Related papers: Linear Regression from 1-bit Quantized Data
Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…
Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…
Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
We consider covariance estimation of any subgaussian distribution from finitely many i.i.d. samples that are quantized to one bit of information per entry. Recent work has shown that a reliable estimator can be constructed if uniformly…
A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
This work is concerned with the problem of recovering high-dimensional signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of low-complexity from a small number of quantized measurements. We propose to estimate the signals…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…
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…
Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…
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…