Context-Specific Approximation in Probabilistic Inference

There is evidence that the numbers in probabilistic inference don't really matter. This paper considers the idea that we can make a probabilistic model simpler by making fewer distinctions. Unfortunately, the level of a Bayesian network seems too coarse; it is unlikely that a parent will make little difference for all values of the other parents. In this paper we consider an approximation scheme where distinctions can be ignored in some contexts, but not in other contexts. We elaborate on a notion of a parent context that allows a structured context-specific decomposition of a probability distribution and the associated probabilistic inference scheme called probabilistic partial evaluation (Poole 1997). This paper shows a way to simplify a probabilistic model by ignoring distinctions which have similar probabilities, a method to exploit the simpler model, a bound on the resulting errors, and some preliminary empirical results on simple networks.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998

Exploiting the Rule Structure for Decision Making within the Independent Choice Logic

This paper introduces the independent choice logic, and in particular the "single agent with nature" instance of the independent choice logic, namely ICLdt. This is a logical framework for decision making uncertainty that extends both logic programming and stochastic models such as influence diagrams. This paper shows how the representation of a decision problem within the independent choice logic can be exploited to cut down the combinatorics of dynamic programming. One of the main problems with influence diagram evaluation techniques is the need to optimise a decision for all values of the 'parents' of a decision variable. In this paper we show how the rule based nature of the ICLdt can be exploited so that we only make distinctions in the values of the information available for a decision that will make a difference to utility.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

The use of conflicts in searching Bayesian networks

This paper discusses how conflicts (as used by the consistency-based diagnosis community) can be adapted to be used in a search-based algorithm for computing prior and posterior probabilities in discrete Bayesian Networks. This is an "anytime" algorithm, that at any stage can estimate the probabilities and give an error bound. Whereas the most popular Bayesian net algorithms exploit the structure of the network for efficiency, we exploit probability distributions for efficiency; this algorithm is most suited to the case with extreme probabilities. This paper presents a solution to the inefficiencies found in naive algorithms, and shows how the tools of the consistency-based diagnosis community (namely conflicts) can be used effectively to improve the efficiency. Empirical results with networks having tens of thousands of nodes are presented.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

A Framework for Decision-Theoretic Planning I: Combining the Situation Calculus, Conditional Plans, Probability and Utility

This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is essentially Reiter's solution to the frame problem, in terms of the completion of the axioms defining the state change. Uncertainty is handled in terms of the independent choice logic, which allows for independent choices and a logic program that gives the consequences of the choices. As part of the consequences are a specification of the utility of (final) states. The robot adopts robot plans, similar to the GOLOG programming language. Within this logic, we can define the expected utility of a conditional plan, based on the axiomatization of the actions, the uncertainty and the utility. The ?planning' problem is to find the plan with the highest expected utility. This is related to recent structured representations for POMDPs; here we use stochastic situation calculus rules to specify the state transition function and the reward/value function. Finally we show that with stochastic frame axioms, actions representations in probabilistic STRIPS are exponentially larger than using the representation proposed here.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Constraint Processing in Lifted Probabilistic Inference

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference from the perspective of constraint processing and, through this viewpoint, we analyze and compare existing approaches and expose their advantages and limitations. Our theoretical results show that the wrong choice of constraint processing method can lead to exponential increase in computational complexity. Our empirical tests confirm the importance of constraint processing in lifted inference. This is the first theoretical and empirical study of constraint processing in lifted inference.Comment: Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009

Towards Solving the Multiple Extension Problem: Combining Defaults and Probabilities

The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference, some extensions seem to be simply wrong and we use qualitative techniques to weed out the unwanted ones. In the area of diagnosis, however, the multiple explanations may all seem reasonable, however improbable. Choosing among them is a matter of quantitative preference. Quantitative preference works well in diagnosis when knowledge is modelled causally. Here we suggest a framework that combines probabilities and defaults in a single unified framework that retains the semantics of diagnosis as construction of explanations from a fixed set of possible hypotheses. We can then compute probabilities incrementally as we construct explanations. Here we describe a branch and bound algorithm that maintains a set of all partial explanations while exploring a most promising one first. A most probable explanation is found first if explanations are partially ordered.Comment: Appears in Proceedings of the Third Conference on Uncertainty in Artificial Intelligence (UAI1987

Efficient Inference in Large Discrete Domains

In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables that have as domains, the set of all names, the set of all postal codes, or the set of all credit card numbers. We cannot just have big tables of the conditional probabilities, but need compact representations. We provide an inference algorithm, based on variable elimination, for belief networks containing both large domain and normal discrete random variables. We use intensional (i.e., in terms of procedures) and extensional (in terms of listing the elements) representations of conditional probabilities and of the intermediate factors.Comment: Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003

Why is Compiling Lifted Inference into a Low-Level Language so Effective?

First-order knowledge compilation techniques have proven efficient for lifted inference. They compile a relational probability model into a target circuit on which many inference queries can be answered efficiently. Early methods used data structures as their target circuit. In our KR-2016 paper, we showed that compiling to a low-level program instead of a data structure offers orders of magnitude speedup, resulting in the state-of-the-art lifted inference technique. In this paper, we conduct experiments to address two questions regarding our KR-2016 results: 1- does the speedup come from more efficient compilation or more efficient reasoning with the target circuit?, and 2- why are low-level programs more efficient target circuits than data structures?Comment: 6 pages, 3 figures, accepted at IJCAI-16 Statistical Relational AI (StaRAI) worksho

RelNN: A Deep Neural Model for Relational Learning

Statistical relational AI (StarAI) aims at reasoning and learning in noisy domains described in terms of objects and relationships by combining probability with first-order logic. With huge advances in deep learning in the current years, combining deep networks with first-order logic has been the focus of several recent studies. Many of the existing attempts, however, only focus on relations and ignore object properties. The attempts that do consider object properties are limited in terms of modelling power or scalability. In this paper, we develop relational neural networks (RelNNs) by adding hidden layers to relational logistic regression (the relational counterpart of logistic regression). We learn latent properties for objects both directly and through general rules. Back-propagation is used for training these models. A modular, layer-wise architecture facilitates utilizing the techniques developed within deep learning community to our architecture. Initial experiments on eight tasks over three real-world datasets show that RelNNs are promising models for relational learning.Comment: 9 pages, 8 figures, accepted at AAAI-201

What is an Optimal Diagnosis?

Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990