no code implementations • 15 Dec 2022 • Daniel Alabi, Pravesh K. Kothari, Pranay Tankala, Prayaag Venkat, Fred Zhang

We prove a new lower bound on differentially private covariance estimation to show that the dependence on the condition number $\kappa$ in the above sample bound is also tight.

no code implementations • 23 Nov 2022 • Aravind Gollakota, Adam R. Klivans, Pravesh K. Kothari

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to require that the learner succeed whenever the unknown distribution passes the corresponding test.

no code implementations • 22 Jun 2022 • Misha Ivkov, Pravesh K. Kothari

For any $\alpha > 0$, our algorithm takes input a sample $Y \subseteq \mathbb{R}^d$ of size $n\geq d^{\mathsf{poly}(1/\alpha)}$ obtained by adversarially corrupting an $(1-\alpha)n$ points in an i. i. d.

no code implementations • 7 Dec 2021 • Pravesh K. Kothari, Pasin Manurangsi, Ameya Velingker

Prior works obtained private robust algorithms for mean estimation of subgaussian distributions with bounded covariance.

no code implementations • 5 Jul 2021 • Sumegha Garg, Pravesh K. Kothari, Pengda Liu, Ran Raz

We show that any learning algorithm for the learning problem corresponding to $M$, with error, requires either a memory of size at least $\Omega\left(\frac{k \cdot \ell}{\varepsilon} \right)$, or at least $2^{\Omega(r)}$ samples.

no code implementations • 3 Dec 2020 • Ainesh Bakshi, Ilias Diakonikolas, He Jia, Daniel M. Kane, Pravesh K. Kothari, Santosh S. Vempala

We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions.

no code implementations • 12 Nov 2020 • Tommaso d'Orsi, Pravesh K. Kothari, Gleb Novikov, David Steurer

Despite a long history of prior works, including explicit studies of perturbation resilience, the best known algorithmic guarantees for Sparse PCA are fragile and break down under small adversarial perturbations.

no code implementations • 12 Feb 2020 • Ainesh Bakshi, Pravesh K. Kothari

As a result, in addition to Gaussians, our algorithm applies to the uniform distribution on the hypercube and $q$-ary cubes and arbitrary product distributions with subgaussian marginals.

no code implementations • NeurIPS 2019 • Sushrut Karmalkar, Adam R. Klivans, Pravesh K. Kothari

To complement our result, we prove that the anti-concentration assumption on the inliers is information-theoretically necessary.

no code implementations • 13 Feb 2019 • Pravesh K. Kothari, Roi Livni

We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels.

no code implementations • 8 Mar 2018 • Adam Klivans, Pravesh K. Kothari, Raghu Meka

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels.

no code implementations • 5 Mar 2018 • Sanjeev Arora, Wei Hu, Pravesh K. Kothari

A first line of attack in exploratory data analysis is data visualization, i. e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable.

no code implementations • 30 Nov 2017 • Pravesh K. Kothari, David Steurer

We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers.

no code implementations • 20 Nov 2017 • Pravesh K. Kothari, Jacob Steinhardt

As an immediate corollary, for any $\gamma > 0$, we obtain an efficient algorithm for learning the means of a mixture of $k$ arbitrary \Poincare distributions in $\mathbb{R}^d$ in time $d^{O(1/\gamma)}$ so long as the means have separation $\Omega(k^{\gamma})$.

no code implementations • 12 Sep 2017 • Pravesh K. Kothari, Roi Livni

We introduce \emph{refutation complexity}, a natural computational analog of Rademacher complexity of a Boolean concept class and show that it exactly characterizes the sample complexity of \emph{efficient} agnostic learning.

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