271 research outputs found
Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The
assumption that an infinite sequence of data points is exchangeable is at the
core of Bayesian statistics. However, finite exchangeability as a statistical
property that renders probabilistic inference tractable is less
well-understood. We develop a theory of finite exchangeability and its relation
to tractable probabilistic inference. The theory is complementary to that of
independence and conditional independence. We show that tractable inference in
probabilistic models with high treewidth and millions of variables can be
understood using the notion of finite (partial) exchangeability. We also show
that existing lifted inference algorithms implicitly utilize a combination of
conditional independence and partial exchangeability.Comment: In Proceedings of the 28th AAAI Conference on Artificial Intelligenc
Generating and Sampling Orbits for Lifted Probabilistic Inference
A key goal in the design of probabilistic inference algorithms is identifying
and exploiting properties of the distribution that make inference tractable.
Lifted inference algorithms identify symmetry as a property that enables
efficient inference and seek to scale with the degree of symmetry of a
probability model. A limitation of existing exact lifted inference techniques
is that they do not apply to non-relational representations like factor graphs.
In this work we provide the first example of an exact lifted inference
algorithm for arbitrary discrete factor graphs. In addition we describe a
lifted Markov-Chain Monte-Carlo algorithm that provably mixes rapidly in the
degree of symmetry of the distribution
Lifted graphical models: a survey
Lifted graphical models provide a language for expressing dependencies between different types of entities, their attributes, and their diverse relations, as well as techniques for probabilistic reasoning in such multi-relational domains. In this survey, we review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We discuss inference algorithms, including lifted inference algorithms, that efficiently compute the answers to probabilistic queries over such models. We also review work in learning lifted graphical models from data. There is a growing need for statistical relational models (whether they go by that name or another), as we are inundated with data which is a mix of structured and unstructured, with entities and relations extracted in a noisy manner from text, and with the need to reason effectively with this data. We hope that this synthesis of ideas from many different research groups will provide an accessible starting point for new researchers in this expanding field
Automatic Bayesian Density Analysis
Making sense of a dataset in an automatic and unsupervised fashion is a
challenging problem in statistics and AI. Classical approaches for {exploratory
data analysis} are usually not flexible enough to deal with the uncertainty
inherent to real-world data: they are often restricted to fixed latent
interaction models and homogeneous likelihoods; they are sensitive to missing,
corrupt and anomalous data; moreover, their expressiveness generally comes at
the price of intractable inference. As a result, supervision from statisticians
is usually needed to find the right model for the data. However, since domain
experts are not necessarily also experts in statistics, we propose Automatic
Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible
at large. Specifically, ABDA allows for automatic and efficient missing value
estimation, statistical data type and likelihood discovery, anomaly detection
and dependency structure mining, on top of providing accurate density
estimation. Extensive empirical evidence shows that ABDA is a suitable tool for
automatic exploratory analysis of mixed continuous and discrete tabular data.Comment: In proceedings of the Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19
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