Learning the distribution of natural images is one of the hardest and most important problems in machine learning. The problem remains open, because the enormous complexity of the structures in natural images spans all length scales. We break down the complexity of the problem and show that the hierarchy of structures in natural images fuels a new class of learning algorithms based on the theory of critical phenomena and stochastic processes. We approach this problem from the perspective of the theory of critical phenomena, which was developed in condensed matter physics to address problems with infinite length-scale fluctuations, and build a framework to integrate the criticality of natural images into a learning algorithm. The problem is broken down by mapping images into a hierarchy of binary images, called bitplanes. In this representation, the top bitplane is critical, having fluctuations in structures over a vast range of scales. The bitplanes below go through a gradual stochastic heating process to disorder. We turn this representation into a directed probabilistic graphical model, transforming the learning problem into the unsupervised learning of the distribution of the critical bitplane and the supervised learning of the conditional distributions for the remaining bitplanes. We learnt the conditional distributions by logistic regression in a convolutional architecture. Conditioned on the critical binary image, this simple architecture can generate large, natural-looking images, with many shades of gray, without the use of hidden units, unprecedented in the studies of natural images. The framework presented here is a major step in bringing criticality and stochastic processes to machine learning and in studying natural image statistics.

Granger causality has been used for the investigation of the inter-dependence structure of the underlying systems of multi-variate time series. In particular, the direct causal effects are commonly estimated by the conditional Granger causality index (CGCI). In the presence of many observed variables and relatively short time series, CGCI may fail because it is based on vector autoregressive models (VAR) involving a large number of coefficients to be estimated. In this work, the VAR is restricted by a scheme that modifies the recently developed method of backward-in-time selection (BTS) of the lagged variables and the CGCI is combined with BTS. Further, the proposed approach is compared favorably to other restricted VAR representations, such as the top-down strategy, the bottom-up strategy, and the least absolute shrinkage and selection operator (LASSO), in terms of sensitivity and specificity of CGCI. This is shown by using simulations of linear and nonlinear, low and high-dimensional systems and different time series lengths. For nonlinear systems, CGCI from the restricted VAR representations are compared with analogous nonlinear causality indices. Further, CGCI in conjunction with BTS and other restricted VAR representations is applied to multi-channel scalp electroencephalogram (EEG) recordings of epileptic patients containing epileptiform discharges. CGCI on the restricted VAR, and BTS in particular, could track the changes in brain connectivity before, during and after epileptiform discharges, which was not possible using the full VAR representation.

In order to properly handle a dangerous Artificially Intelligent (AI) system it is important to understand how the system came to be in such a state. In popular culture (science fiction movies/books) AIs/Robots became self-aware and as a result rebel against humanity and decide to destroy it. While it is one possible scenario, it is probably the least likely path to appearance of dangerous AI. In this work, we survey, classify and analyze a number of circumstances, which might lead to arrival of malicious AI. To the best of our knowledge, this is the first attempt to systematically classify types of pathways leading to malevolent AI. Previous relevant work either surveyed specific goals/meta-rules which might lead to malevolent behavior in AIs (\"Ozkural, 2014) or reviewed specific undesirable behaviors AGIs can exhibit at different stages of its development (Alexey Turchin, July 10 2015, July 10, 2015).

Recognising literary characters in various narrative texts is challenging both from the literary and technical perspective. From the literary viewpoint, the meaning of the term "character" leaves space to various interpretations. From the technical perspective, literary texts contain a lot of data about emotions, social life or inner life of the characters, while they are very thin on technical, straightforward messages. To infer the character type from literary texts might pose problems even to the human readers [4]. Interactions between literary characters contain rich social networks.

We present a semi-supervised learning algorithm for learning discrete factor analysis models with arbitrary structure on the latent variables. Our algorithm assumes that every latent variable has an "anchor", an observed variable with only that latent variable as its parent. Given such anchors, we show that it is possible to consistently recover moments of the latent variables and use these moments to learn complete models. We also introduce a new technique for improving the robustness of method-of-moment algorithms by optimizing over the marginal polytope or its relaxations. We evaluate our algorithm using two real-world tasks, tag prediction on questions from the Stack Overflow website and medical diagnosis in an emergency department.

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutions to the problem and has revamped its practical applications in machine learning. In this paper, we exploit the widely used kernel methods and provide a family of provably positive definite kernels based on the Sliced Wasserstein distance and demonstrate the benefits of these kernels in a variety of learning tasks. Our work provides a new perspective on the application of optimal transport flavored distances through kernel methods in machine learning tasks.

There are two main different setups for statistical learning: centralized learning and distributed learning. In the centralized learning, which has been studied extensively, all data is available at a centralized location. In the distributed learning, data is stored in multiple terminals. The distributed learning setup has attracted significant recent research interests as the data involved in learning is increasingly large in volume and might be stored in multiple terminals [1], [2], [3], [4]. For the distributed learning, each terminal either has a few observations about all variables, or has full knowledge about a subset of variables (all observations about a subset of variables). The first scenario is relatively easier since each terminal can still make its own local inference without even communicating with each other, while communication between terminals is essential for the second scenario. In this paper, we focus on the more challenging second scenario. In particular, we consider a distributed parameter estimation problem.

Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and convergent variational algorithms, such as dual decomposition, exist. In this work, we generalize dual decomposition to a generic power sum inference task, which includes marginal MAP, along with pure marginalization and MAP, as special cases. Our method is based on a block coordinate descent algorithm on a new convex decomposition bound, that is guaranteed to converge monotonically, and can be parallelized efficiently. We demonstrate our approach on marginal MAP queries defined on real-world problems from the UAI approximate inference challenge, showing that our framework is faster and more reliable than previous methods.

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a theoretical analysis of the number of required samples for a given approximation error, leading to both upper and lower bounds that are based solely on the eigenvalues of the associated integral operator and match up to logarithmic terms. In particular, we show that the upper bound may be obtained from independent and identically distributed samples from a specific non-uniform distribution, while the lower bound if valid for any set of points. Applying our results to kernel-based quadrature, while our results are fairly general, we recover known upper and lower bounds for the special cases of Sobolev spaces. Moreover, our results extend to the more general problem of full function approximations (beyond simply computing an integral), with results in L2- and L$\infty$-norm that match known results for special cases. Applying our results to random features, we show an improvement of the number of random features needed to preserve the generalization guarantees for learning with Lipschitz-continuous losses.

A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank of the Jacobian in the limit of large parameters. The limit is described by the tropical morphism; a piecewise linear map with pieces corresponding to slicings of the visible matrix by the normal fan of the hidden matrix. We obtain combinatorial conditions under which the model has the expected dimension, equal to the minimum of the number of natural parameters and the dimension of the ambient probability simplex. Additionally, we prove that the binary restricted Boltzmann machine always has the expected dimension.