So I will ask spiteful question: is PR about fan fiction or 'canon'?
... Yes it would be interesting, perhaps special tech-tree for small CG 20-30 planets?
Well, if you think about it, PR has the Imperial class SD mk4 right now. How is that for canon? I'd say PR is about keeping the "canon feeling", and a truckload of upgrades.
Anyway under fan fiction I meant actual data (and ship models) with actual sources like this or this. Most of the fan fiction is about the legacy era though, which I personally don't fancy that much, so I'm far from requesting a MC130.
There's only one tech tree file per side for all campaigns, so its an either or.


text:
Home » Teaching in Virginia » Career Resources & Professional Development » National Board Certification Incentive Awards
Teaching in Virginia. You are here.
Career Resources & Incentives
Educator Recognition
Performance & Evaluation
Highly Qualified Teachers & Paraprofessionals
Education Workforce Data & Reports
Regulations, Standards & Guidelines
Professional Learning & Development
Licensure Regulations for School Personnel
Regulations Governing the Review and Approval of Education Programs in Virginia
Board of Education Advisory Board on Teacher Education & Licensure (ABTEL)
Guidance and Resources on Highly Qualified Teachers, Paraprofessionals & Professional Development
Virginia Teacher Computer Purchase Program
The State Council of Higher Education for Virginia (SCHEV)
Information on this page is provided by the Department of Teacher Education and Licensure.
Department email: licensure@doe.virginia.gov
Career Resources & Professional Development
National Board Certification Incentive Awards
National Board Certification is a voluntary process for teachers that is designed to complement initial state licensure. Individuals interested in seeking National Board Certification must have earned a baccalaureate degree from a regionally accredited institution, have completed three years of full-time teaching or school counseling experience and have held a valid state license without deficiencies (not an interim or emergency license) during the three years of employment, possess a valid five-year Virginia license, and be employed as a public school teacher or school counselor in a Virginia public school. In the past, Virginia has been awarded a federal subsidy grant to provide partial financial support for national board candidates. Beginning with the 2013-2014 school year, the federal subsidy grant will no longer be available. Teachers interested in pursuing National Board Certification may find additional information regarding possible scholarships on the National Board for Professional Teaching Standards website.
Guidelines for Distributing National Board Certification Incentive Awards – Approved by the Board of Education on June 28, 2012
Revised Guidelines for Distributing National Board Incentive Awards (PDF)
Also see June 28, 2012 Board of Education action item – Final Review of Revised Guidelines for Distributing National Board Certification Incentive Awards (PDF)
Also see Superintendent's Memo #178-12 –Revised Guidelines for Distributing National Board Certification Incentive Awards (PDF) – July 27, 2012
Eligibility Criteria for the National Board Certification Incentive Awards
An individual seeking a National Board Certification Incentive Award must:
hold an active National Board Certificate issued by the National Board for Professional Teaching Standards and be employed as a teacher in a public school in Virginia on September 30 of the current school year with at least 50 percent of the regular school day engaged in direct instruction with students; and
be a teacher holding an active five-year renewable license issued by the Virginia Board of Education.
An individual who holds an active National Board Certificate issued by the National Board for Professional Teaching Standards and is assigned as a building administrator, a supervisor in a central office position, or a teacher who is teaching less than 50 percent of the regular school day shall be excluded from the incentive awards.
The teacher's employment shall be verified annually by the division superintendent or designee pursuant to the Appropriation Act.
Procedures for Distributing Incentive Awards
An initial award not to exceed $5,000, contingent upon available funding, will be issued to teachers who meet the eligibility criteria described above and who achieved National Board Certification while teaching in a Virginia public school.
Continuing awards not to exceed $2,500, contingent upon available funding, will be issued annually for the life of the active certificate to teachers who meet the above eligibility criteria each year the award is granted. An individual will not receive an initial award and a continuing award in the same year.
For those individuals who receive notification that they achieved National Board Certification while teaching in another state, no initial award will be granted. These individuals will be eligible for the continuing award, contingent upon available funding, for the life of the active certificate provided the individual continues to meet the eligibility criteria described above.
Contingent upon available funding, awards shall be granted to all National Board Certified teachers who meet the eligibility criteria as of September 30 of each school year and whose names are reported to the Virginia Department of Education. Funds will be distributed to employing school divisions on or before December 31 of the same school year for distribution to their eligible teachers. The incentive payment is taxable to the recipient, and the school division assumes responsibility for ensuring all taxes are remitted.
The procedure for disbursement of funds if the program is not fully funded shall be based on a 2:1 ratio (The initial award would be twice that of the continuing award).
The procedure for disbursement of funds following a year when no funds are appropriated or available shall be as follows:
An individual who meets the criteria for an initial award would be granted such an award once funds are available; and
An individual who meets the criteria for a continuing award would be granted such an award once funds are available (awards for previous years when funds were not available would not be granted).
In school years when funding has been appropriated, school divisions must complete
and submit to the Virginia Department of Education a signed National Board Certification Incentive Award verification report. It is the responsibility of each school division to determine the eligibility of each individual who meets the Board of Education eligibility criteria and to submit individuals' names on the National Board Certification Incentive Award verification report and signed affidavit every school year pursuant to the Appropriation Act.
Additional information about the National Board Certification process is available at the NBPTS website.

redpajama_set_name: RedPajamaCommonCrawl


text:
Education Israel Project #24939
Help Palestinian Students in Israel #MakeTheGrade
by Adalah - The Legal Center for Arab Minority Rights in Israel
Reports Photos Share
Step-by-step: Ensuring safe access to school
By Rina Rosenberg (Jabareen) - International Advocacy Director, Adalah
Children going on the bus to preschool
Many greetings to you from Adalah.
This update follows up our past reports concerning the lack of access to preschools, kindergartens, and schools in general for Arab Bedouin children from unrecognized villages in the Naqab (Negev) desert region in southern Israel. Thousands of children in these communities are facing two main challenges preventing them from safely accessing school every day: the lack of school buses for preschool-aged children and the absence of safe and protected school bus stops for Bedouin children of all ages.
We are very proud to report that due to Adalah's persistence before the Israeli courts, we have succeeded to obtain transport for preschool-aged children from three Bedouin villages to school, and a commitment by the state and the local Regional Council to build proper bus stops near 47 schools in the Naqab.
During the past year, the Israeli Education Ministry and Al-Qasoum Regional Council, the local governing authority, have twice promised the Beer Sheva District Court in legal proceedings that they would act to provide transportation for 3- and 4-year-old preschool children from unrecognized Bedouin villages. The Court approved this commitment, but the Israeli authorities violated the decision, leaving the kids with no way to get to school. The Compulsory Education Law requires free, pre-school education for all children in Israel, and thus the state is in direct violation of the law.
In response to the state's failure to provide the buses, Adalah filed a motion for contempt of court against the Education Ministry and the Regional Council in February 2018 on behalf of parents from three Bedouin villages of Al Sira, Al-Jaraf and Umm Namila.
The authorities' violation of the court decisions constitutes a serious, ongoing violation of the most basic rights of the children and their parents:
"Due to the conduct of the respondents, the petitioners have been forced time and again to appeal to the legal system in order to obtain basic services – services which no one is disputing their right to receive, and which they have been repeatedly promised would be provided."
At a hearing in March 2018, the court ordered that buses must be supplied to the three petitioning villages within five days, and that the state had 30 days in which to provide transport to the remaining villages' preschool children, estimated at around 5000 children.
However, at a further hearing on 29 May 2018, the Court switched positions, refused to continue with a general remedy for all children without transport, and decided to close the case.
Adalah will consider further legal steps and continue to monitor the situation to ensure that all children in all unrecognized villages are provided with transportation to school.
Naqab Bedouin children of all ages face potentially life-threatening challenges just making their way to school every day as hundreds don't have access to safe, standardized bus stops but are instead forced to gather on the shoulders of local desert roads and busy highways to wait for their school buses.
Following the submission of a petition and a protracted legal battle led by Adalah, Israeli authorities agreed in early May 2018 to fund the construction of school bus stops in the Neve Midbar and Al-Qasoum Regional Councils, adjacent to 47 schools – including 10 high schools, 37 elementary schools, and four planned schools that are not yet operational. This commitment exceeded Adalah's demand before the Court, as the petition was filed on behalf of parents of children who attend schools in 6 villages, and thus marks a major achievement.
The Be'er Sheva District Court accepted the state's commitment to establish bus stations, but refrained at a hearing in June 2018 from ordering the authorities to establish a timeline for the construction, noting that 12 months from the time in which the regional council received budgets from the Education Ministry was reasonable. Adalah will continue to monitor the implementation of the state's commitment, as the Court regrettably refused to keep the case pending, as Adalah requested.
In its ruling, Be'er Sheva District Court Judge Yael Raz-Levy noted that Adalah's petition demanding the construction of safe bus stops for Bedouin kids was important:
"The submission of this petition was important and its arguments were significant… [The petition] bore fruit." (Emphasis in original)
Thanks again for your support for Adalah.
Children walking to school in the Naqab desert
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Adalah - The Legal Center for Arab Minority Rights in Israel
Location: Haifa - Israel
Website: http://adalah.org/eng
Twitter: @AdalahEnglish
Haifa, Haifa Israel
Funded Project!
Combined with other sources of funding, this project raised enough money to fund the outlined activities and is no longer accepting donations.
Support another project run by Adalah - The Legal Center for Arab Minority Rights in Israel that needs your help, such as:
Protect the Protest in Palestine & Israel


Kristian has worked for a number of different housing associations over a 15 year career and specialises in customer service roles, usually involving taking the lead on ensuring effective complaints management. During his time as both an executive and non-executive he has gained significant experience in this area, helping to set up resident scrutiny structures, conducting policy and performance reviews, and chairing complaint panels.
Kristian currently works as Director of Customer Contact at Moat, a housing association owning and managing almost 20,000 homes in London and the South East, and has responsibility for a variety of customer-facing functions across the business. He also sits on the London Board of the Chartered Institute of Housing.


text:
MySpace Tom beat Facebook in the long run
Wouldn't you rather be a rich nobody than whatever Mark Zuckerberg is?
Mark Mainz/Getty Images
Jeremy Gordon Apr—11—2018 05:22PM EST
My MySpace profile was abandoned when, at the ripe age of 18, I decided it was just a little too juvenile — the glittering GIFs affixed to every page, the garish customized designs, the pressure on maintaining your top 8. By 2006, Facebook offered a cleaner social experience; by 2009, Twitter offered a more casual one. MySpace was a complete relic by this point, even though only a few years had passed since its launch.
Back in 2005, though, long before MySpace burned out, its founder, Tom Anderson — whose grinning face greeted every new user as their first "friend" — sold the site for $580 million to Rupert Murdoch's News Corporation. While his site was becoming a punchline during the rise of Facebook, Twitter, Instagram, and the other social media networks we now use everyday, Anderson disappeared entirely from the tech scene. Now, he travels the world, documenting his visits to exotic locations.
Contrast that with what's currently happening to Facebook's Mark Zuckerberg, who's on day two of being grilled by a Senate committee for Facebook's role in haphazardly collecting all of our personal data, and possibly swinging the 2016 presidential election toward Donald Trump. What was supposed to be a basic networking tool has now become one of the chief mediators of how people interact with each other and the world around them, and how information is absorbed and disseminated on the internet. It's now apparent that Facebook and Zuckerberg didn't really consider any of this when aggressively pursuing growth, and now we're all screwed as we try to untangle the consequences.
MySpace Tom? His most recent Instagram post from seven days ago is a giveaway for a stay at an Iceland hotel. He doesn't have to issue any terse statements about his company's commitment to fostering a healthy society; he doesn't have to sit on a booster seat for seven hours and take dipshit questions from a procession of Senate ghouls. He isn't worth as much money as Zuckerberg, of course, but unless you're an oil baron, $580 million is enough to tide you over for the length of your lifetime, and your children's lifetime, and your children's children's lifetime, and so on. (Even after taxes!) And yes, yes, being that rich is good for nobody, but without getting into an argument about the perils of capitalism, we can agree that personally speaking, Anderson is having a much better go of things.
It puts MySpace's failure to evolve in a new light, as perhaps the healthy thing is for a platform to die and for everyone to move on. Its aesthetic and form, back when everyone had emo bangs and listened to Hawthorne Heights, couldn't change without altering the meaning of the site altogether, and by that time, everyone was gone. Had Facebook not gotten too good at inserting itself between human users, there's no way it would've run into their current problems at such a wide scope. The suspicious CEO is not the one who cashes out; it's the one who sticks around and creates a behemoth.
Zuckerberg could have sold off his share and avoided becoming literally one of the most disliked people in the present moment. I never thought we'd declare MySpace the winner over Facebook, but then again, I never thought a lot of things about the moment we're in.
We'll get out of your way when it's time, but for now... subscribe.
TTYS.


text:
Lisa R. Sahli, Esq. Attorney at Law
Colorado Gender Discrimination Attorney
Women in the workplace must still, unfortunately, contend with assumptions about their abilities and commitment to their jobs when starting or managing a family. Even with the passage of landmark legislation like Title VII of the Civil Rights Act, Pregnancy Discrimination Act and the Lilly Ledbetter Fair Pay Act, unequal pay and employment discrimination are still realities for women in the workforce.
Attorney Lisa R. Sahli represents women throughout Colorado and the surrounding areas who believe they are being paid less than male counterparts for the same jobs or are experiencing other forms of discrimination, retaliation or harassment. With more than 18 years of experience in employment litigation, Ms. Sahli is committed to helping all employees earn equal pay and work in environments free of unlawful discrimination.
Pregnancy Discrimination — A Prevalent Phenomenon
Pregnancy should be a joyful time for women who work. Instead, far too often, employers have knee-jerk reactions when female workers announce their pregnancies or request family leave. Some make assumptions about a woman's commitment to her career or her employer. As unfounded as these are, many employers carry these biases and can end up basing employment decisions on them. Pregnancy discrimination places women in financial distress when the need for health care benefits and financial security are highest.
Legislation Exists To Protect You From Discrimination
Under Title VII of the Civil Rights Act and Colorado law, employers are prohibited from discriminating on the basis of several characteristics, including sex. While sexual orientation is not protected by federal law, it is a protected status under Colorado law, which provides additional protections and remedies for those suffering discriminatory treatment, retaliation or harassment due to their sexual orientation, gender identity or gender expression.
Colorado law and the Lilly Ledbetter Fair Pay Act expand protections to women who are paid less than their male counterparts. If you believe you are being paid less than your male co-workers for the same job duties, Ms. Sahli can help you explore your options for compensation.
Contact An Experienced Gender Equality In The Workplace Lawyer In Colorado
Be aware that gender discrimination can often occur in combination with other forms of discriminatory behavior. Older women, for example, may suffer both gender and age discrimination. Gender discrimination can also be influenced by racial and other biases.
If you think that you are experiencing discrimination on the basis of gender or other characteristics, contact Denver gender discrimination lawyer Lisa R. Sahli. Send an email or call 720-545-1690 to schedule a consultation. Ms. Sahli can help put a stop to discrimination in the workplace.
Employer Compliance And Consulting
Wage And Hour Law
Littleton Law Office Map
Lisa R. Sahli, Esq, is an employment law attorney in Denver, Colorado. I represent employees in discrimination and wrongful termination cases throughout Colorado.
© 2021 Lisa R. Sahli, Esq. Attorney at Law. All Rights Reserved.
Map data © Mapbox © OpenStreetMap.


text:
\section{Introduction}

Bayesian methods tend to emphasize { inference}, which involves modeling the uncertainty over model parameters given an observed dataset. However, in most cases we perform Bayesian inference in order to make decisions or take actions in some end-use task \citep{von2012clustering}.
Bayesian decision theory asserts that the posterior distribution learned from inference is sufficient for Bayes-optimal decision-making \citep{berger2013statistical}.  This theoretical result is of limited value if the posterior distribution is intractable---an increasingly common occurrence in modern machine learning settings with
large datasets and/or complex models.

To address this intractability, approximate Bayesian inference methods seek to compute tractable approximations to the posterior distribution.  It is tempting to use these approximations as a plug-in replacement for the posterior during prediction and decision-making. However, information is lost in these approximations, and our goal {\it should} be to retain information that allows us to make optimal decisions, i.e., decisions that maximize utility. Unfortunately, common approximate inference methods such as variational inference (VI) and expectation propagation (EP) do not take account of utility, or of the loss of information that could compromise optimal decision-making.
The key intuition is that if we change the utility function, we do not change the posterior distribution, but we may change the best approximation to it. Loss-calibrated approximate inference has only recently emerged as a general framework optimizing and evaluating approximations in a ``loss-aware'' way \citep{lacoste2011approximate}. Analogously to how Bayesian decision theory prescribes that optimal decision-making under uncertainty maximizes expected utility---an expectation over the posterior distribution of the models' parameters---loss-calibrated inference proposes that the optimal approximation too should maximize expected utility.

With this paper, we introduce loss-calibrated expectation propagation (loss-EP). Like other loss-calibrated inference methods, loss-EP aims to embed features of the decision-making problem into the inference procedure. We show  loss-EP is tantamount to standard EP  augmented by one additional site factor that ``calibrates'' the approximate posterior to the decision-making problem. In Section 2, we outline the core machinery of Bayesian decision theory and loss-calibrated inference. In Section 3, we introduce EP and loss-calibrated EP. In Section 4, we demonstrate the performance of loss-calibrated and standard approximate inference methods in the familiar Gaussian process classification. In Section 5, we discuss opportunities for future work that could complement and/or improve Loss-EP as presented here.

\section{Background
\subsection{Bayesian decision theory}
The Bayesian approach to decision-making starts from a model with parameters $\varphi$, likelihood $p(y\mid \mathbf{x}, \varphi)$, and prior $p(\varphi)$. Given an observed training dataset $\mathcal{D}=\{\mathbf{x}_n, y_n\}_{n=1}^N$, the posterior follows from Bayes' rule:
\begin{flalign}
\label{eq:generic-posterior}
p(\varphi\mid\mathcal{D})=\frac{p(\varphi)p(\mathcal{D}\mid\varphi)}{p(\mathcal{D})}\propto p(\varphi)\prod_{n=1}^N p(y_n\mid\mathbf{x}_n,\varphi)
\end{flalign}
Given novel datapoints $\mathbf{x}_*$, we can make predictions (incorporating uncertainty) about future observations using the posterior predictive distribution, which incorporates all relevant information from the training data via the posterior:
\begin{flalign}
\label{eq:generic-prediction}
p(y_* \mid \mathbf{x}_*, \mathcal{D})=\int p(y_* \mid \mathbf{x}_*, \varphi) p(\varphi \mid \mathcal{D}) d\varphi
\end{flalign}
The end-use decision-making problem selects an action $a(\mathbf{x}_*)$ and receives a utility $\mathfrak{u}(y_*, a(\cdot))$, depending on the observation $y_*$ thereafter. To select the optimal action, we briefly suppose we can compute the posterior in eq. \eqref{eq:generic-posterior}. Bayesian decision theory prescribes that we choose the action(s) that maximize the full expected utility, inversely minimize the full Bayes risk. The full expected utility computes the utility received for future (predictive) data $(\mathbf{x}_*, y_*)$, in expectation over those posterior beliefs about the model parameters:
\begin{flalign}
\label{eq:full-expected-util}
\mathcal{U}_p(a)&=\int p(\varphi\mid\mathcal{D})\iint p(\mathbf{x}_*)p(y_*\mid\mathbf{x}_*,\varphi)\,\mathfrak{u}(a(\mathbf{x}_*), y_*)\: dy_* d\mathbf{x}_*\cdot d\varphi \triangleq \int p(\varphi\mid\mathcal{D}) U(a, \varphi) d\varphi
\end{flalign}
where $U(a, \varphi)$ is the predictive utility, marginalized over data given a fixed value of model parameters. In practice, the data-generating distribution $p(\mathbf{x}_*)$ is often unknown, for which we can define the conditional expected utility given some $\mathbf{x}_*$ to be
\begin{flalign}
\label{eq:cond-expected-util}
\mathcal{U}_p(a(\mathbf{x}_*)\mid\mathbf{x}_*) = \iint p(\varphi\mid\mathcal{D})p(y_*\mid\mathbf{x}_*,\varphi)\mathfrak{u}(a(\mathbf{x}_*), y_*)\: dy_*\cdot d\varphi
\end{flalign}
The optimal action function $a_\text{opt}$ maximizes the full expected utility in \eqref{eq:full-expected-util} as
\begin{flalign}
a_{\text{opt}} = \underset{a}{\arg\min}\:\mathcal{U}_p(a) \label{eq:opt-action}
\end{flalign}
This would be a cumbersome optimization over several intractable integrals, but importantly it is equivalent to the optimal actions achieved by maximizing the conditional expected utility in (\ref{eq:cond-expected-util}) pointwise, such that $a_{\text{opt}}(\mathbf{x}_*) = {\arg\min_a}\:\:\mathcal{U}_p(a(\mathbf{x}_*)\mid\mathbf{x}_*)$ also.

\subsection{Loss-calibration as approximate action selection}

In most applications of interest, exact inference of the true posterior is intractable, which poses a major challenge for Bayes-optimal decision-making. Conceivably, the next-best thing we can do is to make actions optimal under some tractable approximation $q(\varphi)$ of the posterior $p(\varphi\mid\mathcal{D})$. In such case, we could define the analogous approximate full and conditional expected utilities under the approximation; the latter, along with the action that maximizes it, would be
\begin{flalign}
\label{eq:q-cond-expected-util}
\mathcal{U}_q(a(\mathbf{x}_*)\mid\mathbf{x}_*) &= \iint q(\varphi)p(y_*\mid\mathbf{x}_*,\varphi)\mathfrak{u}(a(\mathbf{x}_*), y_*)\: dy_*\cdot d\varphi\\
\label{eq:q-action}
\text{with}\quad a_{q}(\mathbf{x}_*) &= \underset{a}{\arg\max}\:\:\mathcal{U}_q(a(\mathbf{x}_*)\mid\mathbf{x}_*).
\end{flalign}
Whether or not this $q$-optimal action $a_q$ maximizes the true expected utility in \eqref{eq:full-expected-util} will depend on how we select the approximation $q(\varphi)$. Our approximate utility maximization using $q(\varphi)$ and $a_q$ in eqs. (\ref{eq:q-cond-expected-util}, \ref{eq:q-action}) will be suboptimal---relative to the Bayes-optimal $p(\varphi\mid\mathcal{D})$ and $a_\text{opt}$---to the extent that for any $\mathbf{x}_*$, we select a suboptimal action, i.e. $a_q(\mathbf{x}_*)\neq a_\text{opt}(\mathbf{x}_*)$.
In expectation, we can define the discrepancy in utility between $q$-optimal actions and true optimal actions as
\begin{flalign}
d_\mathfrak{u}(p\,\|\, q) = \mathcal{U}_p(a_\text{opt}) - \mathcal{U}_p(a_q) \label{eq:regret}
\end{flalign}
This discrepancy is neither a proper divergence nor regret---there can be many $q$ and $a_q$ such that $d_\mathfrak{u}=0$, but still serves as a useful guide for how we should define the ``best'' approximate posterior. Problematically, optimizing expected utility as a function of $q$ is not the objective of approximate inference methods. Loss-calibrated approximate inference was proposed to bridge this gap, and jointly perform approximate Bayesian inference and action selection, by incorporating the expected utility explicitly into the optimization program that performs inference.

\subsection{Variational inference and loss-calibrated variational inference}

For example, variational inference (VI) optimizes a bound on the marginal likelihood \citep{blei2017variational}:
\begin{flalign}
\log p(\mathcal{D}) &\ge \int q(\varphi)\cdot \log\left(\frac{p(\varphi,\mathcal{D})}{q(\varphi)}\right)\,d\varphi \\
\text{s.t.}\quad q_\text{VI}(\varphi)&=\underset{q}{\arg\min}\: D_{KL}\left(p(\varphi\mid\mathcal{D})\,\|\, q(\varphi)\right)
\end{flalign}
Minimizing KL divergence optimizes generic statistical features of the posterior, but such an approximation could still result in arbitrarily poor decisions or arbitrarily large discrepancy $d_\mathfrak{u}(p\,\|\, q)$. Matching probability density is not important---matching actions is.

Loss-calibrated variational inference (LossVI) approximates the posterior by maximizing a lower-bound on the {\it $\log$-full expected utility} using the same approach \citep{lacoste2011approximate, kusmierczyk2019variational}:
\begin{flalign}
\log \mathcal{U}_p(a) &\ge \int q(\varphi)\cdot \log\left(\frac{p(\varphi\mid\mathcal{D})U(a, \varphi)}{q(\varphi)}\right)\,d\varphi \\
\text{s.t.}\quad q_\text{LossVI}(\varphi) &= \underset{q}{\arg\min}\: D_{KL}\left(\tilde p_a(\varphi)\,\|\, q(\varphi)\right), \:\:\text{where}\:\: \tilde p_a(\varphi) = \frac{p(\varphi\mid\mathcal{D})U(a, \varphi)}{\mathcal{U}_p(a)} \label{eq:lossvi-kl}
\end{flalign}
The resulting bound is exactly the variational inference objective, but minimizes the KL divergence from a {\it utility-weighted} posterior $\tilde p_a(\varphi)$.

Implementation of LossVI requires joint optimization of the approximation $q(\varphi)$ and the actions $a(\cdot)$, and \citep{lacoste2011approximate} propose an EM procedure that alternates coordinate descents between the two, with applications to Gaussian processes.

\section{Loss-calibrated expectation propagation}

Expectation propagation (EP) approximates the posterior by decomposing the global inference into a collection of local inferences by message-passing \citep{minka2001expectation, minka2001ep, gelman2014expectation}. These local inferences operate on each term of some factorization of the posterior, typically the product of the prior and the likelihoods of each of the i.i.d. data:
\begin{flalign}
    p(\varphi\mid\mathcal{D}) = \frac{1}{Z}p_0(\varphi) \prod_i p(\mathcal{D}_i\mid\varphi) &\propto p_0(\varphi) \prod_i t_i(\varphi)\quad\approx\quad p_0(\varphi) \prod_i \tilde t_i(\varphi) = q(\varphi)
\end{flalign}
Each likelihood term $t_i(\varphi)$ is approximated in EP by a site potential $\tilde t_i(\varphi)$, such that the approximation shares the factorization of the true posterior. EP iteratively performs local approximate inferences for each site $\tilde t_i(\varphi)$, over three steps---Deletion, Projection, and Update---that replaces one site with its true likelihood term, optimizes a new approximation that matches moments to this hybrid distribution, and updates the original site accordingly ({\it cf.} box below, Algorithm 1). All of these operations are powered by properties of distributions in the same exponential family (EF), for which purpose we assign all sites to have the (unnormalized) exponential family form
\begin{flalign}
\tilde t_i(\varphi) \propto \exp\left(\langle \mathbf{s}(\varphi), \boldsymbol{\theta}\rangle\right) \label{eq:site-ef}
\end{flalign}
where $\mathbf{s}(\varphi)$ are the sufficient statistics and $\boldsymbol{\theta}$ are the natural parameters \citep{seeger2005expectation,nielsen2009statistical}.

These updates are repeated across all site potentials until convergence. While these local inferences only minimize the forward KL divergence from $N$ different tilted distributions, this iterative message-passing procedure approximates the global minimization forward KL divergence from the posterior, $D_{KL}(p(\varphi\mid\mathcal{D}\,\|\,q(\varphi))$ \citep{minka2001ep}. Convergence is not guaranteed, but empirically EP performs well.

Our contribution begins with the observation that the full expected utility in (\ref{eq:full-expected-util}) admits a factorization similar to that utilized by EP:
\begin{flalign}
\mathcal{U}_p(a) = \int \frac{1}{Z} p_0(\varphi)\prod_n p(y_n\mid\mathbf{x}_n,\varphi) U(\varphi, a) df
&\propto \int p(\varphi)\prod_n t_n(\varphi) t_\ell(\varphi) d\varphi
\end{flalign}
where the the utility function $U(a, \varphi)$ becomes the $N+1$\textsuperscript{th} term $t_\ell(\varphi)$.
As before, we approximate the $N$ likelihood terms and the new utility term with $N+1$ exponential family site potentials $\tilde t_i(\varphi)$ and $\tilde t_\ell(\varphi)$, respectively. The resulting loss-calibrated EP approximation $\overline{q}(\varphi)$ takes the form
\begin{flalign}
\overline{q}(\varphi)= p_0(\varphi)\prod_i \tilde{t}_i(\varphi) \tilde{t}_\ell(\varphi) \propto q(\varphi) \tilde{t}_\ell(\varphi)
\end{flalign}
and approximates the same utility-weighted posterior $\tilde p_a(\varphi)$ as LossVI in eq. \eqref{eq:lossvi-kl}. The approximation to the posterior $p(\varphi\mid\mathcal{D})\approx q(\varphi)$ is a partial product of the site potentials that comprise $\overline{q}(\varphi)$: all except the utility site $\tilde t_\ell(\varphi)$. EP updates for the $N$ site approximations $\tilde t_i(\varphi)$ follow the standard EP procedure; the update for the new site approximation $\tilde t_\ell(\varphi)$ requires one extra computation. We present a single site update below in full detail, and give the aggregate LossEP procedure in Algorithm 1.

\begin{tcolorbox}[center, breakable, width=0.95\textwidth, colback={pale-gray}, boxrule=0pt]
   {\bf Deletion:} Divide the utility site $\tilde t_\ell(\varphi)$ from $\overline{q}(\varphi)$ to form the cavity distribution, which {\it for the utility site} is identically the posterior approximation:
    \begin{flalign}
        q\scav{\ell}(\varphi) &= \overline{q}(\varphi)/\tilde t_\ell(\varphi) \propto p_0(\varphi) \prod_{i} \tilde t_i(\varphi) \propto q(\varphi)
    \end{flalign}
    In natural parameters, $\boldsymbol{\theta}\scav{\ell} = \overline{\boldsymbol{\theta}} - \boldsymbol{\theta}_\ell$.

   {\bf Projection:} Reinsert the true term $t_\ell(\varphi)$ into $q\scav{\ell}(\varphi)$ to form the tilted distribution, and project back into the approximating family:
    \begin{flalign}
        \overline{q}^{\text{new}}(\varphi) &= \proj\big[t_\ell(\varphi)q\scav{\ell}(\varphi)\big] \triangleq \underset{\overline{q}}{\arg\min}\:D_{KL}(t_\ell(\varphi)q\scav{\ell}(\varphi)\,\|\, \overline{q}(\varphi))
    \end{flalign}
    In natural parameters, this divergence minimization is equivalent to the gradient update $\overline{\boldsymbol{\eta}}^{\text{new}} = \boldsymbol{\eta}\scav{\ell} + \nabla_{\boldsymbol{\theta}\scav{i}}\log Z_\ell$, where $\boldsymbol{\eta}=\mathbb{E}[\mathbf{s}(\varphi)]$ are the mean parameters and and
    \begin{flalign}
        \log Z_\ell = \log \int t_\ell(\varphi)q\scav{\ell}(\varphi)\,d\varphi = \mathcal{U}_q(a)
    \end{flalign}
    is the log-normalizer of the tilted distribution. {\it For the utility site}, the true term $t_\ell(\varphi)=U(a, \varphi)$ is the full predictive utility and the log-normalizer is identically the $q$-full expected utility. To resolve the dependence on actions $a$, introduce the following prerequisite step:

    {\bf Action Selection:} [Utility site only] Select the $q\cav{\ell}$-optimal actions
   \begin{flalign}
   a_{q}&=\underset{a}{\arg\max}\:\mathcal{U}_{q\cav{\ell}}(a)
   \end{flalign}
   Performing this step only requires information already available at the local site update.

    {\bf Update:} Divide the utility-cavity distribution from the projected $\overline{q}^{\text{new}}(\varphi)$ to back out the updated site $\tilde t_\ell(\varphi)$. With damping $\delta\in[0, 1)$,
    \begin{flalign}
        \tilde{t}_\ell^{\text{new}}(\varphi) &= (\overline{q}^{\text{new}}(\varphi)\,/\, q\scav{\ell}(\varphi))^\delta\cdot \tilde{t}_\ell(\varphi)^{1-\delta}
    \end{flalign}
    In natural parameters, $\boldsymbol{\theta}_\ell^{\text{new}} = \delta(\overline{\boldsymbol{\theta}}^{\text{new}} - \boldsymbol{\theta}\scav{\ell})+(1-\delta)\boldsymbol{\theta}_\ell$.
\end{tcolorbox}

Only the tilted distribution of the utility site is an explicit function of actions $a$, presenting the only opportunity to optimize actions $a$ during LossEP. Performing action selection at this site maximizes the $q$-gain, which is consistent with other loss-calibrated methods, albeit motivated more naturally in this context. Critically though, loss-calibration is still occuring at {\it all} site updates, as the Gaussian approximation to the utility $\tilde t_\ell(\varphi)$ is present in every cavity distribution $q\scav{i}(\varphi)$, and it contains information about the decision-making process.

{\SetAlgoNoLine \DontPrintSemicolon
\begin{algorithm}
 \textit{Given:} Dataset of $N$ i.i.d. datapoints $\mathcal{D}=\{\mathbf{x}_i,y_i\}$, Model with posterior over parameters $p(\varphi\mid\mathcal{D})$ that admits factorization of the form $p(\varphi\mid\mathcal{D})\propto p_0(\varphi) \prod_i t_i(\varphi)$, Decision problem with utility function $\mathfrak{u}(a(\cdot),\cdot)$\;
 Initialize site approximations $\tilde t_i(\varphi)$ and $\tilde t_\ell(\varphi)$ {\it s.t.} $\overline{q}(\varphi)=p_0(\varphi)\prod_{i=1}^N \tilde t_i(\varphi)\tilde t_\ell(\varphi)$ approximates the utility-weighted posterior $p(\varphi\mid\mathcal{D})U(a,\varphi)$\;
 \Repeat{convergence}{
    {\it In random order:}\;
 	For each $n$\;
	(\textbf{Deletion}) Compute the cavity distribution $q\scav{i}(\varphi)=\overline{q}(\varphi)/\tilde t_i(\varphi)$\;
	(\textbf{Projection}) Minimize $\overline{q}^{\text{new}}(\varphi)=\proj[t_i(\varphi)q\scav{i}(\varphi)]$ by matching moments\;
	(\textbf{Update}) Back out the site update $\tilde t_i^\text{new}(\varphi)=(q^{\text{new}}(\varphi)/q\scav{i}(\varphi))^\delta\cdot \tilde t_i(\varphi)^{1-\delta}$\;
	For $\ell$\;
	(\textbf{Deletion}) Compute the cavity distribution $q\cav{\ell}(\varphi)=\overline{q}(\varphi)/t_\ell(\varphi)$\;
	(\textbf{\textit{Action Selection}}) Select the $q\scav{\ell}$-optimal actions $a_{q}={\arg\max}_a\:\mathcal{U}_{q\cav{\ell}}(a)$\;
	(\textbf{Projection}) Minimize $\overline{q}^{\text{new}}(\varphi)=\proj[U(a_q, \varphi)q\scav{\ell}(\varphi)]$ by matching moments\;
	(\textbf{Update}) Back out the site update $\tilde t_\ell^\text{new}(\varphi)=(\overline{q}^{\text{new}}(\varphi)/q\scav{\ell}(\varphi))^\delta\cdot \tilde t_\ell(\varphi)^{1-\delta}$\;
 }
 \caption{Loss-calibrated expectation propagation}
\end{algorithm}
}

\subsection{Example: the clutter/nuclear reactor problem}

To illustrate loss-calibration, we repurpose the ``nuclear reactor'' problem used by \citep{lacoste2011approximate} and \citep{abbasnejad2015loss} in those works on loss calibration. Conveniently, this decision problem can be superimposed on the generative model of the clutter problem used in \citep{minka2001expectation} in that work on expectation propagation. We consider a decision-maker receiving noisy measurements of the temperature $\varphi$ of a nuclear reactor, tasked with shutting it down ($a=1$) if that temperature has exceeded a ``meltdown'' point ($\varphi>T_\text{crit}$) or leaving it on ($a=0$) otherwise. Defining $\mathfrak{u}_{ij}$ as the utility received for taking action $a=i$ when the state $\mathbb{I}[\varphi>T_\text{crit}]=j$ was true \citep{poor2013introduction}, this decision problem features a natural asymmetry, with a maximal penalty for the False Negative case of leaving it on during a meltdown ($\mathfrak{u}_{01}= 0$) and a modest penalty for the False Positive of shutting down despite normal operation ($\mathfrak{u}_{10}$).

After a small number of observations, suppose we have a complicated, bimodal posterior distribution $p(\varphi\mid\mathcal{D})$ with the minor mode informing a potential meltdown (Figure 1). Under a Gaussian approximation, we may underrepresent or ignore this probability mass, and select the suboptimal action of ``leaving it on'' when the Bayes-optimal action is to ``shut it down'' (see figure legend). For not only VI and EP {\it but also} LossVI, this is exactly what happens (Figure 1; blue curves). Only LossEP captures the tail and can select the Bayes-optimal action (Figure 1; red curves). It is a poor visual approximation of the true posterior, but when our goal is decision-making, this is not important.

\begin{figure}[b]
\centering
\includegraphics[width=0.45\textwidth]{figs/clutter-reactor-better.png}
\caption{{\bf Nuclear reactor decision problem for a small dataset observed under the clutter problem.} A decision-maker must act to leave the reactor running or shut it down, based on whether the true mean temperature, inferred from that dataset, is greater than a critical meltdown threshold. Given this bimodal posterior distribution (black), the optimal action shuts it down (see legend, $a_\text{opt}=1$). However, the Gaussian approximations from VI, LossVI, and EP (pale blue, dark blue, and pale red, {\it resp.}) do not capture the second mode and do not select this action ($a_q=0$). The Gaussian approximation from LossEP (dark blue) skews to overrepresent the second mode, and selects the optimal action ($a_q=1$).}
\label{fig:clutter}
\end{figure}

\section{Applications to data with Gaussian process models}

We explore the differences in the approximations achieved between loss-calibrated EP and standard EP, as well as VI and LossVI, using a simulated decision-making problem with asymmetric utility functions. When the inference and/or decision-making is difficult enough to yield loss of information and/or ambiguous predictions, we suspect that our loss-calibrated methods will be most differentially successful. We use Gaussian process classification in all cases for its analytical tractability. We present two applications: the first is a minimal two-point dataset \citep{nickisch2008approximations} to visualize the various approximations, and the second a sweep of different utility functions and predictive datasets \citep{lacoste2011approximate}. Together, they show that loss-calibration---at least within this context---can yield modest increases in performance, as measured by utility.

\StopCensoring
We implement all of EP, and LossEP in python using JAX \citep{jax2018github}, and MCMC, VI, and LossVI in numpyro \citep{phan2019composable, bingham2019pyro}.
To begin, we derive the relevant equations for loss-calibrated inference in the GP context, with notation following \citet{rasmussen2005gaussian}.

\subsection{Approximate inference and loss-calibration for Gaussian process classifiers}

Approximate inference in GP classification provides an approximation to the intractable posterior $p(\mathbf{f}\mid X, \mathbf{y})\xrightarrow{\text{approx.}}q(\mathbf{f}\mid X,\mathbf{y})=\mathcal{N}(\mathbf{f};\, \boldsymbol{\mu}_q, \Sigma_q)$, where the latent function at the observed datapoints $\mathbf{f}$ assumes the role of the parameters $\varphi$. We assume the probit likelihood model throughout such that all integrals can be resolved in closed-form. The prior, likelihood, and posterior take the form
\begin{flalign}
\nonumber p(\mathbf{f}\mid X) &= \mathcal{N}(\mathbf{f};\, 0, K),\quad
p(\mathbf{y}\mid\mathbf{f}) = \prod_{i=1}^N \Phi(y_i f_i),\quad
p(\mathbf{f}\mid X, \mathbf{y}) = \frac{p(\mathbf{y}\mid\mathbf{f})p(\mathbf{f}\mid X)}{p(\mathbf{y}\mid X)}
\end{flalign}
where $K$ is the covariance kernel which, in our case, is the radial basis function kernel defined by
\begin{flalign}
K_{ij}=k_\xi(\mathbf{x}_i, \mathbf{x}_j)=\sigma^2\exp(- \|\mathbf{x}_i-\mathbf{x}_j\|^2_2 / 2\ell^2)
\end{flalign}
with variance and lengthscale hyperparameters $\xi=\{\sigma^2,\ell\}$. To make predictions for latent function values outside the dataset, we can marginalize the product of any approximation $q(\mathbf{f})$ and the conditional distribution, yielding the posterior predictive distribution.
\begin{flalign}
p_q(f_*\mid X, \mathbf{y}, \mathbf{x}_*) &= \int d\mathbf{f}\, p(f_*\mid X, \mathbf{x}_*, \mathbf{f}) q(\mathbf{f}\mid X, \mathbf{y}) = \mathcal{N}(f_*;\, m_{f_*}, v_{f_*})
\end{flalign}
\vspace*{-18pt}
\begin{flalign}
\text{where}\quad m_{f_*} &= \mathbf{k}_*K^{-1}\boldsymbol{\mu}_q \label{eq:postpred-mean}\\
v_{f_*} &= k_{**}-\mathbf{k}_*K^{-1}\mathbf{k}_*^\top+\mathbf{k}_*K^{-1}\Sigma_qK^{-1}\mathbf{k}_*^\top \label{eq:postpred-var}
\end{flalign}
and $\mathbf{k}_*$ is the predictive covariance kernel, with ${\mathbf{k}_*}_j = k_\xi(\mathbf{x}_*, \mathbf{x}_j)$.

The expected utility depends on the marginal predictive distribution, which is available in closed-form for the probit likelihood. As above, we marginalize the product of the probit likelihood and the posterior predictive distribution, yielding
\begin{flalign}
p_q(y_*\mid X, \mathbf{y}, \mathbf{x}_*) &= \int df_*\, p(y_*\midf_*) p_q(f_*\mid X, \mathbf{y}, \mathbf{x}_*) = \Phi\left(y_*\cdot \frac{m_{f_*}}{\sqrt{1+v_{f_*}}} \right)  \label{eq:gpc-post-pred}
\end{flalign}

For action selection in GPC, we can rearrange the order of integration in  \eqref{eq:gpc-post-pred} of the conditional expected utility in \eqref{eq:cond-expected-util}, reducing it to a single integral of this predictive likelihood and the utility function \citep{vehtari2012survey}, which decomposes into four pieces for each of the four outcomes. We define them as $u_{00}$, $u_{01}$, $u_{10}$, and $u_{11}$, where $u_{ij}$ is the utility of selection action $i$ when outcome $j$ occurred \citep{poor2013introduction}.
\begin{flalign}
\mathcal{U}_q(a(\mathbf{x}_*)\mid\mathbf{x}_*) &= \int dy_*\,p_q(y_*\mid\mathbf{x}_*,X, \mathbf{y})\,\mathfrak{u}(y_*,a(\mathbf{x}_*)) \label{ep:gpc-conditional-util}
\\
&= \mathbb{I}[a=+1]\left(u_{10}\Phi(-z)+u_{11}\Phi(z)\right) + \mathbb{I}[a=-1]\left(u_{00}\Phi(-z)+u_{01}\Phi(z)\right) \\
\nonumber &\quad\text{where}\quad z=\frac{m_{f_*}}{\sqrt{1+v_{f_*}}}
\end{flalign}
and $\mathbb{I}[\cdot]$ is an indicator function with value $1$ if the condition is true and $0$ otherwise. The conditional expected utility, when minimized pointwise, minimizes the full expected utility \citep{berger2013statistical}. No matter the procedure for selecting $q(\mathbf{f})$, we select actions by minimizing this term, which generates the following $q$-action in closed form:
\begin{flalign}
a_q(\mathbf{x}_*) &= \text{sign}\left(\frac{m_{f_*}}{\sqrt{1+v_{f_*}}} - b\right),\quad b=\Phi^{-1}\left(\frac{u_{00} - u_{10}}{(u_{00}- u_{10}) - (u_{01}- u_{11})}\right)
\end{flalign}
The "bias" $b$ reflects the asymmetry of the utilities, and acts to move the decision boundary / threshold up if its more favorable to select $-1$ or down if its more favorable to select $+1$.

\subsection{Visualizing a two-point dataset}

Suppose we had a dataset of only two points, $\mathcal{D}=\{(-\sqrt{2},-1), (\sqrt{2},+1)\}$. In this case, we can compute the exact posterior $p(\mathbf{f}\mid X,\mathbf{y})$ on a grid and plot it against the various approximations. We select hyperparameters $\log \sigma=1.5$ and $\log \ell=1.0$ (cf. \citep{nickisch2008approximations}, Figs. 3, 4) and a decision problem with an asymmetric utility function: $u_{00}=u_{11}=1.0$, $u_{01}=0.0$, and $u_{10}=0.5$ (cf. \citep{lacoste2011approximate}, Table 4).

Together, these induce a non-Gaussian posterior---the product of a joint Gaussian prior with steep, sigmoidal likelihoods yields a posterior with tails strongly skewed into one quadrant. The predictive utility skews this posterior very slightly towards the upper right quadrant, as overestimating the latent function's values is more favorable under the utility function which disproportionately penalizes underestimating (Fig. \ref{fig:nr-2point}A). Compared to standard EP and VI, their loss-calibrated counterparts do not modify the means, and LossEP increases the covariance estimate (Fig. \ref{fig:nr-2point}C).

\begin{figure}
    \centering
    \includegraphics[width=0.8\textwidth]{figs/nrfig.png}
    \caption{{\bf Loss-calibrated approximate inference for GP classification on a two-point dataset}.  {\bf A}, The utility-weighted posterior approximated by loss-calibration, achieved by multiplying the jointly Gaussian GP prior and the probit likelihood for the two datapoints, $(-\sqrt{2}, -1)$ and $(\sqrt{2},+1)$, and the predictive utility. {\bf B}, Approximations to the posterior for VI (pale blue) EP (pale red), and to the utility-weighted posterior for loss-calibrated VI (dark blue) and loss-calibrated EP (dark red).}
    \label{fig:nr-2point}
\end{figure}

\subsection{Assessing the impact of loss-calibration under asymmetric utilities}

We continued with a quantitive performance test of Loss-EP versus EP as well as Loss-VI and VI (Table \ref{tab:util-asymm}). We simulated datasets as $N=15$ datapoints $\mathbf{x}_i$ sampled uniformly from $[-10, 10]$, followed by draws from the GP prior and binary observations $y_i$ under the GPC model with hyperparameters as above. Action selection was performed for each of five increasingly asymmetric utility functions, with the False Negative utility always taking the minimum-possible value $u_{01}=0.0$ and the False Positive utility ranging from minimum-possible $u_{10}=0.0$ to nearly maximum-possible $u_{10}=0.95$. Utilities were evaluated at 1000 predictive datapoints uniformly sampled from each of $[-10, 10]$, $[-8, 12]$, or $[-5, 15]$, increasing covariate shift from the observed datasets. Using this finite dataset for prediction can be viewed in the transductive scenario in which we are interested in evaluating the utility {\it at these points}. This is beneficial, as it reduces the unknown data-generating distribution $p(\mathbf{x}_*)$ to a trivial ``comb'' distribution over that dataset $p(\mathbf{x}_*)=\sum_{c} \delta(\mathbf{x}_* - {\mathbf{x}_*}_c)$. The resulting experiment is identical to that used in \citep{lacoste2011approximate}.

The performance is the full expected utility $\mathcal{U}_p(a_q)$ of the actions selected under any of the four approximations $q$: EP, Loss-EP, VI, and Loss-VI. This utility is at best $\mathcal{U}_p(a_\text{opt})$---the utility of the Bayes-optimal action---and is at worst $\mathcal{U}_p(-a_\text{opt})$---the utility of always taking the opposite of the Bayes-optimal action. The following metric normalizes the utility discrepancy in eq. \eqref{eq:regret} from $0$ to $1$:
\begin{flalign}
\widetilde U(q) = \frac{\mathcal{U}_p(a_\text{opt}) - \mathcal{U}_p(a_q)}{\mathcal{U}_p(a_\text{opt}) - \mathcal{U}_p(-a_\text{opt})} \label{eq:utility-metric}
\end{flalign}
Different datasets vary in their best-case and worst-case expected utilities, and the metric permits meaningful averaging across datasets. We report this utility metric for each inference method, utility function, and covariate shift as averages over 20 simulated datasets each in Table \ref{tab:util-asymm}.

Recall that the motivation of loss-calibrated approximate inference was that the expected utility $\mathcal{U}_p(a_\text{opt})$ is difficult to compute. For GPC, we can compute it using MCMC \citep{hoffman2014no}, generating samples $\mathbf{f}\sim p(\mathbf{f}\mid X, \mathbf{y})$ and computing an sample-based estimate of the conditional expected utility in \eqref{eq:full-expected-util}. Averaging over the dataset defining $p(\mathbf{x}_*)$, we recover an estimate of $\mathcal{U}_p(a)$.
We can either optimize this function for $a$ to estimate $a_\text{opt}$ (and $-a_\text{opt}$) or plug in $a_q$ for one of the approximations $q$ to estimate $\widetilde{U}(q)$ for each of VI, LossVI, EP, and LossEP.

All methods report near-ceiling performance across all utility functions and degrees of predictive covariate shift, though EP and LossEP consistently outperform VI and LossVI by several orders of magnitude (Table \ref{tab:util-asymm}). While LossVI does not outperform VI in any case, LossEP offers very small improvements over EP when the utility asymmetry is moderate and covariate shift is {\it not} large, echoing the results visualized in the previous section {\it and} those observed by \cite{lacoste2011approximate} in their original report. No differences between EP and Loss-EP or VI and Loss-VI were significant by a Wilcoxon signed-rank test after corrections for multiple comparisons.

\begin{table}
\centering
\includegraphics[width=0.85\textwidth]{figs/utility-assay.png}
\caption{{\bf Performance comparison of loss-calibrated methods on simulated datasets.} Expected utility from actions selected under approximate posterior distributions from each of VI, loss-calibrated VI, EP, and loss-calibrated EP, for utility functions of increasing asymmetry and predictive datasets with increasing covariate shift. Performance is reported using the normalized expected utility metric in eq. \eqref{eq:utility-metric}, averaged over 20 repeats of the simulation. Zero is Bayes-optimal performance, and does not mean perfect performance. EP is consistently better than both VI-type methods, and LossEP is better still for moderate utility asymmetries. Bolded results are best performances within each experimental category.}
\label{tab:util-asymm}
\end{table}

\section{Discussion and future work}

With this paper, we introduced loss-calibrated expectation propagation, diversifying the suite of loss-calibrated inference methods to include the message-passing-like iterative computations of EP. We showed that the factorization of the posterior distribution approximated by EP can be repurposed to a factorization of the expected utility, and appends one site factor to the resultant approximation: $\tilde t_\ell(\varphi)$ which approximates the predictive utility function $U(a,\varphi)$. When iteratively updating all data site factors $\tilde t_i(\varphi)$, the utility site factor $\tilde t_\ell(\varphi)$ is included in all cavity distributions $q\scav{i}(\varphi)$, making all sites ``aware'' of the utility function. When iteratively updating the utility site itself, the tilted distribution's log-normalizer is precisely the $q$-expected utility, providing a principled justification of optimizing $\mathcal{U}_q(a)$ as a surrogate for the true expected utility $\mathcal{U}_p(a)$. As a bonus, action selection can be transparently performed within this site update.
In these ways, Loss-EP shares the elegant, intuitive, and desirable theoretical foundations of loss-calibrated approximate inference more broadly.

That said, it also shares the situational, modest performance increases in practice observed in previous works, which spans not only Gaussian process models \citep{lacoste2011approximate} but also Bayesian neural networks \citep{cobb2018loss} and continuous-valued estimation tasks \citep{kusmierczyk2019variational} not considered here. Using {\it any} EP-type approximation, loss-calibrated or not, does grant dramatic performance improvements, however, and is an important, novel observation from our efforts.
Curiously, we observe that there is likely more than one way to develop a loss-calibrated inference procedure around the flexible machinery of expectation propagation, and future work could better harness the desirable computational properties commonly associated with EP to improve performance.

Following \citep{kusmierczyk2020correcting}, future work could develop an EP-type approximation to Generalized Bayesian Inference \citep{bissiri2016general}, which updates prior beliefs about a parameter of interest that is connected to our observations by arbitrary loss functions, rather than likelihood functions. Following the substantial body of theory work into loss functions and machine learning \citep{reid2011information}, we could perform iterative EP updates that minimize not the KL divergence, but instead some general divergence measure (also suggested in \citep{gelman2014expectation}) that is uniquely determined by the loss function in the classification case. This could be considered optimization in the natural ``geometry'' of the decision problem \citep{dawid2005geometry}, of which a certain subclass of problems are well-defined \citep{dawid1994proper}.

\subsection{Related work}

Loss-calibrated approximate inference is only one family of approaches for ``loss-aware'' model learning. Direct loss minimization \citep{wei2021direct} directly minimizes expected loss, but in a constrained optimization akin to rate-distortion theory \citep{cover1999elements}, which has a natural connection to variational inference \citep{alemi2018fixing}. Accuracy-versus-uncertainty calibration \citep{krishnan2020improving} provides a heuristic objective for training deep networks to enforce better-calibrated estimators. Target-aware Bayesian inference \citep{rainforth2020target} formalizes an sampling-based approach to estimating the expected utility with importance sampling (IS). Loss-calibrated Monte Carlo action selection \citep{abbasnejad2015loss} also optimizes an importance sampling proposal distribution, but minimizing the probability of selecting suboptimal actions with minimal number of samples.

This last work echoes the deep theory of surrogate loss functions from statistical learning theory, which minimize a bound on the generalization error (equivalently, the 0-1 loss, or the probability of error) that depends directly on the utility/loss function of the decision problem \citep{bartlett2006convexity, steinwart2008support, reid2011information}. \citet{nguyen2009surrogate} even select actions according to an approximation, and such results hinge on an expected loss {\it over datasets}. In contrast, our complementary Bayesian viewpoint has emphasized how to make optimal decisions conditionally on a given dataset rather than in expectation over all possible datasets.

\section*{Broader Impact}

Optimal decision-making under specific design constraints (as represented by a utility function and/or tolerances on error rates) is a fundamental aspect of fair and safe applications of ML to real-world data. While loss-calibration as we present it here is a generic theoretical tool, principles such as these could be leveraged to better-constrain the decision-making faculties of modern Bayesian ML tools. For example, it could be productive for researchers to think explicitly about the costs/utilities of decision-making in their applications {\it at inference time}. Because Bayesian decision theory only prescribes optimal decision-making under exact Bayesian inference, a modernized theory will be critical as approximate methods for complex models become more and more prevalent.

\begin{ack}

MJM was supported by an NSF Graduate Research Fellowship.

\end{ack}

redpajama_set_name: RedPajamaArXiv


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Lucky daughter! It's beautiful, Thelma!
584 pieces? That is a lot of love. Your quilt is wonderful. I clicked on the picture and got a larger view and the colors all go so well together.
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Absolutly love the quilt! The leftover blocks would make a great mini quilt too. The blocks all play well together.


text:
Home » Scott Declares March 16-20 Down Syndrome Awareness Week
Scott Declares March 16-20 Down Syndrome Awareness Week
By Space Coast Daily // March 17, 2015
Gov. Rick Scott
TALLAHASSEE, FLORIDA — Governor Rick Scott today issued a proclamation declaring Down Syndrome Awareness Week in Florida from March 16-20th.
Florida will be joining New Jersey's 2015 Light the Way campaign this week, and the Florida Governor's Mansion will be lit blue on the evening of Saturday, March 21, 2015 in recognition of Down syndrome cognitive research.
"We are proud to join Floridians across the state in recognizing Down Syndrome Awareness Week," Governor Rick Scott said. "Individuals with Down syndrome are active participants in Florida businesses and communities, and deserve every opportunity to find a great job and have their shot at the American Dream. We will keep working everyday to provide these individuals with the support they need, and to increase opportunities for every person in Florida."
Ann Scott
"Down Syndrome Awareness Week serves as an important opportunity to recognize our family, friends and community members with Down syndrome," First Lady Ann Scott said I am honored to join New Jersey First Lady Mary Pat Christie and First Spouses across the country in this awareness campaign by lighting the Governor's Mansion blue on Saturday in recognition of the many incredible individuals with Down Syndrome and their families."
Space Coast Daily Exclusive Q&A With Florida First Lady Ann Scott
Andy Gardiner
Florida Senate President Andy Gardiner said "People born with Down Syndrome have many unique abilities and can make a tremendous contribution to Florida's workforce. By expanding career and education opportunities that help individuals with Down Syndrome fine-tune their own unique abilities, we can establish a pathway to economic independence that will help all people with unique abilities have a better quality of life."
Steve Crisafulli
Florida House Speaker Steve Crisafulli said, "President Gardiner and I are committed to finding ways for Floridians with Down syndrome to achieve economic independence to better their own lives and the lives of their families. I'm honored to join Governor Scott as we recognize these unique individuals."
This week, families and health-care workers across Florida are encouraged to share their own research, knowledge and experiences with the public in order to raise awareness and encourage further research about one of the world's most common chromosomal conditions, also known as Trisomy 21.
Down Syndrome Facts: (dsatallahassee.org)
Down syndrome has for too long been shrouded in fear and darkness; the facts are far better than the myths. Here are the facts.
Down syndrome is the most common chromosomal abnormality, occurring in approximately 1 in 900 births. More than 350,000 individuals with Down syndrome have an extra chromosome and thus have 47 chromosomes in every cell instead of 46. To date, medical researchers have not determined the cause. What is known is that Down syndrome occurs among all races, ethnic groups, nationalities, and socioeconomic classes. It also occurs evenly in boys and girls. It is important to realize that nothing that the mother or father does – or fails to do – before or during pregnancy, can cause Down syndrome.
Because chromosomes and the genetic information they carry determine how we grow and develop, the presence of an extra chromosome does affect a child in a number of ways. The word "syndrome" means that many different characteristics are seen together as a package. Some of these physical characteristics may include low muscle tone, eyes that appear to slant upward, a flat nasal bridge, extra skin folds at the back of the neck, relatively small nose and ears, a larger gap between the first and second toes, and a single horizontal crease on either palm. While these characteristics are more common in an individual with Down syndrome, they are features that can be seen in anyone in the general population.
Since people with Down syndrome have the extra chromosome, they have features that cause them to resemble other individuals with Down syndrome. However, because there are 46 completely normal chromosomes, individuals with Down syndrome will also resemble their parents, brothers and sisters, and will possess their own unique personality.
Current research indicates that the majority of people with Down syndrome have mild to moderate developmental delays. There is NO correlation between physical characteristics and cognitive abilities. Today, less than five percent of individuals with Down syndrome have severe to profound intellectual disabilities; the majority have only a mild to moderate intellectual disability. An intellectual disability means that a person does not just learn more slowly, but that she or he actually learns differently and develops different strategies and mechanisms for learning.
It is impossible, either prior to birth or early in life, to determine any person's future strengths or weaknesses. Individuals with Down syndrome are lifelong learners and acquire new skills and talents when offered a variety of life experiences and opportunities. Just like their peers, they attend school, develop friendships, maintain jobs, participate in important personal decisions and make positive contributions to the community. People with Down syndrome are more like their nondisabled peers than they are different and they deserve the same opportunities.
Individuals with Down syndrome may have a greater incidence of health certain complications than that of the average person. Ongoing medical assessment with early detection and treatment are important.


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Cult Of Luna frontman calls out Tim Lambesis, As I Lay Dying
Tuesday, October 1, 2019 11:56 AM PT
[ 28,957 views ]
Cult Of Luna frontman Johannes Persson isn't mincing words when it comes to Tim Lambesis and his As I Lay Dying bandmates, in addition to their fans and any media outlets that cover the band.
In a new interview with The Quietus, Persson says that Lambesis, who went to jail for hiring a hitman to kill his estranged wife in 2013, hasn't shown enough remorse for his actions, or waited enough time before returning to the spotlight. Persson also called the other members of As I Lay Dying cowards for putting money before integrity.
For whatever reason, Persson didn't mention Lambesis or his band by name, but it's quite obvious whom he's talking about. Here is the relevant excerpt:
"The background that I'm from – the musical background – was very much integrated with a lot of ethics and it was a very political scene too, which when you come from that kind of scene you think that everybody else thinks the same way in a sense.
"So, for example, when a person that just tried to [have his wife killed] – something that happened just a couple of years ago – is out touring and people are happy to have a forgive and forget attitude about it? I cannot get my head around it. I cannot. How is that not a person you now don't want anything to do with in your entire life?
"How can [journalists] write about that band? There are a thousand other bands you can write about. How can you go to their show? How can they not be constantly questioned every single day about it? I don't understand because with my background we call bullshit on people.
"However, it might not sound like it, but I'm all for second chances, as long as that person has shown deep regret and I think that some time must-have passed before you can actually see if a person is sincere enough, and most of all you see it through their actions, not through their words.
"For example, Ok, let's talk about this case right now – I'm not even going to say his name – but if you're sincerely sorry, like I said: fine. Take all your proceedings, everything from every tour and donate it to a battered women's shelter. Of course, you can take enough to make ends meet but just saying, 'I'm sorry', doesn't cut it, especially when your band called you a sociopath before.
"That's how they work. They adapt to what fits them at this moment. I'm not buying it. You donate your money – at least that's an action, that's something that shows you're going to do something that's not for yourself. This is also about those coward fucking band members who threw shit on him one second and then when their other band didn't work well [they welcomed him back] – money talks. That's how it works."
[via ThePRP]
Related: Cult Of Luna, Tim Lambesis, As I Lay Dying
• As I Lay Dying's Tim Lambesis hospitalized with serious burns
• Andy Dick attends As I Lay Dying show, hangs with Tim Lambsis
• August Burns Red vocalist explains support for As I Lay Dying
• House Of Blues defends decision to book As I Lay Dying
• As I Lay Dying release new mini-documentary


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State Cracking Down On Bars That Over Serve Alcohol
BOSTON (AP) — State officials say they'll be cracking down on bars that over serve patrons this Memorial Day weekend.
Treasurer Deb Goldberg said the state Alcoholic Beverages Control Commission will be focusing enforcement over the holiday weekend on bars in summer communities that have been most identified as the last bar to sell alcohol to a convicted drunk driver.
She says the commission has been working with local police departments to identify these high-risk locations. Goldberg says bars that continue to serve alcohol to individuals who are very intoxicated puts other drivers at risk and can lead to increases in other criminal activity.
Her office says alcohol is involved in 40 percent of traffic crash fatalities and that well over 50 percent of drunken driving arrests originate at bars.


Single parents have to develop a culture of accountability in their home once the separation or divorce has taken place. A "culture of accountability" position is one that says, "You are still accountable for your behavior here at home." So no matter what else is going on outside the house or whatever feelings the child is having, including those that come from legitimate sources, the child is responsible for his or her behavior. I would say that being structured and clear after a divorce is much more helpful to kids than compromising your values because your children are going through a tough time. Remember, it's during tough times that we need reliable structure the most. Limits, accountability, parental support, outside support when necessary—these are all part of a culture of accountability in the family. Kids experience a whole range of emotions when a separation and divorce occur. Remember that "divorce" and "separation" are legalistic terms. Once one parent moves out, the kids' adverse emotional experience begins, no matter how it's labeled.
My opinion is that therapy should be flexible enough to involve everyone in various combinations, but still avoid involving sessions with both the parents and the children present unless absolutely necessary. Before those sessions, strict ground rules and agendas must be agreed upon by both parents. Remember, it is very likely the differences in perception, interpretation, and behaviors which led to the divorce in the first place could be acted out in the artificial situation. In some cases, kids will not want to participate in these types of therapeutic activities. In my experience, if kids are managing the divorce and the other areas of their life well, they should not be pushed to be involved. On the other hand, if they're having behavioral or academic performance problems, behavior management therapy should be on the menu.


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