Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming Interface (API) requests, poses serious concerns over the the guarantees of the estimates. In this work, we focus on making reliable statistical inference with limited API crawls. Based on regenerative properties of the random walks, we propose an unbiased estimator for the aggregated sum of functions over edges and proved the connection between variance of the estimator and spectral gap. In order to facilitate Bayesian inference on the true value of the estimator, we derive the approximate posterior distribution of the estimate. Later the proposed ideas are validated with numerical experiments on inference problems in real-world networks.

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* + \epsilon \\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$ design matrix with independent subgaussian row vectors, $\epsilon \in \mathbb{R}^f$ is a noise vector and $W$ is a mean zero $f \times m$ random noise matrix with independent subgaussian column vectors, independent of $X_0$ and $\epsilon$. This model is significantly different from those analyzed in the literature in the sense that we allow the measurement error for each covariate to be a dependent vector across its $f$ observations. Such error structures appear in the science literature when modeling the trial-to-trial fluctuations in response strength shared across a set of neurons. Under sparsity and restrictive eigenvalue type of conditions, we show that one is able to recover a sparse vector $\beta^* \in \mathbb{R}^m$ from the model given a single observation matrix $X$ and the response vector $y$. We establish consistency in estimating $\beta^*$ and obtain the rates of convergence in the $\ell_q$ norm, where $q = 1, 2$ for the Lasso-type estimator, and for $q \in [1, 2]$ for a Dantzig-type conic programming estimator. We show error bounds which approach that of the regular Lasso and the Dantzig selector in case the errors in $W$ are tending to 0.

Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as digital communications. Anti-sparse regularization can be naturally expressed through an $\ell_{\infty}$-norm penalty. This paper derives a probabilistic formulation of such representations. A new probability distribution, referred to as the democratic prior, is first introduced. Its main properties as well as three random variate generators for this distribution are derived. Then this probability distribution is used as a prior to promote anti-sparsity in a Gaussian linear inverse problem, yielding a fully Bayesian formulation of anti-sparse coding. Two Markov chain Monte Carlo (MCMC) algorithms are proposed to generate samples according to the posterior distribution. The first one is a standard Gibbs sampler. The second one uses Metropolis-Hastings moves that exploit the proximity mapping of the log-posterior distribution. These samples are used to approximate maximum a posteriori and minimum mean square error estimators of both parameters and hyperparameters. Simulations on synthetic data illustrate the performances of the two proposed samplers, for both complete and over-complete dictionaries. All results are compared to the recent deterministic variational FITRA algorithm.

The purpose of this paper is to provide further understanding into the structure of the sequential allocation ("stochastic multi-armed bandit", or MAB) problem by establishing probability one finite horizon bounds and convergence rates for the sample (or "pseudo") regret associated with two simple classes of allocation policies $\pi$. For any slowly increasing function $g$, subject to mild regularity constraints, we construct two policies (the $g$-Forcing, and the $g$-Inflated Sample Mean) that achieve a measure of regret of order $ O(g(n))$ almost surely as $n \to \infty$, bound from above and below. Additionally, almost sure upper and lower bounds on the remainder term are established. In the constructions herein, the function $g$ effectively controls the "exploration" of the classical "exploration/exploitation" tradeoff.

Nowadays, saturation-based reasoners for the OWL EL profile of the Web Ontology Language are able to handle large ontologies such as SNOMED very efficiently. However, it is currently unclear how saturation-based reasoning procedures can be extended to very expressive Description Logics such as SROIQ--the logical underpinning of the current and second iteration of the Web Ontology Language. Tableau-based procedures, on the other hand, are not limited to specific Description Logic languages or OWL profiles, but even highly optimised tableau-based reasoners might not be efficient enough to handle large ontologies such as SNOMED. In this paper, we present an approach for tightly coupling tableau- and saturation-based procedures that we implement in the OWL DL reasoner Konclude. Our detailed evaluation shows that this combination significantly improves the reasoning performance for a wide range of ontologies.

Model selection is an important challenge, if one works with data sets containing many predictors. Finding relevant variables helps to understand better the problem and improves statistical inference. In t he literature there are many methods solving such problems. One of them is empiri cal risk minimization with the penalty, for instance Lasso (Tibshir ani, 1996). The main characteristic of this procedure is an ability to selec t relevant predictors and estimate unknown parameters simultaneously. In th e paper we apply these ideas to the pairwise ranking problem (ordinal r egression) that 1 relates to predicting or guessing the ordering between obje cts on the basis of their observed predictors. The problem of ranking has num erous applications in practice, for instance in information retrieval, banking or quality control.

We propose Macau, a powerful and flexible Bayesian factorization method for heterogeneous data. Our model can factorize any set of entities and relations that can be represented by a relational model, including tensors and also multiple relations for each entity. Macau can also incorporate side information, specifically entity and relation features, which are crucial for predicting sparsely observed relations. Macau scales to millions of entity instances, hundred millions of observations, and sparse entity features with millions of dimensions. To achieve the scale up, we specially designed sampling procedure for entity and relation features that relies primarily on noise injection in linear regressions. We show performance and advanced features of Macau in a set of experiments, including challenging drug-protein activity prediction task.

Transfer learning is a recent field of machine learning research that aims to resolve the challenge of dealing with insufficient training data in the domain of interest. This is a particular issue with traditional deep neural networks where a large amount of training data is needed. Recently, StochasticNets was proposed to take advantage of sparse connectivity in order to decrease the number of parameters that needs to be learned, which in turn may relax training data size requirements. In this paper, we study the efficacy of transfer learning on StochasticNet frameworks. Experimental results show ~7% improvement on StochasticNet performance when the transfer learning is applied in training step.

We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the controller wishes to select a population to sample, with the goal of sampling from a population that optimizes some "score" function of its distribution, e.g., maximizing the expected sum of outcomes or minimizing variability. We define a class of \textit{Uniformly Fast (UF)} sampling policies and show, under mild regularity conditions, that there is an asymptotic lower bound for the expected total number of sub-optimal population activations. Then, we provide sufficient conditions under which a UCB policy is UF and asymptotically optimal, since it attains this lower bound. Explicit solutions are provided for a number of examples of interest, including general score functionals on unconstrained Pareto distributions (of potentially infinite mean), and uniform distributions of unknown support. Additional results on bandits of Normal distributions are also provided.

We develop asymptotically optimal policies for the multi armed bandit (MAB), problem, under a cost constraint. This model is applicable in situations where each sample (or activation) from a population (bandit) incurs a known bandit dependent cost. Successive samples from each population are iid random variables with unknown distribution. The objective is to design a feasible policy for deciding from which population to sample from, so as to maximize the expected sum of outcomes of $n$ total samples or equivalently to minimize the regret due to lack on information on sample distributions, For this problem we consider the class of feasible uniformly fast (f-UF) convergent policies, that satisfy the cost constraint sample-path wise. We first establish a necessary asymptotic lower bound for the rate of increase of the regret function of f-UF policies. Then we construct a class of f-UF policies and provide conditions under which they are asymptotically optimal within the class of f-UF policies, achieving this asymptotic lower bound. At the end we provide the explicit form of such policies for the case in which the unknown distributions are Normal with unknown means and known variances.