Related papers: Improved Estimation of High-dimensional Ising Mode…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Using a multiplicative reparametrization, I show that a subclass of $L_q$ penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a…
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…
Sparse methods are the standard approach to obtain interpretable models with high prediction accuracy. Alternatively, algorithmic ensemble methods can achieve higher prediction accuracy at the cost of loss of interpretability. However, the…
Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Spatial prediction refers to the estimation of unobserved values from spatially distributed observations. Although recent advances have improved the capacity to model diverse observation types, adoption in practice remains limited in…
In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In…
The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression…
We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…
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…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…