards interpretability for understanding decisions}
Imitation and apprenticeship learning solutions have been developed to tackle the challenges of fully-offline learning in partially-observable decision environments, as required by the clinical context \citep{chan2021medkit}: in IL, \citet{Sun2017} learn belief states through RNNs, and IRL was adapted for partial-observability \citep{Choi2011} and offline learning \citep{Makino2012}. However, while black-box neural networks typically provide best results, a transparent description of behaviour requires parametrising the learned policy to be informative and understandable. This often involves sacrificing action-matching performance \citep{Lage2018,chan2021inverse}, and introduces assumptions which limit the applicability of the proposed method, such as Markovianity \citep{Silva2020} or low-dimensional state spaces \citep{Huyuk2021}. The latter work, for instance, parametrises action choice through decision boundaries within the agent's belief space. In addition to leaving the observations-to-action mapping obscure, this imposes constraints on modelled states and dynamics -- which limit predictive performance, scalability and policy identifiability \citep{Biasutti2012}.

One approach to achieve interpretability in decision models is to implement \emph{interpretable reward functions} for IRL \citep{chan2020scalable}, providing insight into demonstrating agents' inner objectives. Behaviour has thus been explained as preferences over counterfactual outcomes \citep{Bica2021}, or over information value in a time-pressured context \citep{Jarrett2020a}. Still, the need for black-box RL algorithms to extract a policy obscures how observations affect action choice. Instead, the agent's policy function can be directly \emph{parametrised as an interpretable structure}. RL policies have been represented through a high-level programming syntax \citep{Verma2018}, or through explanations in terms of intended outcomes \citep{Yau2020}. Related work on building interpretable models for time-series in general is also discussed in Appendix \ref{appendix:tree_growth}.

\paragraph{Adaptive decision trees for time-series}
Related soft and grown tree architectures have been proposed for image-based tasks \citep{Frosst2017, Tanno2019} -- little research has been reported on probabilistic decision trees for the dynamic, heterogeneous and sparse nature of time-series data. Tree structures have been proposed for representation learning, relying for instance on projecting inputs to more informative features in between decision nodes \citep{Tanno2019} or on cascaded trees, sequentially using their outputs as input to subsequent ones \citep{Ding2021}. In all cases, however, models lose interpretability, as decisions are based on unintuitive variables: in contrast, we build thresholds over native observation variables, meaningful to human experts. Our work is further contrasted with established tree models in Appendix \ref{appendix:tree_growth}.

\section{Illustrative Examples}
\label{sec:results}

\subsection{Experimental Setup}

\paragraph{Decision-Making Environments}

Three medical datasets were studied to evaluate our work. First, as ground-truth policies $\pi_E$ are inaccessible in real data, a synthetic dataset of 1000 patient trajectories over 9 timesteps, denoted \textbf{SYNTH}, was simulated. In a POMDP with binary disease state space, observations include one-dimensional diagnostic tests $\{z_+,\:z_{-}\}$ as well as 10 noisy dimensions disregarded by the agent (e.g. irrelevant measurements); and actions $\{a_+,\: a_{-}\}$ correspond to treatment and lack thereof. Assuming treatments require exposure beyond the end of symptoms \citep{Entsuah1996}, the expert policy treats patients who tested positive over the last three timesteps: $a_t = \pi_E(h_t, z_t) = a_+$ if $z_+ \in \{z_{t-2}, z_{t-1},z_{t} \}$; $a_{-}$ else. Next, a real medical dataset was explored, following 1,625 patients from the Alzheimer's Disease Neuroimaging Initiative (\textbf{ADNI}), as in \citet{Huyuk2021} for benchmarking. We consider the task of predicting, at each visit, whether a Magnetic Resonance Imaging (MRI) scan is ordered for cognitive disorder diagnosis \citep{NICEguideline}. Patient observations consist of the Clinical Dementia Rating (CDR-SB) on a severity scale (normal; questionable impairment; severe dementia) following \citet{OBryant2008}; and the MRI outcome of the previous visit, categorised into four possibilities (no MRI scan; and below-average, average and above-average hippocampal volume $V_h$). Finally, we also consider a dataset of 4,222 ICU patients over up to 6 timesteps extracted from the third Medical Information Mart for Intensive Care (\textbf{MIMIC-III}) database \citep{Johnson2016} and predict antibiotic prescription based on 8 observations -- temperature, white blood cell count, heart rate, hematocrit, hemoglobin, blood pressure, creatinine and potassium; as in \citet{Bica2021}. By dataset design or by the nature of real-world clinical practice, observation history must be considered by the acting policies -- making our decision-making environments partially-observable.

\paragraph{Success Metrics}

Reflecting our unconventional priority for \emph{policy interpretability} over imitation performance, we provide illustrative examples evidencing greater insight into observed behaviour through decision tree representations. For a more quantitative assessment of interpretability, we also surveyed five practising UK clinicians of different seniority level, asking them to score models out of ten on how well they could understand the decision-making process -- with details in Appendix \ref{appendix:cliniciancs}. \emph{Action-matching performance} was also evaluated through
the areas under the receiver-operating-characteristic curve (AUROC) and precision-recall curve (AUPRC), and through Brier calibration.

\paragraph{Benchmark Algorithms}
For benchmarking, we implemented different behavioural cloning models, mapping observations or belief states to actions: (i) decision tree (\textbf{Tree BC-IL}) and logistic regression models with no patient history; (ii) a partially-observable BC algorithm (\textbf{PO-BC-IL}) extracting history embeddings through an RNN \citep{Sun2017}, on which a feature importance analysis is carried out \citep{Lundberg2017}; (iii) and an interpretable PO-BC-IL model, \textbf{\textsc{interpole}} \citep{Huyuk2021}, described in Section \ref{sec:relatedwork}.
Benchmarks also include (iv) model-based imitation learning \textbf{PO-MB-IL} \citep{Englert2013}, adapted for partial-observability with a learned environment model; (v) Bayesian Inverse Reinforcement Learning for POMDPs (\textbf{PO-IRL}), based on \citet{Jarrett2020a}; and (vi) a \textbf{Offline PO-IRL} version of this algorithm as in \citet{Makino2012}. Implementation details are provided in Appendix \ref{appendix:benchmarks}.

\subsection{Interpretability}
\label{sec:results_interpretability}

In light of our priority on recovering an interpretable policy, we first propose several clinical examples and insights from the ADNI dataset to highlight the usefulness of our tree representation.

\begin{figure}[ht]
    \centering

    \sbox{\bigimage}{%
      \begin{subfigure}[b]{.56\textwidth}
      \centering
      \includegraphics[width=\textwidth]{Figs/ADNI_demo_highlighted.pdf}
      \caption{Adaptive decision tree policy}\label{fig:adni_main}
      \vspace{0pt
      \end{subfigure}%
    }
    \usebox{\bigimage}\hfill
    \begin{minipage}[b][\ht\bigimage][s]{.42\textwidth} \vspace{-1em}
    \centering
      \begin{subfigure}[b]{0.48\textwidth}
      \centering
      \includegraphics[width=0.9\textwidth]{Figs/interpole_decision_boundary2.pdf}
      \caption{\centering Decision boundary over belief}\label{fig:ADNI_interpole}
      \end{subfigure}%
      \hfill
      \begin{subfigure}[b]{0.48\textwidth}
      \centering
      \includegraphics[width=\textwidth]{Figs/ADNI_static.pdf}
      \caption{\centering Static decision tree policy} \label{fig:static_DT}
      \end{subfigure} \\
      \vfill
      \begin{subfigure}[b]{0.48\textwidth}
      \centering
      \includegraphics[width=\textwidth]{Figs/ADNI_logisticregression2.pdf}
      \caption{\centering Logistic regression}
      \end{subfigure}%
      \hfill
      \begin{subfigure}[b]{0.48\textwidth}
      \centering
      \includegraphics[width=\textwidth]{Figs/ADNI_featureimportance2.pdf}
      \caption{\centering Feature importance}\label{fig:feature_importance}
      \end{subfigure}
      \vspace{0pt
    \end{minipage}
    \caption{\textbf{Comparison of interpretable policy learning methods on ADNI.} Crosses stand for no action. Fig. (b) follows a method from \citet{Huyuk2021}.
\end{figure}

\paragraph{Explaining patient trajectories}

Our first example studies decision-making within typical ADNI trajectories. Let \textbf{Patient A} be healthy with normal CDR score and average $V_h$ on initial scan. Let \textbf{Patient B} initially have mild cognitive impairment (MCI), progressing towards dementia: their CDR degrades from questionable to severe at the last timestep and a below-average $V_h$ is measured at each visit. \textbf{Patient C} is diagnosed with dementia at the first visit, with severe CDR and low $V_h$: no further scans are ordered as they would be uninformative \citep{NICEguideline}. Figure \ref{fig:adni_main} illustrates our learned tree policy, both varying with and determining patient history at each timestep (see Appendix \ref{appendix:datasets} for the distinct policy of each patient). Patient A is not ordered any further scan, as they never show low $V_h$ or abnormal CDR, but may be ordered one if they develop cognitive impairment. For Patient B with low $V_h$ but a CDR score not yet severe, another MRI is ordered to monitor disease progression. At the following visit, patient history conditions the physician to be more cautious of scan results: even if $V_h$ is found to be acceptable, another scan may be ordered if the CDR changes. Finally, Patient C's observations already give a certain diagnosis of dementia: no scan is necessary. At following timesteps, unless the patient unexpectedly recovers, their history suggests to {not} carry out any further scans. We must highlight the similar strategy between our decision tree policy and \emph{published guidelines} for Alzheimer's diagnosis in \citet{Biasutti2012}, reproduced in Appendix \ref{appendix:datasets}: our policy correctly learns that investigations are only needed until diagnosis is confirmed.

In contrast, the black-box history extraction procedure required by most benchmarks for partial-observability (PO-BC-IL, PO-IRL, Offline PO-IRL, PO-MB-IL) is difficult to interpret, with no clear decision-making process. The policy learned by \textsc{interpole} \citep{Huyuk2021} in Figure \ref{fig:ADNI_interpole}, defined by decision boundaries over a subjective disease belief space, provides more insight: this model suggests respectively few and frequent scans for healthy Patient A and MCI Patient B, at different vertices of the belief space, but cannot account for scan reduction in diagnosed Patient C as this requires discontinuous action regions. This policy representation only relies on disease beliefs and thus cannot identify the effect of different observations on treatment strategies. Finally, common interpretable models proposed in Figures \ref{fig:static_DT}--\ref{fig:feature_importance} fail to convey an understanding of behavioural strategy and evolution.

\paragraph{Decision-making uncertainty}

\begin{comment}
\begin{figure}
    \centering
    \begin{subfigure}[b]{0.33\textwidth}
    \centering
      \includegraphics[width=\linewidth]{Figs/ADNI_uncertainty_ABC3.pdf}
      \caption{\centering $\sigma_{\pi}$ over time, with\hspace{\textwidth}shaded 95\% confidence intervals.}\label{fig:ADNI_ind_uncertainty}
     \end{subfigure}\hfill
    \begin{subfigure}[b]{0.32\textwidth}
    \centering
        \includegraphics[height=2.3cm]{Figs/MOD_ADNI_demo_mci_AAP.pdf} \vspace{1.5em
        \caption{\centering Patient  B, $t=1$:\hspace{\textwidth
        $\sigma_\pi(h_1,z_1) = 0.43$\footnotemark.}\label{fig:B1_uncertainty}
    \end{subfigure}\hfill
    \begin{subfigure}[b]{0.32\textwidth}\centering
        \includegraphics[height=2.3cm]{Figs/MOD_ADNI_demo_mci_AAP3.pdf}\vspace{1.5em}
        \caption{\centering Patient  B, $t=4$:\hspace{\textwidth}$\sigma_\pi(h_4,z_4) = 0.34$.}\label{fig:B4_uncertainty}
    \end{subfigure}
    \caption[Policy decision uncertainty for ADNI.]{\textbf{Policy decision uncertainty $\sigma_\pi$ for ADNI.} Maximum tree probability paths are highlighted in blue, with action probabilities in green/red. Less probable paths not pictured.}
    \label{fig:ADNI_uncertainty}
\end{figure}
\end{comment}

\begin{figure}
    \centering
      \includegraphics[width=0.95\linewidth]{Figs/ADNI_uncertainty_ABC5.pdf}
      \caption{\textbf{Policy confidence on ADNI}. Maximum probability paths are highlighted in blue, with action probabilities in green/red.}\label{fig:ADNI_uncertainty}
\end{figure}

Our behaviour model also inherently captures the useful notion of decision confidence thanks to its probabilistic nature:\begin{equation}\label{eq:uncertainty}
    \pi(a_t = k|h_t, z_t) = \sum_{l \in Leaf} P^{l}(h_t, z_t) \cdot {a}_{t,k}^l
\end{equation}
where, for each leaf node $l$, $P^{l}(h_t, z_t)$ and ${a}_{t,k}^l$ are the path and output probability for action $k$. Figure \ref{fig:ADNI_uncertainty} highlights how policy confidence varies over time for each typical patient. Uncertainty for Patient A can be attributed to variability in healthy patient care in the demonstrations dataset, as scans may provide information about their state, but must be balanced with cost and time considerations \citep{NICEguideline}. For Patient C with a dementia diagnosis, further investigations are not required \citep{Biasutti2012}, reflected in confidence increase. As a result, for Patient B with degrading symptoms, scans are initially ordered with low confidence to monitor progression, but as symptoms worsen and the patient is diagnosed, decision confidence increases. Figure \ref{fig:ADNI_uncertainty} also evidences both greater inter-path and intra-leaf uncertainty\footnote{Inter-path uncertainty can be measured as the entropy within leaf path probabilities $-\sum_l P^l(\mathbf{x}) \log P^l(\mathbf{x})$, while intra-leaf uncertainty can be measured as the average leaf output entropy: $- 1/l \sum_l \sum_k \hat{a}^l_{t,k} \log \hat{a}^l_{t,k}$.} for MRI prediction: our policy model identifies clear conditions \textit{not} warranting a scan after diagnosis, whereas conditions warranting one are more ambiguous. This example illustrates the value of uncertainty estimation afforded by our framework, modulating probability values within tree paths and leaf outputs.

\begin{figure}
    \centering

    \begin{subfigure}[b]{0.72\textwidth}
    \centering

    \includegraphics[width=\linewidth]{Figs/ADNI_anomalous_belated3.pdf}
    \caption{\centering Anomalous behaviour per cohort.
    \label{fig:results_ADNIanomalous}
    \end{subfigure}\hfill
    \begin{subfigure}[b]{0.24\textwidth}\centering
        \includegraphics[width=\linewidth]{Figs/ADNI_uninformative_typicalABC.pdf}
        \caption{Uninformative actions.}\label{fig:adni_uninformative}
    \end{subfigure}
    \caption{\textbf{Anomalous and low-value actions in various patient cohorts}: patients over 75 years old, patients carrying the $\epsilon$4 allele of the apolipoprotein E gene (ApoE4), patients with signs of MCI or dementia at their first visit, female and male patients.}

\end{figure}

\paragraph{Anomalous behaviour detection} Learned models of behaviour are also valuable to flag actions incompatible with observed policies. Visits where an MRI is predicted with 90\% certainty, yet the physician agent does not order it -- as in Figure \ref{fig:results_ADNIanomalous} -- make up 8.4\% of ADNI. This may highlight demonstration flaws, as the learned policy is confident and has well-calibrated probability estimates (low Brier score in Table \ref{tab:benchmark_results}). Anomalous behaviour {followed} by an MRI `correcting' the off-policy action can also be detected, suggesting 6.7\% of patients are thus investigated late -- comparable to belated diagnoses found in 6.5\% of patients by \citet{Huyuk2021}. As shown in Figure \ref{fig:results_ADNIanomalous}, high-risk cohorts due to age, female gender or ApoE4 allele \citep{Launer1999, Lindsay2002} are more often subject to late actions. Most anomalous actions on patients with ApoE4 or female patients end up corrected, in contrast to older patients or ones with early symptoms -- imaging is less paramount for the latter, as they may be diagnosed clinically \citep{NICEguideline}.

\paragraph{Action value quantification through counterfactual evolution}
Our joint expected evolution and policy learning model allows action value to be quantified \citep{Yau2020, Bica2021}. Low-value actions correspond to an ordered scan showing similar observations to the previous timestep, when this could already be foreseen from expected evolution $\tilde{z}$ (less than average variation minus one standard deviation). As shown in Figure \ref{fig:adni_uninformative}, ill patients are more often monitored with uninformative MRIs than healthy ones. This analysis explains the high rate of uninformative actions for patients with early signs of disease, found in previous work \citep{Huyuk2021}: the policy recommends investigation for diagnosis, yet their expected evolution is typically unambiguous. Overall, our decision tree architecture enables straightforward assessment of counterfactual patient evolution under different observation values.

Overall, our decision tree policy parametrisation explains demonstrated decision-making behaviour in terms of \textit{how actions are chosen based on observations and prior history}, and, in the above illustrative analyses, allows a formalisation of abstract notions -- such as uncertain, anomalous or low-value choices -- for quantitative policy evaluation. Next, we show that these insights are not gained at the cost of imitation performance.

\subsection{Policy fidelity}
\label{sec:results_accuracy}

\paragraph{Action-matching performance}
As shown in Table \ref{tab:benchmark_results}, our approach outperforms or comes second-best \emph{on all success metrics} compared to benchmark algorithms. This confirms the expressive power of our recurrent tree policies over decision boundaries \citep{Huyuk2021} and even over neural-network-based methods \citep{Sun2017}, specifically optimised for action-matching. The poor action-matching performance of static decision trees (Tree BC-IL) highlights the importance of history representation learning in overcoming the partial-observability of the decision-making environment. Mean relative evolution error between $z_t$ and $\tilde{z}_t$ was measured as 13 $\pm$ 4\% and 26 $\pm$ 9\% on ADNI and MIMIC respectively, giving reasonable and insightful values. Our model was scored as the second most understandable in our user survey, following the overly-simplistic static decision tree (Fig. \ref{fig:static_DT}). Collected feedback is provided in Appendix \ref{appendix:cliniciancs}.

\paragraph{Policy identifiability}
Figure \ref{fig:results_SYNTH} illustrates policies learned from our high-dimensional SYNTH dataset with \textsc{Poetree} and the closest related work \citep{Huyuk2021}. Despite the apparent simplicity of the decision-making problem, \textsc{Interpole} fails to identify the outlined treatment strategy, as evidenced by its inferior performance in Table \ref{tab:benchmark_results}. This illustrates greater flexibility of our
\begin{wrapfigure}[21]{r}{0.3\textwidth}
    \centering
    \vspace{-0.5\baselineskip}
    \begin{subfigure}[c]{0.3\textwidth}
    \centering
        \includegraphics[width=\linewidth]{Figs/interpole_POC3.pdf}
        \caption{\centering Decision-boundary policy \newline \citep{Huyuk2021}.} \label{fig:results_SYNTH_interpole}\hspace{1em}
    \end{subfigure}
    \begin{subfigure}[c]{0.3\textwidth}
    \centering
        \includegraphics[width=\linewidth]{Figs/POC_policy_inkscape.pdf}
        \caption{\centering Adaptive decision tree policy.}\label{fig:results_SYNTH_ADTP}
    \end{subfigure}
    \caption{\textbf{Recovered policies for SYNTH.}}
    \label{fig:results_SYNTH
\end{wrapfigure}tree representation in \emph{disambiguating decision-making factors} which simply cannot be captured by previous work; and, due to not relying on HMM-like dynamics, can be credited to \emph{fewer modelling assumptions} and \textit{scalability} to high-dimensional environments.

\begin{table}
    \centering
    \caption{\textbf{Comparison of the performance of  policy learning algorithms\protect\footnotemark on medical datasets.} Interpretability scores out of ten were obtained through our clinician survey. Lower is better for Brier calibration. Standard errors for MIMIC and SYNTH were $\leq$ 0.04.}
    \label{tab:benchmark_results}
    \resizebox{\textwidth}{!}
    \begin{tabular}{lcccccccc}
    \toprule
        Task & \multicolumn{4}{c}{ADNI MRI scans}  & \multicolumn{2}{c}{MIMIC antibiotics}  & \multicolumn{2}{c}{SYNTH} \\
        \cmidrule(lr){2-5} \cmidrule(lr){6-7} \cmidrule(lr){8-9}
        Algorithm & Interpretability & AUROC & AUPRC & Brier & AUROC & Brier & AUROC & Brier\\\midrule

        Tree BC-IL & \textbf{9.3 $\pm$ 0.3} & {0.53 $\pm$ 0.01} & {0.72 $\pm$ 0.01}& {0.25 $\pm$ 0.01} & 0.50 & 0.23 & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} \\
        PO-BC-IL [\citenum{Sun2017}] & 0.3 $\pm$ 0.3 &  0.59 $\pm$ 0.04 & 0.80 $\pm$ 0.08 &  \textbf{0.18 $\pm$ 0.05} & 0.67 & \textbf{0.16} & 0.98 & 0.02 \\
        \textsc{Interpole} [\citenum{Huyuk2021}] & 7.3 $\pm$ 0.5 & 0.44 $\pm$ 0.04 & 0.75 $\pm$ 0.09 & 0.19 $\pm$ 0.07 & 0.65 & 0.21& 0.84 & 0.12 \\
        PO-MB-IL [\citenum{Englert2013}] & \textcolor{lightgray}{--} & 0.54 $\pm$ 0.08 & 0.81 $\pm$ 0.07 & 0.19 $\pm$ 0.03 & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} & \textcolor{lightgray}{--}\\
        PO-IRL [\citenum{Jarrett2020a}] & \textcolor{lightgray}{--} & 0.50 $\pm$ 0.08 & 0.82 $\pm$ 0.04 & 0.23 $\pm$ 0.01  & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} & \textcolor{lightgray}{--}\\
        Offline PO-IRL [\citenum{Makino2012}] & \textcolor{lightgray}{--} & 0.54 $\pm$ 0.06 & \textbf{0.83 $\pm$ 0.04} & 0.23 $\pm$ 0.01 & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} & \textcolor{lightgray}{--} & \textcolor{lightgray}{--}\\
        \midrule
        \textbf{\textsc{Poetree}} & {8.3 $\pm$ 0.3} & \textbf{0.62 $\pm$ 0.01} & {0.82 $\pm$ 0.01} & \textbf{0.18 $\pm$ 0.01} & \textbf{0.68} & 0.19 & \textbf{0.99} & \textbf{0.01}\\
        \bottomrule
    \end{tabular}}
\end{table}

\paragraph{Inductive bias}

Having demonstrated that our policy learning framework allows us to \emph{recover} domain expertise, we investigated the effect of incorporating \emph{prior} policy knowledge on learning performance. In practice, our model's action prediction structure can be initialised based on a published guideline \citep{Biasutti2012} as in Appendix \ref{appendix:datasets}: training time was reduced by a factor of 1.4 and action-matching AUPRC was improved to 0.84 $\pm$ 0.01. This `warm-start' is a promising strategy to learn from physician observation while building on established clinical practice standards.

\footnotetext{References: [\citenum{Sun2017}] \citet{Sun2017}; [\citenum{Huyuk2021}] \citet{Huyuk2021}; [\citenum{Englert2013}] \citet{Englert2013}; [\citenum{Jarrett2020a}] \citet{Jarrett2020a}; [\citenum{Makino2012}] \citet{Makino2012}.}

\paragraph{Accuracy-interpretability trade-off: complexity analysis}
Incrementally grown trees outperform fixed structures by eliminating unnecessary partitions, with $\sim$40\% fewer parameters for the same depth, greater readability \citep{Lage2018} and reasonable training time. Grown structures adapt their depth and complexity to avoid overfitting while capturing the modelling task, in a form of Occam's razor -- jointly optimising policy accuracy and interpretability. In particular, sample complexity modulates learned policies in training. Detailed experimental results are provided in Appendix \ref{appendix:poetree_implementation}.

\section{Conclusion}

Established paradigms to replicate demonstrated behaviour fall short of explaining learned decision policies, whereas the state-of-the-art in interpretable policy learning was criticised by end-users for restrictive modelling assumptions \citep{Huyuk2021} -- thus not fully capturing diagnostic strategies. Policy Extraction with Decision Trees (\textsc{Poetree}) overcomes these challenges, outputting most likely actions and uncertainty estimates, given patients' observations and medical history. Our algorithm carries out joint policy learning, history representation learning and evolution prediction tasks through a recurrent, multi-output tree model -- justifying agent decisions by comparing counterfactual patient evolutions. Optimised structures outperform the state-of-the-art in interpretability, policy fidelity and action-matching, thus providing an understanding of demonstrated behaviour without compromising accuracy. In particular, we can formalise and quantify concepts of practice variation with time; uncertain, anomalous, or low-value behaviour detection; and domain knowledge integration through inductive bias. Finally, we validate clinical insights through a survey of intended users.

Beyond policy learning, our novel interpretable framework for time-series modelling shows promise for alternative tasks relevant to clinical decision support, such as patient trajectory prediction, outcome estimation or human-in-the-loop learning for treatment recommendation -- a promising avenue of research for further work.

\subsubsection*{Acknowledgments}
We thank all NHS clinicians who participated in our survey and the Alzheimer's Disease Neuroimaging Initiative and Medical Information Mart for Intensive Care for access to datasets. This publication was partially made possible by an ETH AI Center doctoral fellowship to AP. AJC would like to acknowledge and thank Microsoft Research for its support through its PhD Scholarship Program with the EPSRC. Many thanks to group members of the van der Schaar Lab and to our reviewers for their valuable feedback.

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Toluca Lake is an emo trio brought up in the college basement scene of Lowell, MA who has crafted a sound that twists and turns in new evolutions with each new release, bringing out a softer side in 2018's "Breath in Passing" and a triumphant, accessible side in 2020's "How You Like to Waste Your Day".
TOLUCA LAKE, by Matt Cohen/Mike Jannino
Toluca Lake is an emo trio brought up in the college basement scene of Lowell, MA and currently based in and around Boston. Toluca Lake consists of Mike Jannino (they/them, guitar, vocals, producer), Cullen Ryan (he/him, percussion), and Matt Cohen (he/him, bass, backing vocals, producer). On the local circuit since 2015's freshman record, "Walker", Toluca Lake has crafted a sound that twists and turns in new evolutions with each new release, bringing out a softer side in 2018's "Breath in Passing" and a triumphant, accessible side in 2020's "How You Like to Waste Your Day".
"Co-writing and food fighting four songs together for a blend of our taste"
Through their local New England emo community and an evolving taste in music, Toluca Lake has always tried to push the boundaries of what they are capable of and challenge their audience's perception of what their music could be – the latest split with Pittsburgh's own overtheweather, Food Fight (2022) is a prime example. Above all else, Toluca Lake wishes to be heard and to help, and are pushing their music as far as it can go.
OVERTHEWEATHER by Tyler Blau
overtheweather is an alternative, emo, post-punk band born and raised in Pittsburgh PA. The band consists of Julian Mascilli (vocals, guitar, producer/recording engineer), Dixon Frank (vocals, percussion), Christian Price (bass, backing vocals) and Ryan McMahon (guitar).
Following their first self-produced release "party socks" in 2021, overtheweather hit the local music scene ambitious to make a name for themselves opening up for national acts. During that time, the band continued to write new music and refine their sound.
The band is currently releasing a self-produced split (2022) and recording a full length album to follow. overtheweather aims to share their music and explore the music world outside of Pittsburgh in the near future.
"food fight, the food songs to fight food with food"
For fans of: Have Mercy, Free Throw, modern baseball, All Get Out, Balance and Composure, microwave, the Hotelier
Related Items:alternative rock, emo, emo rock, indie, indie rock, overtheweather, punk rock, Toluca Lake
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text:
22-year-old man killed in crash, coroner says
Highway Patrol and the Spartanburg County coroner's office are investigating
Updated: 7:46 AM EDT Jul 30, 2018
Joe Ripley
WEBVTT A SHORT TIME AFTER THE CRASH. IN SPARTANBURG COUNTY, A MAN DIED AN HOUR AFTER THE COLLISION. THE CORONER'S OFFICE SAID THE WRECK HAPPENED ON VALLEY FALLS ROAD NEAR BOILING SPRINGS, AROUND 4:30 THIS AFTERNOON. HE SAID 22-YEAR-OLD SEBASTIAN VANCE DIED AT THE HOSPITAL,
An Upstate man was killed in a single-car crash in Spartanburg County, according to officials. The Spartanburg County coroner told WYFF News 4 Sebastian Darcy Vance from Boiling Springs died an hour after crashing.Highway Patrol said he was not wearing a seat belt and was ejected on Valley Falls Road in Boiling Springs.South Carolina Highway Patrol said the crash happened around 4:40 p.m. Saturday Vance, 22, went to the hospital, where he later died.State troopers and the Spartanburg County Coroner's Office are investigating.
BOILING SPRINGS, S.C. —
An Upstate man was killed in a single-car crash in Spartanburg County, according to officials.
The Spartanburg County coroner told WYFF News 4 Sebastian Darcy Vance from Boiling Springs died an hour after crashing.
Highway Patrol said he was not wearing a seat belt and was ejected on Valley Falls Road in Boiling Springs.
South Carolina Highway Patrol said the crash happened around 4:40 p.m. Saturday Vance, 22, went to the hospital, where he later died.
State troopers and the Spartanburg County Coroner's Office are investigating.