Related papers: Kurtosis-based projection pursuit for matrix-value…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions,…

Multivariate data is often visualized using linear projections, produced by techniques such as principal component analysis, linear discriminant analysis, and projection pursuit. A problem with projections is that they obscure low and high…

Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…

In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two…

Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985)…

Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique…

We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximised. For a fixed dimension of the…

This paper studies the subspace clustering problem in which data points collected from high-dimensional ambient space lie in a union of linear subspaces. Subspace clustering becomes challenging when the dimension of intersection between…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…

We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…

The problem of obtaining optimal projections for performing discriminant analysis with Gaussian class densities is studied. Unlike in most existing approaches to the problem, the focus of the optimisation is on the multinomial likelihood…

Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance…

Extensive literature exists on how to test for normality, especially for identically and independently distributed (i.i.d) processes. The case of dependent samples has also been addressed, but only for scalar random processes. For this…

The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution.…