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

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We consider the problem of finding an approximate solution to $\ell_1$ regression while only observing a small number of labels. Given an $n \times d$ unlabeled data matrix $X$, we must choose a small set of $m \ll n$ rows to observe the…

Machine Learning · Computer Science 2021-05-21 Aditya Parulekar , Advait Parulekar , Eric Price

We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity…

Optimization and Control · Mathematics 2026-04-08 Kaito Ito , Alexandre Proutiere

Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…

Data Structures and Algorithms · Computer Science 2020-01-13 Deeksha Adil , Richard Peng , Sushant Sachdeva

We give a simple algorithm to efficiently sample the rows of a matrix while preserving the p-norms of its product with vectors. Given an $n$-by-$d$ matrix $\boldsymbol{\mathit{A}}$, we find with high probability and in input sparsity time…

Data Structures and Algorithms · Computer Science 2014-12-02 Michael B. Cohen , Richard Peng

A coreset of a dataset with $n$ examples and $d$ features is a weighted subset of examples that is sufficient for solving downstream data analytic tasks. Nearly optimal constructions of coresets for least squares and $\ell_p$ linear…

Data Structures and Algorithms · Computer Science 2024-06-05 David P. Woodruff , Taisuke Yasuda

While the state-of-the-art performance on entity resolution (ER) has been achieved by deep learning, its effectiveness depends on large quantities of accurately labeled training data. To alleviate the data labeling burden, Active Learning…

Machine Learning · Computer Science 2020-12-25 Youcef Nafa , Qun Chen , Zhaoqiang Chen , Xingyu Lu , Haiyang He , Tianyi Duan , Zhanhuai Li

We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data, improving upon the previous best algorithm whose sampling complexity has at least cubic dependence on…

Data Structures and Algorithms · Computer Science 2020-06-16 Yi Li , Ruosong Wang , Lin Yang , Hanrui Zhang

We present faster high-accuracy algorithms for computing $\ell_p$-norm minimizing flows. On a graph with $m$ edges, our algorithm can compute a $(1+1/\text{poly}(m))$-approximate unweighted $\ell_p$-norm minimizing flow with…

Data Structures and Algorithms · Computer Science 2020-01-10 Deeksha Adil , Sushant Sachdeva

Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the…

Machine Learning · Computer Science 2024-11-11 Deheng Yuan , Tao Guo , Zhongyi Huang

In this work we consider active local learning: given a query point $x$, and active access to an unlabeled training set $S$, output the prediction $h(x)$ of a near-optimal $h \in H$ using significantly fewer labels than would be needed to…

Machine Learning · Computer Science 2020-09-07 Arturs Backurs , Avrim Blum , Neha Gupta

We propose simple active sampling and reweighting strategies for optimizing min-max fairness that can be applied to any classification or regression model learned via loss minimization. The key intuition behind our approach is to use at…

The Lp regression problem takes as input a matrix $A \in \Real^{n \times d}$, a vector $b \in \Real^n$, and a number $p \in [1,\infty)$, and it returns as output a number ${\cal Z}$ and a vector $x_{opt} \in \Real^d$ such that ${\cal Z} =…

Data Structures and Algorithms · Computer Science 2007-07-13 Anirban Dasgupta , Petros Drineas , Boulos Harb , Ravi Kumar , Michael W. Mahoney

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…

Machine Learning · Computer Science 2020-06-05 Adam Klivans , Pravesh K. Kothari , Raghu Meka

We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…

Machine Learning · Computer Science 2022-06-30 Eric Price , Sandeep Silwal , Samson Zhou

We address the problem of active logistic regression in the realizable setting. It is well known that active learning can require exponentially fewer label queries compared to passive learning, in some cases using $\log \frac{1}{\eps}$…

Machine Learning · Computer Science 2025-04-21 Yihan Zhou , Eric Price , Trung Nguyen

We present algorithms for solving a large class of flow and regression problems on unit weighted graphs to $(1 + 1 / poly(n))$ accuracy in almost-linear time. These problems include $\ell_p$-norm minimizing flow for $p$ large ($p \in…

Data Structures and Algorithms · Computer Science 2019-06-26 Rasmus Kyng , Richard Peng , Sushant Sachdeva , Di Wang

The seminal work of Cohen and Peng introduced Lewis weight sampling to the theoretical computer science community, yielding fast row sampling algorithms for approximating $d$-dimensional subspaces of $\ell_p$ up to $(1+\epsilon)$ error.…

Data Structures and Algorithms · Computer Science 2022-12-20 David P. Woodruff , Taisuke Yasuda

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees…

Data Structures and Algorithms · Computer Science 2024-01-04 David P. Woodruff , Taisuke Yasuda

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…

Methodology · Statistics 2015-11-24 Rong Zhu , Ping Ma , Michael W. Mahoney , Bin Yu

Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…

Data Structures and Algorithms · Computer Science 2014-03-19 David P. Woodruff , Qin Zhang