100,054 research outputs found
Ideal Reformulation of Belief Networks
The intelligent reformulation or restructuring of a belief network can
greatly increase the efficiency of inference. However, time expended for
reformulation is not available for performing inference. Thus, under time
pressure, there is a tradeoff between the time dedicated to reformulating the
network and the time applied to the implementation of a solution. We
investigate this partition of resources into time applied to reformulation and
time used for inference. We shall describe first general principles for
computing the ideal partition of resources under uncertainty. These principles
have applicability to a wide variety of problems that can be divided into
interdependent phases of problem solving. After, we shall present results of
our empirical study of the problem of determining the ideal amount of time to
devote to searching for clusters in belief networks. In this work, we acquired
and made use of probability distributions that characterize (1) the performance
of alternative heuristic search methods for reformulating a network instance
into a set of cliques, and (2) the time for executing inference procedures on
various belief networks. Given a preference model describing the value of a
solution as a function of the delay required for its computation, the system
selects an ideal time to devote to reformulation.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in
Artificial Intelligence (UAI1990
Monte Carlo Inference via Greedy Importance Sampling
We present a new method for conducting Monte Carlo inference in graphical
models which combines explicit search with generalized importance sampling. The
idea is to reduce the variance of importance sampling by searching for
significant points in the target distribution. We prove that it is possible to
introduce search and still maintain unbiasedness. We then demonstrate our
procedure on a few simple inference tasks and show that it can improve the
inference quality of standard MCMC methods, including Gibbs sampling,
Metropolis sampling, and Hybrid Monte Carlo. This paper extends previous work
which showed how greedy importance sampling could be correctly realized in the
one-dimensional case.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
Posterior Predictive Treatment Assignment for Estimating Causal Effects with Limited Overlap
Estimating causal effects with propensity scores relies upon the availability
of treated and untreated units observed at each value of the estimated
propensity score. In settings with strong confounding, limited so-called
"overlap" in propensity score distributions can undermine the empirical basis
for estimating causal effects and yield erratic finite-sample performance of
existing estimators. We propose a Bayesian procedure designed to estimate
causal effects in settings where there is limited overlap in propensity score
distributions. Our method relies on the posterior predictive treatment
assignment (PPTA), a quantity that is derived from the propensity score but
serves different role in estimation of causal effects. We use the PPTA to
estimate causal effects by marginalizing over the uncertainty in whether each
observation is a member of an unknown subset for which treatment assignment can
be assumed unconfounded. The resulting posterior distribution depends on the
empirical basis for estimating a causal effect for each observation and has
commonalities with recently-proposed "overlap weights" of Li et al. (2016). We
show that the PPTA approach can be construed as a stochastic version of
existing ad-hoc approaches such as pruning based on the propensity score or
truncation of inverse probability of treatment weights, and highlight several
practical advantages including uncertainty quantification and improved
finite-sample performance. We illustrate the method in an evaluation of the
effectiveness of technologies for reducing harmful pollution emissions from
power plants in the United States
Bayesian Time-of-Flight for Realtime Shape, Illumination and Albedo
We propose a computational model for shape, illumination and albedo inference
in a pulsed time-of-flight (TOF) camera. In contrast to TOF cameras based on
phase modulation, our camera enables general exposure profiles. This results in
added flexibility and requires novel computational approaches.
To address this challenge we propose a generative probabilistic model that
accurately relates latent imaging conditions to observed camera responses.
While principled, realtime inference in the model turns out to be infeasible,
and we propose to employ efficient non-parametric regression trees to
approximate the model outputs. As a result we are able to provide, for each
pixel, at video frame rate, estimates and uncertainty for depth, effective
albedo, and ambient light intensity. These results we present are
state-of-the-art in depth imaging.
The flexibility of our approach allows us to easily enrich our generative
model. We demonstrate that by extending the original single-path model to a
two-path model, capable of describing some multipath effects. The new model is
seamlessly integrated in the system at no additional computational cost.
Our work also addresses the important question of optimal exposure design in
pulsed TOF systems. Finally, for benchmark purposes and to obtain realistic
empirical priors of multipath and insights into this phenomena, we propose a
physically accurate simulation of multipath phenomena
Time-Dependent Utility and Action Under Uncertainty
We discuss representing and reasoning with knowledge about the time-dependent
utility of an agent's actions. Time-dependent utility plays a crucial role in
the interaction between computation and action under bounded resources. We
present a semantics for time-dependent utility and describe the use of
time-dependent information in decision contexts. We illustrate our discussion
with examples of time-pressured reasoning in Protos, a system constructed to
explore the ideal control of inference by reasoners with limit abilities.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in
Artificial Intelligence (UAI1991
Improving pairwise comparison models using Empirical Bayes shrinkage
Comparison data arises in many important contexts, e.g. shopping, web clicks,
or sports competitions. Typically we are given a dataset of comparisons and
wish to train a model to make predictions about the outcome of unseen
comparisons. In many cases available datasets have relatively few comparisons
(e.g. there are only so many NFL games per year) or efficiency is important
(e.g. we want to quickly estimate the relative appeal of a product). In such
settings it is well known that shrinkage estimators outperform maximum
likelihood estimators. A complicating matter is that standard comparison models
such as the conditional multinomial logit model are only models of conditional
outcomes (who wins) and not of comparisons themselves (who competes). As such,
different models of the comparison process lead to different shrinkage
estimators. In this work we derive a collection of methods for estimating the
pairwise uncertainty of pairwise predictions based on different assumptions
about the comparison process. These uncertainty estimates allow us both to
examine model uncertainty as well as perform Empirical Bayes shrinkage
estimation of the model parameters. We demonstrate that our shrunk estimators
outperform standard maximum likelihood methods on real comparison data from
online comparison surveys as well as from several sports contexts.Comment: 9 page
Generalized Variational Inference: Three arguments for deriving new Posteriors
We advocate an optimization-centric view on and introduce a novel
generalization of Bayesian inference. Our inspiration is the representation of
Bayes' rule as infinite-dimensional optimization problem (Csiszar, 1975;
Donsker and Varadhan; 1975, Zellner; 1988). First, we use it to prove an
optimality result of standard Variational Inference (VI): Under the proposed
view, the standard Evidence Lower Bound (ELBO) maximizing VI posterior is
preferable to alternative approximations of the Bayesian posterior. Next, we
argue for generalizing standard Bayesian inference. The need for this arises in
situations of severe misalignment between reality and three assumptions
underlying standard Bayesian inference: (1) Well-specified priors, (2)
well-specified likelihoods, (3) the availability of infinite computing power.
Our generalization addresses these shortcomings with three arguments and is
called the Rule of Three (RoT). We derive it axiomatically and recover existing
posteriors as special cases, including the Bayesian posterior and its
approximation by standard VI. In contrast, approximations based on alternative
ELBO-like objectives violate the axioms. Finally, we study a special case of
the RoT that we call Generalized Variational Inference (GVI). GVI posteriors
are a large and tractable family of belief distributions specified by three
arguments: A loss, a divergence and a variational family. GVI posteriors have
appealing properties, including consistency and an interpretation as
approximate ELBO. The last part of the paper explores some attractive
applications of GVI in popular machine learning models, including robustness
and more appropriate marginals. After deriving black box inference schemes for
GVI posteriors, their predictive performance is investigated on Bayesian Neural
Networks and Deep Gaussian Processes, where GVI can comprehensively improve
upon existing methods.Comment: 103 pages, 23 figures (comprehensive revision of previous version
Approximate Computational Approaches for Bayesian Sensor Placement in High Dimensions
Since the cost of installing and maintaining sensors is usually high, sensor
locations are always strategically selected. For those aiming at inferring
certain quantities of interest (QoI), it is desirable to explore the dependency
between sensor measurements and QoI. One of the most popular metric for the
dependency is mutual information which naturally measures how much information
about one variable can be obtained given the other. However, computing mutual
information is always challenging, and the result is unreliable in high
dimension. In this paper, we propose an approach to find an approximate lower
bound of mutual information and compute it in a lower dimension. Then, sensors
are placed where highest mutual information (lower bound) is achieved and QoI
is inferred via Bayes rule given sensor measurements. In addition, Bayesian
optimization is introduced to provide a continuous mutual information surface
over the domain and thus reduce the number of evaluations. A chemical release
accident is simulated where multiple sensors are placed to locate the source of
the release. The result shows that the proposed approach is both effective and
efficient in inferring QoI
Using Recursive Partitioning to Find and Estimate Heterogenous Treatment Effects In Randomized Clinical Trials
Heterogeneous treatment effects can be very important in the analysis of
randomized clinical trials. Heightened risks or enhanced benefits may exist for
particular subsets of study subjects. When the heterogeneous treatment effects
are specified as the research is being designed, there are proper and readily
available analysis techniques. When the heterogeneous treatment effects are
inductively obtained as an experiment's data are analyzed, significant
complications are introduced. There can be a need for special loss functions
designed to find local average treatment effects and for techniques that
properly address post selection statistical inference. In this paper, we tackle
both while undertaking a recursive partitioning analysis of a randomized
clinical trial testing whether individuals on probation, who are low risk, can
be minimally supervised with no increase in recidivism.Comment: 21 pages, 1 figure, under revie
False confidence, non-additive beliefs, and valid statistical inference
Statistics has made tremendous advances since the times of Fisher, Neyman,
Jeffreys, and others, but the fundamental and practically relevant questions
about probability and inference that puzzled our founding fathers remain
unanswered. To bridge this gap, I propose to look beyond the two dominating
schools of thought and ask the following three questions: what do scientists
need out of statistics, do the existing frameworks meet these needs, and, if
not, how to fill the void? To the first question, I contend that scientists
seek to convert their data, posited statistical model, etc., into calibrated
degrees of belief about quantities of interest. To the second question, I argue
that any framework that returns additive beliefs, i.e., probabilities,
necessarily suffers from {\em false confidence}---certain false hypotheses tend
to be assigned high probability---and, therefore, risks systematic bias. This
reveals the fundamental importance of {\em non-additive beliefs} in the context
of statistical inference. But non-additivity alone is not enough so, to the
third question, I offer a sufficient condition, called {\em validity}, for
avoiding false confidence, and present a framework, based on random sets and
belief functions, that provably meets this condition. Finally, I discuss
characterizations of p-values and confidence intervals in terms of valid
non-additive beliefs, which imply that users of these classical procedures are
already following the proposed framework without knowing it.Comment: 60 pages, 12 figures. Comments welcome at
https://www.researchers.one/article/2019-02-
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