Related papers: Active Linear Regression for $\ell_p$ Norms and Be…

We propose a novel active learning strategy for regression, which is model-agnostic, robust against model mismatch, and interpretable. Assuming that a small number of initial samples are available, we derive the optimal training density…

We present an approach that improves the sample complexity for a variety of curve fitting problems, including active learning for linear regression, polynomial regression, and continuous sparse Fourier transforms. In the active linear…

We consider partially-specified optimization problems where the goal is to actively, but efficiently, acquire missing information about the problem in order to solve it. An algorithm designer wishes to solve a linear program (LP), $\max…

We study the problem of entrywise $\ell_1$ low rank approximation. We give the first polynomial time column subset selection-based $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an…

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow…

We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a…

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…

Minimization of the $L_\infty$ norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving…

For overparameterized linear regression with isotropic Gaussian design and minimum-$\ell_p$ interpolator $p\in(1,2]$, we give a unified, high-probability characterization for the scaling of the family of parameter norms $ \\{ \lVert…

We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…

Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…

We derive approximation bounds for learning single neuron models using thresholded gradient descent when both the labels and the covariates are possibly corrupted adversarially. We assume the data follows the model $y =…

Given a real-valued weighted function $f$ on a finite dag, the $L_p$ isotonic regression of $f$, $p \in [0,\infty]$, is unique except when $p \in [0,1] \cup \{\infty\}$. We are interested in determining a ``best'' isotonic regression for $p…

We study $\ell_p$ sampling and frequency moment estimation in a single-pass insertion-only data stream. For $p \in (0,2)$, we present a nearly space-optimal approximate $\ell_p$ sampler that uses $\widetilde{O}(\log n \log(1/\delta))$ bits…

Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in \mathbb{R}^n$, we consider the regression problem with $\ell_\infty$ guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $ \|x'-x^*\|_\infty \leq…

Active learning (AL) for multiple target models aims to reduce labeled data querying while effectively training multiple models concurrently. Existing AL algorithms often rely on iterative model training, which can be computationally…

We present a new active learning algorithm based on nonparametric estimators of the regression function. Our investigation provides probabilistic bounds for the rates of convergence of the generalization error achievable by proposed method…

A framework is introduced for actively and adaptively solving a sequence of machine learning problems, which are changing in bounded manner from one time step to the next. An algorithm is developed that actively queries the labels of the…

We consider the problem of linear regression where the $\ell_2^n$ norm loss (i.e., the usual least squares loss) is replaced by the $\ell_p^n$ norm. We show how to solve such problems up to machine precision in $O^*(n^{|1/2 - 1/p|})$…