Guy Van den Broeck

Bio: Guy Van den Broeck is an academic researcher from University of California, Los Angeles. The author has contributed to research in topics: Probabilistic logic & Inference. The author has an hindex of 33, co-authored 199 publications receiving 3357 citations. Previous affiliations of Guy Van den Broeck include University of Copenhagen Faculty of Science & University of Trento.

Inference and learning in probabilistic logic programs using weighted Boolean formulas

Abstract: Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for probabilistic logic programs. Several such tasks such as computing the marginals given evidence and learning from (partial) interpretations have not really been addressed for probabilistic logic programs before. The rst contribution of this paper is a suite of ecient algorithms for various inference tasks. It is based on a conversion of the program and the queries and evidence to a weighted Boolean formula. This allows us to reduce the inference tasks to well-studied tasks such as weighted model counting, which can be solved using state-of-the-art methods known from the graphical model and knowledge compilation literature. The second contribution is an algorithm for parameter estimation in the learning from interpretations setting. The algorithm employs Expectation Maximization, and is built on top of the developed inference algorithms. The proposed approach is experimentally evaluated. The results show that the inference algorithms improve upon the state-of-the-art in probabilistic logic programming and that it is indeed possible to learn the parameters of a probabilistic logic program from interpretations.

Lifted probabilistic inference by first-order knowledge compilation

Abstract: Probabilistic logical languages provide powerful formalisms for knowledge representation and learning. Yet performing inference in these languages is extremely costly, especially if it is done at the propositional level. Lifted inference algorithms, which avoid repeated computation by treating indistinguishable groups of objects as one, help mitigate this cost. Seeking inspiration from logical inference, where lifted inference (e.g., resolution) is commonly performed, we develop a model theoretic approach to probabilistic lifted inference. Our algorithm compiles a first-order probabilistic theory into a first-order deterministic decomposable negation normal form (d-DNNF) circuit. Compilation offers the advantage that inference is polynomial in the size of the circuit. Furthermore, by borrowing techniques from the knowledge compilation literature our algorithm effectively exploits the logical structure (e.g., context-specific independencies) within the first-order model, which allows more computation to be done at the lifted level. An empirical comparison demonstrates the utility of the proposed approach.

Probabilistic sentential decision diagrams

Abstract: We propose the Probabilistic Sentential Decision Diagram (PSDD): A complete and canonical representation of probability distributions defined over the models of a given propositional theory. Each parameter of a PSDD can be viewed as the (conditional) probability of making a decision in a corresponding Sentential Decision Diagram (SDD). The SDD itself is a recently proposed complete and canonical representation of propositional theories. We explore a number of interesting properties of PSDDs, including the independencies that underlie them. We show that the PSDD is a tractable representation. We further show how the parameters of a PSDD can be efficiently estimated, in closed form, from complete data. We empirically evaluate the quality of PS-DDs learned from data, when we have knowledge, a priori, of the domain logical constraints.

A Semantic Loss Function for Deep Learning with Symbolic Knowledge

Abstract: Author(s): Xu, Jingyi | Advisor(s): Van den Broeck, Guy | Abstract: This thesis develops a novel methodology incorporating symbolic knowledge in deep learning.We constructed a logical-constraint semantic loss, using a neural network's output vectors as variables.Semantic loss captures the symbolic knowledge and adds previously-lost information to neural networks.An experimental evaluation shows that it leads the neural network to achieve (near-)state-of-the-art performance on semi-supervised multi-class classification.Moreover, it is applicable to more complex constraints. We present a process, at the end of the thesis, of calculating the semantic loss and its derivatives for complex constraints to show its generality.The work presented in this thesis was published at the International Conference on Machine Learning.

On the Completeness of First-Order Knowledge Compilation for Lifted Probabilistic Inference

Abstract: Probabilistic logics are receiving a lot of attention today because of their expressive power for knowledge representation and learning. However, this expressivity is detrimental to the tractability of inference, when done at the propositional level. To solve this problem, various lifted inference algorithms have been proposed that reason at the first-order level, about groups of objects as a whole. Despite the existence of various lifted inference approaches, there are currently no completeness results about these algorithms. The key contribution of this paper is that we introduce a formal definition of lifted inference that allows us to reason about the completeness of lifted inference algorithms relative to a particular class of probabilistic models. We then show how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Machine learning

Abstract: Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

A Survey of Monte Carlo Tree Search Methods

Abstract: Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work.