Uncertainty In AI Research Articles

Conditional sum-product networks: Modular probabilistic circuits via gate functions

While probabilistic graphical models are a central tool for reasoning under uncertainty in AI, they are in general not as expressive as deep neural models, and inference is notoriously hard and slow. In contrast, deep probabilistic models such as sum-product networks (SPNs) capture joint distributions and ensure tractable inference, but still lack the expressive power of intractable models based on deep neural networks. In this paper, we introduce conditional SPNs (CSPNs)—conditional density estimators for multivariate and potentially hybrid domains—and develop a structure-learning approach that derives both the structure and parameters of CSPNs from data. To harness the expressive power of deep neural networks (DNNs), we also show how to realize CSPNs by conditioning the parameters of vanilla SPNs on the input using DNNs as gate functions. In contrast to SPNs whose high-level structure can not be explicitly manipulated, CSPNs can naturally be used as tractable building blocks of deep probabilistic models whose modular structure maintains high-level interpretability. In experiments, we demonstrate that CSPNs are competitive with other probabilistic models and yield superior performance on structured prediction, conditional density estimation, auto-regressive image modeling, and multilabel image classification. In particular, we show that employing CSPNs as encoders and decoders within variational autoencoders can help to relax the commonly used mean field assumption and in turn improve performance.

Belief functions on distributive lattices

The Dempster–Shafer theory of belief functions is an important approach to deal with uncertainty in AI. In the theory, belief functions are defined on Boolean algebras of events. In many applications of belief functions in real world problems, however, the objects that we manipulate is no more a Boolean algebra but a distributive lattice. In this paper, we employ Birkhoffʼs representation theorem for finite distributive lattices to extend the Dempster–Shafer theory to the setting of distributive lattices, which has a mathematical theory as attractive as in that of Boolean algebras. Moreover, we use this more general theory to provide a framework for reasoning about belief functions in a deductive approach on non-classical formalisms which assume a setting of distributive lattices. As an illustration of this approach, we investigate the theory of belief functions for a simple epistemic logic the first-degree-entailment fragment of relevance logic R by providing an axiomatization for reasoning about belief functions for this logic and by showing that the complexity of the satisfiability problem of a belief formula with respect to the class of the corresponding Dempster–Shafer structures is NP-complete.

Structured probabilistic inference

Probabilistic inference is among the main topics with reasoning in uncertainty in AI. For this purpose, Bayesian Networks (BNs) is one of the most successful and efficient Probabilistic Graphical Model (PGM) so far. Since the mid-90s, a growing number of BNs extensions have been proposed. Object-oriented, entity-relationship and first-order logic are the main representation paradigms used to extend BNs. While entity-relationship and first-order models have been successfully used for machine learning in defining lifted probabilistic inference, object-oriented models have been mostly underused. Structured inference, which exploits the structural knowledge encoded in an object-oriented PGM, is a surprisingly unstudied technique. In this paper we propose a full object-oriented framework for PRM and propose two extensions of the state-of-the-art structured inference algorithm: SPI which removes the major flaws of existing algorithms and SPISBB which largely enhances SPI by using d-separation.

Generator estimation of Markov jump processes

Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782–805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419–441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753–764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421–430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395–410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.

Decision-Theoretic Planning

The recent advances in computer speed and algorithms for probabilistic inference have led to a resurgence of work on planning under uncertainty. The aim is to design AI planners for environments where there might be incomplete or faulty information, where actions might not always have the same results, and where there might be trade-offs between the different possible outcomes of a plan. Addressing uncertainty in AI, planning algorithms will greatly increase the range of potential applications, but there is plenty of work to be done before we see practical decision-theoretic planning systems. This article outlines some of the challenges that need to be overcome and surveys some of the recent work in the area.

Book review: Representing Uncertain Knowledge by Paul Krause and Dominic Clark (Kluwer Academic Publishers Group, 1993)

Readers looking for a thorough introduction to methods for representing uncertainty in AI will find this book useful. Krause and Clark couple a detailed account of the motivation and context for each technique with a critical eye that avoids presenting any approach as a panacea. This approach allows the reader to develop an understanding of each technique's utility while remaining aware of its limitations. As is appropriate in a field in which the particulars are rapidly changing (over 400 papers are published each year on this topic), the authors focus on the "foundations and intuitions" underlying the technique and do not attempt to provide up to date coverage of its latest refinements.

A note on the infeasibility of some inference processes

We observe that it follows from currently held conjectures in computational complexity that a wide class of inference processes considered for reasoning about uncertainty in AI are computationally infeasible.

The treatment of uncertainty in AI: Is there a better vantage point?

The paper I wrote for the Knowledge Engineering Review was intended primarily to give a balanced review of different techniques developed in (or imported into) Artificial Intelligence to deal with uncertain knowledge.