Standard Monte Carlo simulation needs prohibitive time to achieve reasonable estimations. for untractable integrals (i.e. multidimensional integrals and/or intergals with complex integrand forms). Several statistical technique, called variance reduction methods, are used to reduce the simulation time. In this note, we propose a generalization of the well known antithetic variate method. Princip...

In this work we focus on a sentence retrieval task to present a comparison between Language Modeling based on a multi-variate Bernoulli distribution and Language Modeling based on the popular multinomial models. Nowadays, a view on text generation as a multiple Bernoulli process is not predominant in Language Modeling for Information Retrieval but we show how the characteristics of the task are...

A nonparametric factor analysis framework is developed for tensor-variate data. The dictionary elements (factor loadings) are inferred as tensors, as opposed to vectors. Our tensor-factor analysis (TFA) framework is developed in the context of the beta-process factor analysis (BPFA) using a nonparametric tensor decomposition for each dictionary element. We extend the multiplicative gamma prior ...

(1.1) { Γ(α)Ψ(α,α−γ+1;ξ) }−1 exp(−ξv)v(1+v), v > 0, (1.2) respectively, where α > 0, β > 0, ξ > 0, −∞ < γ,λ < ∞, 1F1, and Ψ are confluent hypergeometric functions. These distributions are extensions of Gamma and Beta distributions, and for α < 1 (and certain values of λ and γ) yield bimodal distributions on finite and infinite ranges, respectively. These distributions are used (i) in the Bayesi...

It is becoming increasingly important to learn from a partially-observed random matrix and predict its missing elements. We assume that the entire matrix is a single sample drawn from a matrix-variate t distribution and suggest a matrixvariate tmodel (MVTM) to predict those missing elements. We show that MVTM generalizes a range of known probabilistic models, and automatically performs model se...

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-ord...

In this note we estimate the asymptotic rates for the L2-error decay and the storage cost when approximating 2πperiodic, d-variate functions from isotropic and mixed Sobolev classes by the recent hierarchical tensor format as introduced by Hackbusch and Kühn. To this end, we survey some results on bilinear approximation due to Temlyakov. The approach taken in this paper improves and generalizes...

A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we enumerate sets of permutations whose consecutive-minima polygons satisfy specific geometric conditions. We deal with 2-variate and 3-variate generating functions.

Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one is able to recover the graphs and covariance matrices with a single random m...

Our previous human fMRI study found brain activations correlated with tactile stickiness perception using the uni-variate general linear model (GLM) (Yeon et al., 2017). Here, we conducted an in-depth investigation on neural correlates of sticky sensations by employing a multivoxel pattern analysis (MVPA) on the same dataset. In particular, we statistically compared multi-variate neural activit...