Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms for sampling, marginalization, conditioning, and other inference tasks. We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world applications like finding diverse sets of high-quality search results, building informative summaries by selecting diverse sentences from documents, modeling non-overlapping human poses in images or video, and automatically building timelines of important news stories.

Automatic continuous speech recognition (CSR) is sufficiently mature that a variety of real world applications are now possible including large vocabulary transcription and interactive spoken dialogues. This paper reviews the evolution of the statistical modelling techniques which underlie current-day systems, specifically hidden Markov models (HMMs) and N-grams. Starting from a description of the speech signal and its parameterisation, the various modelling assumptions and their consequences are discussed. It then describes various techniques by which the effects of these assumptions can be mitigated. Despite the progress that has been made, the limitations of current modelling techniques are still evident. The paper therefore concludes with a brief review of some of the more fundamental modelling work now in progress.

With the advance of efficient analytical methods for sensitivity analysis ofprobabilistic networks, the interest in the sensitivities revealed by real-life networks is rekindled. As the amount of data resulting from a sensitivity analysis of even a moderately-sized network is alreadyoverwhelming, methods for extracting relevant information are called for. One such methodis to study the derivative of the sensitivity functions yielded for a network's parameters. We further propose to build upon the concept of admissible deviation, that is, the extent to which a parameter can deviate from the true value without inducing a change in the most likely outcome. We illustrate these concepts by means of a sensitivity analysis of a real-life probabilistic network in oncology.

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be intractable for many nonrecursive models and impossible in the general case for recursive problems, several research groups are actively developing computational techniques for recursive stochastic languages. We have developed an extension to the traditional lambda-calculus as a framework for families of Turing complete stochastic languages. We have also developed a class of exact inference algorithms based on the traditional reductions of the lambda-calculus. We further propose that using the deBruijn notation (a lambda-calculus notation with nameless dummies) supports effective caching in such systems (caching being an essential component of efficient computation). Finally, our extension to the lambda-calculus offers a foundation and general theory for the construction of recursive stochastic modeling languages as well as promise for effective caching and efficient approximation algorithms for inference.

In this paper we compare three different architectures for the evaluation of influence diagrams: HUGIN, Shafer-Shenoy, and Lazy Evaluation architecture. The computational complexity of the architectures are compared on the LImited Memory Influence Diagram (LIMID): a diagram where only the requiste information for the computation of the optimal policies are depicted. Because the requsite information is explicitly represented in the LIMID the evaluation can take advantage of it, and significant savings in computational can be obtained. In this paper we show how the obtained savings is considerably increased when the computations performed on the LIMID is according to the Lazy Evaluation scheme.

We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding the principle of inheritance with overriding. This is done by using recent approaches to probabilistic default reasoning with conditional constraints. We analyze the semantic properties of the new entailment relations. We also present algorithms for probabilistic logic programming under inheritance with overriding, and program transformations for an increased efficiency.

The search space of Bayesian Network structures is usually defined as Acyclic Directed Graphs (DAGs) and the search is done by local transformations of DAGs. But the space of Bayesian Networks is ordered by DAG Markov model inclusion and it is natural to consider that a good search policy should take this into account. First attempt to do this (Chickering 1996) was using equivalence classes of DAGs instead of DAGs itself. This approach produces better results but it is significantly slower. We present a compromise between these two approaches. It uses DAGs to search the space in such a way that the ordering by inclusion is taken into account. This is achieved by repetitive usage of local moves within the equivalence class of DAGs. We show that this new approach produces better results than the original DAGs approach without substantial change in time complexity. We present empirical results, within the framework of heuristic search and Markov Chain Monte Carlo, provided through the Alarm dataset.

It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete data and a given node ordering this division is a myth, by showing that cross entropy methods for checking conditional independence are mathematically identical to methods based upon discriminating between models by their overall goodness-of-fit logarithmic scores.

The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.

Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the conditioning is either based on the minimum, or the product operator. Benferhat et al. (1999) have investigated the connections between min-based graphs and possibilistic logic bases (made of classical formulas weighted in terms of certainty). This paper deals with a more difficult issue : the product-based graphical representations of possibilistic bases, which provides an easy structural reading of possibilistic bases. Moreover, this paper also provides another reading of possibilistic bases in terms of comparative preferences of the form "in the context p, q is preferred to not q". This enables us to explicit preferences underlying a set of goals with different levels of priority.