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no code implementations • 29 Jun 2021 • Moses Charikar, Lunjia Hu

Given $d$-dimensional data points, we show an efficient algorithm that finds an explainable clustering whose $k$-means cost is at most $k^{1 - 2/d}\,\mathrm{poly}(d\log k)$ times the minimum cost achievable by a clustering without the explainability constraint, assuming $k, d\ge 2$.

no code implementations • NeurIPS 2020 • Nima Anari, Moses Charikar, Kirankumar Shiragur, Aaron Sidford

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation.

no code implementations • 6 Apr 2020 • Nima Anari, Moses Charikar, Kirankumar Shiragur, Aaron Sidford

For each problem we provide polynomial time algorithms that given $n$ i. i. d.\ samples from a discrete distribution, achieve an approximation factor of $\exp\left(-O(\sqrt{n} \log n) \right)$, improving upon the previous best-known bound achievable in polynomial time of $\exp(-O(n^{2/3} \log n))$ (Charikar, Shiragur and Sidford, 2019).

1 code implementation • NeurIPS 2019 • Moses Charikar, Kirankumar Shiragur, Aaron Sidford

In this paper we provide a general framework for estimating symmetric properties of distributions from i. i. d.

no code implementations • 21 May 2019 • Moses Charikar, Kirankumar Shiragur, Aaron Sidford

Generalizing work of Acharya et al. 2016 on the utility of approximate PML we show that our algorithm provides a nearly linear time universal plug-in estimator for all symmetric functions up to accuracy $\epsilon = \Omega(n^{-0. 166})$.

no code implementations • 31 Oct 2018 • Hongyang Zhang, Vatsal Sharan, Moses Charikar, YIngyu Liang

We consider the tensor completion problem of predicting the missing entries of a tensor.

1 code implementation • 1 Oct 2018 • Paul Liu, Austin Benson, Moses Charikar

However, there are no algorithms for fast estimation of temporal motifs counts; moreover, we show that even counting simple temporal star motifs is NP-complete.

Social and Information Networks Data Structures and Algorithms

no code implementations • 7 Aug 2018 • Moses Charikar, Vaggos Chatziafratis, Rad Niazadeh

Hierarchical Clustering (HC) is a widely studied problem in exploratory data analysis, usually tackled by simple agglomerative procedures like average-linkage, single-linkage or complete-linkage.

no code implementations • ICML 2018 • Vaggos Chatziafratis, Rad Niazadeh, Moses Charikar

For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by the set of features available to the algorithm.

no code implementations • 15 Mar 2017 • Jacob Steinhardt, Moses Charikar, Gregory Valiant

We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data.

no code implementations • 18 Feb 2017 • Yuchen Zhang, Percy Liang, Moses Charikar

We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization.

no code implementations • 7 Nov 2016 • Moses Charikar, Jacob Steinhardt, Gregory Valiant

For example, given a dataset of $n$ points for which an unknown subset of $\alpha n$ points are drawn from a distribution of interest, and no assumptions are made about the remaining $(1-\alpha)n$ points, is it possible to return a list of $\operatorname{poly}(1/\alpha)$ answers, one of which is correct?

no code implementations • NeurIPS 2016 • Jacob Steinhardt, Gregory Valiant, Moses Charikar

We consider a crowdsourcing model in which $n$ workers are asked to rate the quality of $n$ items previously generated by other workers.

no code implementations • 7 Mar 2015 • Pranjal Awasthi, Moses Charikar, Kevin A. Lai, Andrej Risteski

We resolve an open question from (Christiano, 2014b) posed in COLT'14 regarding the optimal dependency of the regret achievable for online local learning on the size of the label set.

no code implementations • 18 Aug 2014 • Pranjal Awasthi, Afonso S. Bandeira, Moses Charikar, Ravishankar Krishnaswamy, Soledad Villar, Rachel Ward

Under the same distributional model, the $k$-means LP relaxation fails to recover such clusters at separation as large as $\Delta = 4$.

no code implementations • 14 Nov 2013 • Aditya Bhaskara, Moses Charikar, Ankur Moitra, Aravindan Vijayaraghavan

We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension).

no code implementations • 30 Apr 2013 • Aditya Bhaskara, Moses Charikar, Aravindan Vijayaraghavan

We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: we prove that given a tensor whose decomposition satisfies a robust form of Kruskal's rank condition, it is possible to approximately recover the decomposition if the tensor is known up to a sufficiently small (inverse polynomial) error.

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