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Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme…

A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new…

Image based localization is one of the important problems in computer vision due to its wide applicability in robotics, augmented reality, and autonomous systems. There is a rich set of methods described in the literature how to…

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both…

In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…

Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…

Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery…

We study sparse principal components analysis in high dimensions, where $p$ (the number of variables) can be much larger than $n$ (the number of observations), and analyze the problem of estimating the subspace spanned by the principal…

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…

There are two main approaches in compressed sensing: the geometric approach and the combinatorial approach. In this paper we introduce an information theoretic approach and use results from the theory of Huffman codes to construct a…

Predictive pattern mining is an approach used to construct prediction models when the input is represented by structured data, such as sets, graphs, and sequences. The main idea behind predictive pattern mining is to build a prediction…

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…

In the literature, two series of models have been proposed to address prediction problems including classification and regression. Simple models, such as generalized linear models, have ordinary performance but strong interpretability on a…

High resolution microarrays and second-generation sequencing platforms are powerful tools to investigate genome-wide alterations in DNA copy number, methylation and gene expression associated with a disease. An integrated genomic profiling…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…

Clinical and epidemiological studies encode participant information in multivariate vectors with mixed type variables on continuous, truncated, ordinal, and binary scales. Semiparametric Gaussian Copula (SGC) assumes that observed data is…

Significant pattern mining is a fundamental task in mining transactional data, requiring to identify patterns significantly associated with the value of a given feature, the target. In several applications, such as biomedicine, basket…

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…

Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks…