Related papers: Optimal Estimator for Linear Regression with Shuff…
In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…
We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…
In the face of dataset shift, model calibration plays a pivotal role in ensuring the reliability of machine learning systems. Calibration error (CE) is an indicator of the alignment between the predicted probabilities and the classifier…
In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. Our approach rests on two main elements: (1) the splitting rules for the…
We consider the problem of estimating the mean of a random variable Y subject to non-ignorable missingness, i.e., where the missingness mechanism depends on Y . We connect the auxiliary proxy variable framework for non-ignorable missingness…
Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis,…
We study the domain adaptation problem with label shift in this work. Under the label shift context, the marginal distribution of the label varies across the training and testing datasets, while the conditional distribution of features…
In studies ranging from clinical medicine to policy research, complete data are usually available from a population $\mathscr{P}$, but the quantity of interest is often sought for a related but different population $\mathscr{Q}$ which only…
With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…
We consider high-dimensional sparse regression problems in which we observe $y = X \beta + z$, where $X$ is an $n \times p$ design matrix and $z$ is an $n$-dimensional vector of independent Gaussian errors, each with variance $\sigma^2$.…
We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a…
We study the unlabeled sensing problem that aims to solve a linear system of equations $A x =\pi(y) $ for an unknown permutation $\pi$. For a generic matrix $A$ and a generic vector $y$, we construct a system of polynomial equations whose…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
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…
We study the problem of collaboratively learning least squares estimates for $m$ agents. Each agent observes a different subset of the features$\unicode{x2013}$e.g., containing data collected from sensors of varying resolution. Our goal is…
In multiclass classification, the goal is to learn how to predict a random label $Y$, valued in $\mathcal{Y}=\{1,\; \ldots,\; K \}$ with $K\geq 3$, based upon observing a r.v. $X$, taking its values in $\mathbb{R}^q$ with $q\geq 1$ say, by…
Labelled data often comes at a high cost as it may require recruiting human labelers or running costly experiments. At the same time, in many practical scenarios, one already has access to a partially labelled, potentially biased dataset…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. This problem is magnified in high-dimensional settings where the number of variables $p$ diverges with the sample size $n$, as well…