We present a probabilistic extension of logic programs under the stable model semantics, inspired by the idea of Markov Logic Networks. The proposed language, called LP MLN , is a generalization of logic programs under the stable model semantics, and as such, embraces the rich body of research in knowledge representation. The language is also a generalization of ProbLog, and is closely related to Markov Logic Networks, which implies that the computation can be carried out by the techniques developed for them.  LP MLN appears to be a natural language for probabilistic answer set programming, and as an example we show how an elaboration tolerant representation of transition systems in answer set programs can be naturally extended to the probabilistic setting.

We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of such Gaussian graphical models are also developed. We apply these rules to compare conditional dependencies on Gaussian trees. In particular for trees, we show that such dependence can be completely characterized by the length of the paths joining the dependent vertices to each other and to the vertices conditioned on. We also apply our results to postulate rules for model selection for polytree models. Our rules apply to mutual information of Gaussian random vectors as well.

In the recent years, the desire and need to understand sequential data has been increasing, with particular interest in sequential contexts such as patient monitoring, understanding daily activities, video surveillance, stock market and the like. Along with the constant flow of data, it is critical to classify and segment the observations on-the-fly, without being limited to a rigid number of classes. In addition, the model needs to be capable of updating its parameters to comply with possible evolutions. This interesting problem, however, is not adequately addressed in the literature since many studies focus on offline classification over a pre-defined class set. In this paper, we propose a principled solution to this gap by introducing an adaptive online system based on Markov switching models with hierarchical Dirichlet process priors. This infinite adaptive online approach is capable of segmenting and classifying the sequential data over unlimited number of classes, while meeting the memory and delay constraints of streaming contexts. The model is further enhanced by introducing a learning rate, responsible for balancing the extent to which the model sustains its previous learning (parameters) or adapts to the new streaming observations. Experimental results on several variants of stationary and evolving synthetic data and two video datasets, TUM Assistive Kitchen and collatedWeizmann, show remarkable performance in segmentation and classification, particularly for evolutionary sequences with changing distributions and/or containing new, unseen classes.

Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parametrized by interaction weights and biases. We address the representational power of these models, proving results their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models.

We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is $L_1$ regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. $L_1$ regularization impedes the simple application of the gradient method, which optimizes the cost function that leads to accurate estimations, owing to the cost function's lack of smoothness. In this study, we utilize the majorizer minimization method, which is a well-known technique implemented in optimization problems, to avoid the non-smoothness of the cost function. By using the majorizer minimization method, we elucidate essentially relevant biases and interactions from given data with seemingly strongly-correlated components.

We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs. We address a drawback of this approach, which is the expensive computation of the bisimulation metrics. We propose an algorithm to generate an iteratively improving sequence of state space partitions. Partial metric computations guide the representation search and provide much lower space and computational complexity, while maintaining strong convergence properties. We provide theoretical results guaranteeing convergence as well as experimental illustrations of the accuracy and savings (in time and memory usage) of the new algorithm, compared to traditional bisimulation metric computation.

We examine the fundamental problem of background modeling which is to model the background scenes in video sequences and segment the moving objects from the background. A novel approach is proposed based on the Restricted Boltzmann Machine (RBM) while exploiting the temporal nature of the problem. In particular, we augment the standard RBM to take a window of sequential video frames as input and generate the background model while enforcing the background smoothly adapting to the temporal changes. As a result, the augmented temporally adaptive model can generate stable background given noisy inputs and adapt quickly to the changes in background while keeping all the advantages of RBMs including exact inference and effective learning procedure. Experimental results demonstrate the effectiveness of the proposed method in modeling the temporal nature in background.

One key challenge in statistical relational learning (SRL) is  scalable inference. Unfortunately, most real-world problems in SRL have expressive models that translate into large grounded networks, representing a bottleneck for any inference method and weakening its scalability. In this paper we introduce Preference Relaxation (PR), a two-stage strategy that uses the determinism present in the underlying model to improve the scalability of relational inference. The basic idea of PR is that if the underlying model involves mandatory (i.e. hard) constraints as well as preferences (i.e. soft constraints) then it is potentially wasteful to allocate memory for all constraints in advance when performing inference. To avoid this, PR starts by relaxing preferences and performing inference with hard constraints only. It then removes variables that violate hard constraints, thereby avoiding irrelevant computations involving preferences. In addition it uses the removed variables to enlarge the evidence database. This reduces the effective size of the grounded network. Our approach is general and can be applied to various inference methods in relational domains. Experiments on real-world applications show how PR substantially scales relational inference with a minor impact on accuracy.

In many situations, it is desirable to optimize a sequence of decisions by maximizing a primary objective while respecting some constraints with respect to secondary objectives. Such problems can be naturally modeled as constrained partially observable Markov decision processes (CPOMDPs) when the environment is partially observable. In this work, we describe a technique based on approximate linear programming to optimize policies in CPOMDPs. The optimization is performed offline and produces a finite state controller with desirable performance guarantees. The approach outperforms a constrained version of point-based value iteration on a suite of benchmark problems.

Two other algorithms require the knowledge Markov Decision Processes (MDPs) offer a general framework of the optimal policy and its expected reward. We show to describe probabilistic planning problems of varying that the expected reward of the optimal policy is a lower complexity. The development of algorithms that act successfully bound for the expected performance of both strategies. in MDPs is important to many AI applications. Our final algorithm switches between the application of Since it is often impossible or intractable to evaluate MDP the optimal policy and the policy with the highest possible algorithms based on a theoretical analysis alone, the International outcome, which can be computed without notable overhead Probabilistic Planning Competition (IPPC) was introduced in the Trial-based Heuristic Tree Search (THTS) framework to allow a comparison based on experimental evaluation. (Keller and Helmert 2013). We show theoretically and empirically The idea is to approximate the quality of an MDP that all algorithms outperform the naïve base approach solver by performing a sequence of runs on a problem instance, that ignores the potential of optimizing evaluation and by using the average of the obtained results as runs in hindsight, and that it pays off to take suboptimal base an approximation of the expected reward.