Related papers: Recursive Aggregation of Estimators by Mirror Desc…
Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While…
In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15], based on mirror descent (or Bregman gradient descent), to…
A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…
The problem of least squares regression of a $d$-dimensional unknown parameter is considered. A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence…
We propose a new simulation-based estimation method, adversarial estimation, for structural models. The estimator is formulated as the solution to a minimax problem between a generator (which generates simulated observations using the…
In this work, we study an optimizer, Grad-Avg to optimize error functions. We establish the convergence of the sequence of iterates of Grad-Avg mathematically to a minimizer (under boundedness assumption). We apply Grad-Avg along with some…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $\Omega$ such that one is able to…
We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
We consider the problem of multi-class classification and a stochastic opti- mization approach to it. We derive risk bounds for stochastic mirror descent algorithm and provide examples of set geometries that make the use of the algorithm…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…