Symbolic Probabilistic Inference with Evidence Potential

Recent research on the Symbolic Probabilistic Inference (SPI) algorithm[2] has focused attention on the importance of resolving general queries in Bayesian networks. SPI applies the concept of dependency-directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. In response to this research we have extended the evidence potential algorithm [3] with the same features. We call the extension symbolic evidence potential inference (SEPI). SEPI like SPI can handle generic queries and is incremental with respect to queries and observations. While in SPI, operations are done on a search tree constructed from the nodes of the original network, in SEPI, a clique-tree structure obtained from the evidence potential algorithm [3] is the basic framework for recursive query processing. In this paper, we describe the systematic query and caching procedure of SEPI. SEPI begins with finding a clique tree from a Bayesian network-the standard procedure of the evidence potential algorithm. With the clique tree, various probability distributions are computed and stored in each clique. This is the ?pre-processing? step of SEPI. Once this step is done, the query can then be computed. To process a query, a recursive process similar to the SPI algorithm is used. The queries are directed to the root clique and decomposed into queries for the clique's subtrees until a particular query can be answered at the clique at which it is directed. The algorithm and the computation are simple. The SEPI algorithm will be presented in this paper along with several examples.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991

Symbolic Probabilitistic Inference in Large BN2O Networks

A BN2O network is a two level belief net in which the parent interactions are modeled using the noisy-or interaction model. In this paper we discuss application of the SPI local expression language to efficient inference in large BN2O networks. In particular, we show that there is significant structure, which can be exploited to improve over the Quickscore result. We further describe how symbolic techniques can provide information which can significantly reduce the computation required for computing all cause posterior marginals. Finally, we present a novel approximation technique with preliminary experimental results.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Exact Inference for Relational Graphical Models with Interpreted Functions: Lifted Probabilistic Inference Modulo Theories

Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this paper, we expand PIMT to a lifted version that also processes random functions and relations. This enhancement is achieved by adapting Inversion, a method from Lifted First-Order Probabilistic Inference literature, to also be modulo theories. This results in the first algorithm for exact probabilistic inference that efficiently and simultaneously exploits random relations and functions, arithmetic, equalities and inequalities.Comment: Appeared in the Uncertainty in Artificial Intelligence Conference, August 201

SIMPL: A DSL for Automatic Specialization of Inference Algorithms

Inference algorithms in probabilistic programming languages (PPLs) can be thought of as interpreters, since an inference algorithm traverses a model given evidence to answer a query. As with interpreters, we can improve the efficiency of inference algorithms by compiling them once the model, evidence and query are known. We present SIMPL, a domain specific language for inference algorithms, which uses this idea in order to automatically specialize annotated inference algorithms. Due to the approach of specialization, unlike a traditional compiler, with SIMPL new inference algorithms can be added easily, and still be optimized using domain-specific information. We evaluate SIMPL and show that partial evaluation gives a 2-6x speedup, caching provides an additional 1-1.5x speedup, and generating C code yields an additional 13-20x speedup, for an overall speedup of 30-150x for several inference algorithms and models

Probability Distinguishes Different Types of Conditional Statements

The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the propositional calculus and Boole's mathematical logic: truth-functional and Boolean feasibility (which turn out to be special cases of probabilistic conditionals). Each probabilistic conditional is quantified by a fractional parameter between zero and one that says whether it is purely affirmative, purely negative, or intermediate in its sense. Conditionals can be specialized further by their content to express factuality and counterfactuality, and revised or reformulated to account for exceptions and confounding factors. The various conditionals have distinct mathematical representations: through intermediate probability expressions and logical formulas, each conditional is eventually translated into a set of polynomial equations and inequalities (with real coefficients). The polynomial systems from different types of conditionals exhibit different patterns of behavior, concerning for example opposing conditionals or false antecedents. Interesting results can be computed from the relevant polynomial systems using well-known methods from algebra and computer science. Among other benefits, the proposed framework of analysis offers paraconsistent procedures for logical deduction that produce such familiar results as modus ponens, transitivity, disjunction introduction, and disjunctive syllogism; all while avoiding any explosion of consequences from inconsistent premises. Several example problems from Goodman and Adams are analyzed. A new perspective called polylogicism is presented: mathematical logic that respects the diversity among conditionals in particular and logic problems in general.Comment: Fixed a few typographical error

Predicting upcoming actions by observation: some facts, models and challenges

Predicting another person's upcoming action to build an appropriate response is a regular occurrence in the domain of motor control. In this review we discuss conceptual and experimental approaches aiming at the neural basis of predicting and learning to predict upcoming movements by their observation

An Empirical Evaluation of Possible Variations of Lazy Propagation

As real-world Bayesian networks continue to grow larger and more complex, it is important to investigate the possibilities for improving the performance of existing algorithms of probabilistic inference. Motivated by examples, we investigate the dependency of the performance of Lazy propagation on the message computation algorithm. We show how Symbolic Probabilistic Inference (SPI) and Arc-Reversal (AR) can be used for computation of clique to clique messages in the addition to the traditional use of Variable Elimination (VE). In addition, the paper resents the results of an empirical evaluation of the performance of Lazy propagation using VE, SPI, and AR as the message computation algorithm. The results of the empirical evaluation show that for most networks, the performance of inference did not depend on the choice of message computation algorithm, but for some randomly generated networks the choice had an impact on both space and time performance. In the cases where the choice had an impact, AR produced the best results.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004

Constrained Bayesian Networks: Theory, Optimization, and Applications

We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data for the learning of causal network structure or probability values at nodes are available. Constrained Bayesian Networks generalize a Bayesian Network such that probabilities can be symbolic, arithmetic expressions and where the meaning of the network is constrained by finitely many formulas from the theory of the reals. A formal semantics for constrained Bayesian Networks over first-order logic of the reals is given, which enables non-linear and non-convex optimisation algorithms that rely on decision procedures for this logic, and supports the composition of several constrained Bayesian Networks. A non-trivial case study in arms control, where few or no data are available to assess the effectiveness of an arms inspection process, evaluates our approach. An open-access prototype implementation of these foundations and their algorithms uses the SMT solver Z3 as decision procedure, leverages an open-source package for Bayesian inference to symbolic computation, and is evaluated experimentally.Comment: 43 pages, 18 figure

Neural-Symbolic Learning and Reasoning: A Survey and Interpretation

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.Comment: 58 pages, work in progres

Embedding Vector Differences Can Be Aligned With Uncertain Intensional Logic Differences

The DeepWalk algorithm is used to assign embedding vectors to nodes in the Atomspace weighted, labeled hypergraph that is used to represent knowledge in the OpenCog AGI system, in the context of an application to probabilistic inference regarding the causes of longevity based on data from biological ontologies and genomic analyses. It is shown that vector difference operations between embedding vectors are, in appropriate conditions, approximately alignable with "intensional difference" operations between the hypergraph nodes corresponding to the embedding vectors. This relationship hints at a broader functorial mapping between uncertain intensional logic and vector arithmetic, and opens the door for using embedding vector algebra to guide intensional inference control