Related papers: Adaptive Capped Least Squares
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
This paper presents novel adaptive reduced-rank filtering algorithms based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that…
This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…
This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…
High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…
In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…
We present an adaptive approach for robust learning from corrupted training sets. We identify corrupted and non-corrupted samples with latent Bernoulli variables and thus formulate the learning problem as maximization of the likelihood…
The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…
Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
In the famous least sum of trimmed squares (LTS) of residuals estimator (Rousseeuw (1984)), residuals are first squared and then trimmed. In this article, we first trim residuals - using a depth trimming scheme - and then square the rest of…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
Many biomedical studies collect high-dimensional medical imaging data to identify biomarkers for the detection, diagnosis, and treatment of human diseases. Consequently, it is crucial to develop accurate models that can predict a wide range…
We present the Residual Quadratic Programming Active-Set Subspace (ResQPASS) method that solves large-scale linear least-squares problems with bound constraints on the variables. The problem is solved by creating a series of small problems…
Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world…
It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…