Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus (LC) approach which allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops. Furthermore, we also design an efficient rejection-free MCMC scheme for approximating the full series. The main novelty underlying our design is in utilizing the concept of cycle basis, which provides an efficient decomposition of the generalized loops. In essence, the proposed MCMC schemes run on transformed GM built upon the non-trivial BP solution, and our experiments show that this synthesis of BP and MCMC outperforms both direct MCMC and bare BP schemes.

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectation-maximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.

Over the past few years, neural networks have re-emerged as powerful machine-learning models, yielding state-of-the-art results in fields such as image recognition and speech processing. More recently, neural network models started to be applied also to textual natural language signals, again with very promising results. This tutorial surveys neural network models from the perspective of natural language processing research, in an attempt to bring natural-language researchers up to speed with the neural techniques. The tutorial covers input encoding for natural language tasks, feed-forward networks, convolutional networks, recurrent networks and recursive networks, as well as the computation graph abstraction for automatic gradient computation.

We introduce an Embarrassingly Parallel Search (EPS) method for solving constraint problems in parallel, and we show that this method matches or even outperforms state-of-the-art algorithms on a number of problems using various computing infrastructures. EPS is a simple method in which a master decomposes the problem into many disjoint subproblems which are then solved independently by workers. Our approach has three advantages: it is an efficient method; it involves almost no communication or synchronization between workers; and its implementation is made easy because the master and the workers rely on an underlying constraint solver, but does not require to modify it. This paper describes the method, and its applications to various constraint problems (satisfaction, enumeration, optimization). We show that our method can be adapted to different underlying solvers (Gecode, Choco2, OR-tools) on different computing infrastructures (multi-core, data centers, cloud computing). The experiments cover unsatisfiable, enumeration and optimization problems, but do not cover first solution search because it makes the results hard to analyze. The same variability can be observed for optimization problems, but at a lesser extent because the optimality proof is required. EPS offers good average performance, and matches or outperforms other available parallel implementations of Gecode as well as some solvers portfolios. Moreover, we perform an in-depth analysis of the various factors that make this approach efficient as well as the anomalies that can occur. Last, we show that the decomposition is a key component for efficiency and load balancing.

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits efficient inference. Specifically, we impose a bipartite structure on the GGM and govern the hidden variables by truncated normal distributions. The nonlinearity of the model is revealed by its connection to rectified linear unit (ReLU) neural networks. Meanwhile, thanks to the bipartite structure and appealing properties of truncated normals, we are able to train the models efficiently using contrastive divergence. We consider three output constructs, accounting for real-valued, binary and count data. We further extend the model to deep constructions and show that deep models can be used for unsupervised pre-training of rectifier neural networks. Extensive experimental results are provided to validate the proposed models and demonstrate their superiority over competing models.

Abstract--A number of important applied problems in engineering, finance and medicine can be formulated as a problem of anomaly detection based on a one-class classification. A classical approach to this problem is to describe a normal state using a one-class support vector machine. Then to detect anomalies we quantify a distance from a new observation to the constructed description of the normal class. In this paper we present a new approach to one-class classification. We formulate a new problem statement and a corresponding algorithm that allow taking into account privileged information during the training phase. We evaluate performance of the proposed approach using synthetic datasets, as well as the publicly available Microsoft Malware Classification Challenge dataset. Anomaly detection refers to the problem of finding patterns in data that do not conform to an expected behaviour.

Empirical Risk Minimization (ERM) is a standard technique in machine learning, where a model is selected by minimizing a loss function over constraint set. When the training dataset consists of private information, it is natural to use a differentially private ERM algorithm, and this problem has been the subject of a long line of work started with Chaudhuri and Monteleoni 2008. A private ERM algorithm outputs an approximate minimizer of the loss function and its error can be measured as the difference from the optimal value of the loss function. When the constraint set is arbitrary, the required error bounds are fairly well understood \cite{BassilyST14}. In this work, we show that the geometric properties of the constraint set can be used to derive significantly better results. Specifically, we show that a differentially private version of Mirror Descent leads to error bounds of the form $\tilde{O}(G_{\mathcal{C}}/n)$ for a lipschitz loss function, improving on the $\tilde{O}(\sqrt{p}/n)$ bounds in Bassily, Smith and Thakurta 2014. Here $p$ is the dimensionality of the problem, $n$ is the number of data points in the training set, and $G_{\mathcal{C}}$ denotes the Gaussian width of the constraint set that we optimize over. We show similar improvements for strongly convex functions, and for smooth functions. In addition, we show that when the loss function is Lipschitz with respect to the $\ell_1$ norm and $\mathcal{C}$ is $\ell_1$-bounded, a differentially private version of the Frank-Wolfe algorithm gives error bounds of the form $\tilde{O}(n^{-2/3})$. This captures the important and common case of sparse linear regression (LASSO), when the data $x_i$ satisfies $|x_i|_{\infty} \leq 1$ and we optimize over the $\ell_1$ ball. We show new lower bounds for this setting, that together with known bounds, imply that all our upper bounds are tight.

Data Science for Internet of Things provides a concise introduction to the application of Predictive learning algorithms to Internet of Things. This mini book is based on my teaching at Oxford University, UPM(University of Madrid) and also working with consulting clients.We first outline the key issues involved and then explores three key areas: Stream processing, Deep Learning and Sensor fusion for IoT. The book is also a recommended material for the Stanford University course: Building a Successful Business for the Internet of Things and Mobile (BUS20) $11.99

A product from Japan created quite the stir at Consumer Electronics Show in Las Vegas and CEATEC JAPAN in Tokyo this year. The "harmony" of clothing analysis, artificial intelligence (AI), and robotics blend together to produce a "fully automatic clothes folding machine." Japan technological alliance "seven dreamers laboratories' is the developer. The product details have been released in various places, so I won't get into that, but as the name says, "It's a robot that folds clothes. No further explanation is needed." The company announced a partnership with Panasonic (TSE:6752) and Daiwa House (TSE:1925) last year, and together established the joint venture Seven Dreamers Laundroid with plans to begin sales by reservation for their first machine "Laundroid 1" in March of 2017. The developer, Seven Dreamers, announced on November 14th the securement of 6 billion yen (around $60 million US) in funds from SBI Investment, in addition to Panasonic and Daiwa House. The shareholding ratios and payment date remain undisclosed. The concept began in 2005, and with the realization of "folding" from 2013, Laundroid was born. I heard from Seven Dreamers CEO Shin Sakane about the road it took to get here. I came today with the idea of asking straight out, "What happened to make robots fold the laundry?" Well, to be straight, "It's now possible to recognize clothes using artificial intelligence," is maybe the simplest answer I can give. Let's go through the process. How did the idea first come to you? Before that, first permit me to talk a little about what criteria the Seven Dreamers esteem. For us, there are three criterion for "Things that have not been realized yet but could change our lives, and also enrich them." The technological hurdles are high and our policy is to clear them. You've made something that sets high hurdles. Since first coming up with the idea, I was thinking about different markets to satisfy all the criteria. Looking around we see many products targeted at men. Starting now and into the future, 'women', 'the elderly', and'children' are the keywords that will become important. After thinking, the idea that maybe the answer lies within the home came to me and, while I don't usually talk with my wife about work, I casually mentioned it to her. What do you wish you had? She came back just as fast, "Of course, it has to be a machine that folds the laundry.

To produce a regression analysis of inference that can be justified or trustworthy in the sense that helpful. The term in the statistical methods that generate a linear the best estimator is not bias (best linear unbiased estimator) abbreviated BLUE. Then there are some other things that are also important to note, in which the data to be processed, must meet certain requirements. All terms or phases of the classical assumptions that must be met, in order to build a regression model that could be accounted for. Thus, the need to test that assumption is intended to meet some of the elements of the accuracy of the parameter estimator is not biased to reflect the efficient level of analysis results are consistent so that the regression equation can be trusted.