The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming languages and in Descripion Logics. In this paper, we illustrate the work we have done in this research field by presenting a probabilistic semantics for description logics and reasoning and learning algorithms. In particular, we present in detail the system TRILL P, which computes the probability of queries w.r.t. probabilistic knowledge bases, which has been implemented in Prolog. Note: An extended abstract / full version of a paper accepted to be presented at the Doctoral Consortium of the 30th International Conference on Logic Programming (ICLP 2014), July 19-22, Vienna, Austria

Machine learning (ML) is a powerful data-driven method for learning patterns in high-dimensional spaces via induction, and has had widespread success in many fields including more recent applications in quantum chemistry and materials science [1-9]. Here we are interested in applications of ML to construction of density functionals [10-14], which have focused so far on approximating the kinetic energy (KE) of non-interacting electrons. An accurate, general approximation to this could make orbital-free DFT a practical reality. However, ML methods have been developed within the areas of statistics and computer science, and have been applied to a huge variety of data, including neuroscience, image and text processing, and robotics [15]. Thus, they are quite general and have not been tailored to account for specific details of the quantum problem.

We analyze the problem of sequential probability assignment for binary outcomes with side information and logarithmic loss, where regret---or, redundancy---is measured with respect to a (possibly infinite) class of experts. We provide upper and lower bounds for minimax regret in terms of sequential complexities of the class. These complexities were recently shown to give matching (up to logarithmic factors) upper and lower bounds for sequential prediction with general convex Lipschitz loss functions (Rakhlin and Sridharan, 2015). To deal with unbounded gradients of the logarithmic loss, we present a new analysis that employs a sequential chaining technique with a Bernstein-type bound. The introduced complexities are intrinsic to the problem of sequential probability assignment, as illustrated by our lower bound. We also consider an example of a large class of experts parametrized by vectors in a high-dimensional Euclidean ball (or a Hilbert ball). The typical discretization approach fails, while our techniques give a non-trivial bound. For this problem we also present an algorithm based on regularization with a self-concordant barrier. This algorithm is of an independent interest, as it requires a bound on the function values rather than gradients.

In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine learning as a coding and dimensionality reduction problem, and further proposed a simple unsupervised dimensionality reduction method, entitled deep distributed random samplings (DDRS). In this paper, we further extend it to supervised learning incrementally. The key idea here is to incorporate label information into the coding process by reformulating that each center in DDRS has multiple output units indicating which class the center belongs to. The supervised learning method seems somewhat similar with random forests (\cite{breiman2001random}), here we emphasize their differences as follows. (i) Each layer of our method considers the relationship between part of the data points in training data with all training data points, while random forests focus on building each decision tree on only part of training data points independently. (ii) Our method builds gradually-narrowed network by sampling less and less data points, while random forests builds gradually-narrowed network by merging subclasses. (iii) Our method is trained more straightforward from bottom layer to top layer, while random forests build each tree from top layer to bottom layer by splitting. (iv) Our method encodes output targets implicitly in sparse codes, while random forests encode output targets by remembering the class attributes of the activated nodes. Therefore, our method is a simpler, more straightforward, and maybe a better alternative choice, though both methods use two very basic elements---randomization and nearest neighbor optimization---as the core. This preprint is used to protect the incremental idea from (\cite{zhang2014nonlinear,zhang2014nonlinear2}). Full empirical evaluation will be announced carefully later.

Determining the 3D structures of biological molecules is a key problem for both biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising technique for structure estimation which relies heavily on computational methods to reconstruct 3D structures from 2D images. This paper introduces the challenging Cryo-EM density estimation problem as a novel application for stochastic optimization techniques. Structure discovery is formulated as MAP estimation in a probabilistic latent-variable model, resulting in an optimization problem to which an array of seven stochastic optimization methods are applied. The methods are tested on both real and synthetic data, with some methods recovering reasonable structures in less than one epoch from a random initialization. Complex quasi-Newton methods are found to converge more slowly than simple gradient-based methods, but all stochastic methods are found to converge to similar optima. This method represents a major improvement over existing methods as it is significantly faster and is able to converge from a random initialization.

We present the Bayesian Echo Chamber, a new Bayesian generative model for social interaction data. By modeling the evolution of people's language usage over time, this model discovers latent influence relationships between them. Unlike previous work on inferring influence, which has primarily focused on simple temporal dynamics evidenced via turn-taking behavior, our model captures more nuanced influence relationships, evidenced via linguistic accommodation patterns in interaction content. The model, which is based on a discrete analog of the multivariate Hawkes process, permits a fully Bayesian inference algorithm. We validate our model's ability to discover latent influence patterns using transcripts of arguments heard by the US Supreme Court and the movie "12 Angry Men."

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring some more Bayesian machine learning techniques to adaptive filtering.

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer to our approach as {\em kernel probabilistic programming}. We illustrate it on synthetic data, and show how it can be used for nonparametric structural equation models, with an application to causal inference.

We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences combine data effectively from cross-animal studies to make joint inferences about behavioral decision making that are not possible with the data from a single animal. We focus on data collection, machine learning, and prediction in the representative and long-studied invertebrate nervous system of the European medicinal leech. Acknowledging the computational intractability of the general problem of identifying correspondences among neurons, we introduce efficient computational procedures for matching neurons across animals. The methods include techniques that adjust for missing cells or additional cells in the different data sets that may reflect biological or experimental variation.

Mastering the game of Go has remained a long standing challenge to the field of AI. Modern computer Go systems rely on processing millions of possible future positions to play well, but intuitively a stronger and more 'humanlike' way to play the game would be to rely on pattern recognition abilities rather then brute force computation. Following this sentiment, we train deep convolutional neural networks to play Go by training them to predict the moves made by expert Go players. To solve this problem we introduce a number of novel techniques, including a method of tying weights in the network to 'hard code' symmetries that are expect to exist in the target function, and demonstrate in an ablation study they considerably improve performance. Our final networks are able to achieve move prediction accuracies of 41.1% and 44.4% on two different Go datasets, surpassing previous state of the art on this task by significant margins. Additionally, while previous move prediction programs have not yielded strong Go playing programs, we show that the networks trained in this work acquired high levels of skill. Our convolutional neural networks can consistently defeat the well known Go program GNU Go, indicating it is state of the art among programs that do not use Monte Carlo Tree Search. It is also able to win some games against state of the art Go playing program Fuego while using a fraction of the play time. This success at playing Go indicates high level principles of the game were learned.