Related papers: Exponential convergence of recursive least squares…

We propose a recursive Bayesian estimation procedure for multivariate autoregressive models with exogenous inputs based on message passing in a factor graph. Unlike recursive least-squares, our method produces full posterior distributions…

In this paper, we focus on regression estimation in both the inductive and the transductive case. We assume that we are given a set of features (which can be a base of functions, but not necessarily). We begin by giving a deviation…

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…

Inference is a versatile tool that underlies scientific discovery, machine learning, and everyday decision-making: it describes how an agent updates a probability distribution as partial information is acquired from multiple measurements,…

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…

Randomized iterative algorithms have recently been proposed to solve large-scale linear systems. In this paper, we present a simple randomized extended block Kaczmarz algorithm that exponentially converges in the mean square to the unique…

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…

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…

In this paper we study the problem of driving an agent to an unknown source whose location is estimated in real-time by a recursive optimization algorithm. The optimization criterion is subject to a least-square cost function constructed…

We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…

This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…

We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which…

Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We extend asymptotic results from…

A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…