Related papers: Unbiased estimators for random design regression
We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. Let…
Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…
We consider the problem of performing linear regression over a stream of $d$-dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without…
In this work, we propose a mean-squared error-based risk that enables the comparison and optimization of estimators of squared calibration errors in practical settings. Improving the calibration of classifiers is crucial for enhancing the…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
Supervised learning under measurement constraints is a common challenge in statistical and machine learning. In many applications, despite extensive design points, acquiring responses for all points is often impractical due to resource…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
When the experimental data set is contaminated, we usually employ robust alternatives to common location and scale estimators such as the sample median and Hodges-Lehmann estimators for location and the sample median absolute deviation and…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Recommender systems widely use implicit feedback such as click data because of its general availability. Although the presence of clicks signals the users' preference to some extent, the lack of such clicks does not necessarily indicate a…
Nonparametric estimators of a regression function with circular response and Rd-valued predictor are considered in this work. Local polynomial type estimators are proposed and studied. Expressions for their asymptotic biases and variances…
Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units…
In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular…
We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…
We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The…
We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and…
We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…
We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm…
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…