Related papers: Adaptive Capped Least Squares
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean-square error. The derived models are useful for understanding the algorithm behavior under different environments and can be…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It…
This paper studies the asymptotic properties of the penalized least squares estimator using an adaptive group Lasso penalty for the reduced rank regression. The group Lasso penalty is defined in the way that the regression coefficients…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
In this paper, we address the problem of robust adaptive beamforming of signals received by a linear array. The challenge associated with the beamforming problem is twofold. Firstly, the process requires the inversion of the usually…
Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…
We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding…
Effective containment of spreading processes such as epidemics requires accurate knowledge of several key parameters that govern their dynamics. In this work, we first show that the problem of identifying the underlying parameters of…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph…
This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy.…