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We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…
The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…
Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…
In this paper, the parameter estimation problem for a multi-timescale adaptive threshold (MAT) neuronal model is investigated. By manipulating the system dynamics, which comprise of a non-resetting leaky integrator coupled with an adaptive…
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…
In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous It\^{o} semimartingale. We adapt the principle idea of regularization from linear regression to…
Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…
We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the…