Related papers: Sparse Quadratic Logistic Regression in Sub-quadra…
Topic models have become popular tools for dimension reduction and exploratory analysis of text data which consists in observed frequencies of a vocabulary of $p$ words in $n$ documents, stored in a $p\times n$ matrix. The main premise is…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…
Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…
This work discusses the problem of sparse signal recovery when there is correlation among the values of non-zero entries. We examine intra-vector correlation in the context of the block sparse model and inter-vector correlation in the…
Structural damage due to excessive loading or environmental degradation typically occurs in localized areas in the absence of collapse. This prior information about the spatial sparseness of structural damage is exploited here by a…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for…
We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…