Related papers: Imbalanced Mixed Linear Regression
We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix $X \in \mathbb{C}^{d_1\times d_2}$ of rank $r \ll\min(d_1,d_2)$ from incomplete linear observations, solving a sequence of low complexity…
We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable…
The history of the seemingly simple problem of straight line fitting in the presence of both $x$ and $y$ errors has been fraught with misadventure, with statistically ad hoc and poorly tested methods abounding in the literature. The problem…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
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,…
This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective "unsupervised" implies that the number of mixing components is unknown and has to be determined, ideally by data…
Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally…
We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…
We propose a novel multi-dimensional integration algorithm using a machine learning (ML) technique. After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral.…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…
Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and…
In this paper we explore different regression models based on Clusterwise Linear Regression (CLR). CLR aims to find the partition of the data into $k$ clusters, such that linear regressions fitted to each of the clusters minimize overall…
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…
Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…