We tackle the PAC-Bayesian Domain Adaptation (DA) problem. This arrives when one desires to learn, from a source distribution, a good weighted majority vote (over a set of classifiers) on a different target distribution. In this context, the disagreement between classifiers is known crucial to control. In non-DA supervised setting, a theoretical bound - the C-bound - involves this disagreement and leads to a majority vote learning algorithm: MinCq. In this work, we extend MinCq to DA by taking advantage of an elegant divergence between distribution called the Perturbed Varation (PV). Firstly, justified by a new formulation of the C-bound, we provide to MinCq a target sample labeled thanks to a PV-based self-labeling focused on regions where the source and target marginal distributions are closer. Secondly, we propose an original process for tuning the hyperparameters. Our framework shows very promising results on a toy problem.

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.

To solve the big topic modeling problem, we need to reduce both time and space complexities of batch latent Dirichlet allocation (LDA) algorithms. Although parallel LDA algorithms on the multi-processor architecture have low time and space complexities, their communication costs among processors often scale linearly with the vocabulary size and the number of topics, leading to a serious scalability problem. To reduce the communication complexity among processors for a better scalability, we propose a novel communication-efficient parallel topic modeling architecture based on power law, which consumes orders of magnitude less communication time when the number of topics is large. We combine the proposed communication-efficient parallel architecture with the online belief propagation (OBP) algorithm referred to as POBP for big topic modeling tasks. Extensive empirical results confirm that POBP has the following advantages to solve the big topic modeling problem: 1) high accuracy, 2) communication-efficient, 3) fast speed, and 4) constant memory usage when compared with recent state-of-the-art parallel LDA algorithms on the multi-processor architecture.

Many real-world problem domains generate data in the form of graphs or networks. Examples include social networks (e.g., Facebook), recommendation services (e.g., Netflix or Last.fm), biochemical networks, citation graphs and market analysis. The inferential problem in these settings is often one of link prediction. This problem can be formulated in a static setting where one assumes that a fixed but unknown graph is partially observed, and one wishes to assess whether a pair of nodes that are not known to be linked are in fact linked, given an observed linkage pattern among other nodes. Many real-world graphs are often best modeled, however, as dynamic entities, where links can arise and disappear over time. In the dynamic setting the link prediction problem involves assessing whether two nodes will be linked at time t given the linkage patterns at all previous times. Real-world graphs of current interest are often very large, involving many hundreds of thousands or millions of nodes. The dynamic setting involves sequences of such graphs.

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has gained popularity due to its modular parameterization of joint distributions. Among other properties, copulas provide a recipe for combining flexible models for univariate marginal distributions with parametric families suitable for potentially high dimensional dependence structures. More radically, the extended rank likelihood approach of Hoff (2007) bypasses learning marginal models completely when such information is ancillary to the learning task at hand as in, e.g., standard dimensionality reduction problems or copula parameter estimation. The main idea is to represent data by their observable rank statistics, ignoring any other information from the marginals. Inference is typically done in a Bayesian framework with Gaussian copulas, and it is complicated by the fact this implies sampling within a space where the number of constraints increases quadratically with the number of data points. The result is slow mixing when using off-the-shelf Gibbs sampling. We present an efficient algorithm based on recent advances on constrained Hamiltonian Markov chain Monte Carlo that is simple to implement and does not require paying for a quadratic cost in sample size.

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared l_2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a "gap" between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded.

ABSTRACT Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the source separation problem. This approach has a specific advantage in that it requires the designer to explicitly describe the signal model in addition to any other information or assumptions that go into the problem description. This leads naturally to the idea of informed source separation, where the algorithm design incorporates relevant information about the specific problem. This approach promises to enable researchers to design their own high-quality algorithms that are specifically tailored to the problem at hand. 1. UNDERSTANDING THE PROBLEM To gather information about the physical world, we deploy sensors to make measurements and detect signals. Our sensors, if properly designed, will collect information about the signals of interest. However, very often the signals of interest are comprised of a set of discrete signals, which have been superimposed during propagation, often with signals that are not of interest. Thus our sensors almost invariably detect a mixture of signals--some interesting and some noninteresting.

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in using DPPs defined on continuous spaces. While the discrete-DPP sampler extends formally to the continuous case, computationally, the steps required are not tractable in general. In this paper, we present two efficient DPP sampling schemes that apply to a wide range of kernel functions: one based on low rank approximations via Nyström and random Fourier feature techniques and another based on Gibbs sampling. We demonstrate the utility of continuous DPPs in repulsive mixture modeling and synthesizing human poses spanning activity spaces.

Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected behavior does not hold in general. In fact, counter examples are given that show regularization can increase the degrees of freedom in simple situations, including lasso and ridge regression, which are the most common regularization approaches in use. In such situations, the regularization increases both training error and degrees of freedom, and is thus inherently without merit. On the other hand, two important regularization scenarios are described where the expected reduction in degrees of freedom is indeed guaranteed: (a) all symmetric linear smoothers, and (b) linear regression versus convex constrained linear regression (as in the constrained variant of ridge regression and lasso).

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.