Related papers: Focused Weighted-Average Least Squares Estimator

RANSAC and its variants are widely used for robust estimation, however, they commonly follow a greedy approach to finding the highest scoring model while ignoring other model hypotheses. In contrast, Iteratively Reweighted Least Squares…

Federated active learning (FAL) seeks to reduce annotation cost under privacy constraints, yet its effectiveness degrades in realistic settings with severe global class imbalance and highly heterogeneous clients. We conduct a systematic…

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of least squares (LS) problems $\min_x\|b-Ax\|_2$, where $A…

We present a novel weighted $\ell_2$ projection method for estimating autocovariance sequences and spectral density functions from reversible Markov chains. Berg and Song (2023) introduced a least-squares shape-constrained estimation…

Orthogonal least square (OLS) is an important sparse signal recovery algorithm for compressive sensing, which enjoys superior probability of success over other well-known recovery algorithms under conditions of correlated measurement…

Few-shot classification involves identifying new categories using a limited number of labeled samples. Current few-shot classification methods based on local descriptors primarily leverage underlying consistent features across visible and…

We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…

In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…

The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a…

In some supervised learning settings, the practitioner might have additional information on the features used for prediction. We propose a new method which leverages this additional information for better prediction. The method, which we…

Fisher Discriminant Analysis (FDA) is a subspace learning method which minimizes and maximizes the intra- and inter-class scatters of data, respectively. Although, in FDA, all the pairs of classes are treated the same way, some classes are…

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…

In this work, we develop a distributed least squares approximation (DLSA) method that is able to solve a large family of regression problems (e.g., linear regression, logistic regression, and Cox's model) on a distributed system. By…

We study the problem of exact support recovery: given an (unknown) vector $\theta \in \left\{-1,0,1\right\}^D$, we are given access to the noisy measurement $$ y = X\theta + \omega,$$ where $X \in \mathbb{R}^{N \times D}$ is a (known)…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

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…

The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

This work is about recovering an analysis-sparse vector, i.e. sparse vector in some transform domain, from under-sampled measurements. In real-world applications, there often exist random analysis-sparse vectors whose distribution in the…