Search Results for author: Purnamrita Sarkar

Found 27 papers, 3 papers with code

On hyperparameter tuning in general clustering problemsm

no code implementations ICML 2020 Xinjie Fan, Yuguang Yue, Purnamrita Sarkar, Y. X. Rachel Wang

Tuning hyperparameters for unsupervised learning problems is difficult in general due to the lack of ground truth for validation.

Clustering Community Detection +1

Keep or toss? A nonparametric score to evaluate solutions for noisy ICA

no code implementations16 Jan 2024 Syamantak Kumar, Purnamrita Sarkar, Peter Bickel, Derek Bean

Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a mixture of signals, with little knowledge about the source signals or the mixing process.

blind source separation

An Exponentially Increasing Step-size for Parameter Estimation in Statistical Models

no code implementations16 May 2022 Nhat Ho, Tongzheng Ren, Sujay Sanghavi, Purnamrita Sarkar, Rachel Ward

Therefore, the total computational complexity of the EGD algorithm is \emph{optimal} and exponentially cheaper than that of the GD for solving parameter estimation in non-regular statistical models while being comparable to that of the GD in regular statistical settings.

Bootstrapping the error of Oja's algorithm

no code implementations NeurIPS 2021 Robert Lunde, Purnamrita Sarkar, Rachel Ward

We consider the problem of quantifying uncertainty for the estimation error of the leading eigenvector from Oja's algorithm for streaming principal component analysis, where the data are generated IID from some unknown distribution.

Trading off Accuracy for Speedup: Multiplier Bootstraps for Subgraph Counts

no code implementations14 Sep 2020 Qiaohui Lin, Robert Lunde, Purnamrita Sarkar

We propose a new class of multiplier bootstraps for count functionals, ranging from a fast, approximate linear bootstrap tailored to sparse, massive graphs to a quadratic bootstrap procedure that offers refined accuracy for smaller, denser graphs.


A Robust Spectral Clustering Algorithm for Sub-Gaussian Mixture Models with Outliers

no code implementations16 Dec 2019 Prateek R. Srivastava, Purnamrita Sarkar, Grani A. Hanasusanto

Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers.


A Unified Framework for Tuning Hyperparameters in Clustering Problems

no code implementations17 Oct 2019 Xinjie Fan, Yuguang Yue, Purnamrita Sarkar, Y. X. Rachel Wang

In this paper, we provide a framework with provable guarantees for selecting hyperparameters in a number of distinct models.

Clustering Community Detection +1

Mean Field for the Stochastic Blockmodel: Optimization Landscape and Convergence Issues

no code implementations NeurIPS 2018 Soumendu Sundar Mukherjee, Purnamrita Sarkar, Y. X. Rachel Wang, Bowei Yan

Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures.

Bayesian Inference Community Detection

Hierarchical community detection by recursive partitioning

no code implementations2 Oct 2018 Tianxi Li, Lihua Lei, Sharmodeep Bhattacharyya, Koen Van den Berge, Purnamrita Sarkar, Peter J. Bickel, Elizaveta Levina

This can be done with a simple top-down recursive partitioning algorithm, starting with a single community and separating the nodes into two communities by spectral clustering repeatedly, until a stopping rule suggests there are no further communities.

Clustering Community Detection +1

Overlapping Clustering Models, and One (class) SVM to Bind Them All

no code implementations NeurIPS 2018 Xueyu Mao, Purnamrita Sarkar, Deepayan Chakrabarti

People belong to multiple communities, words belong to multiple topics, and books cover multiple genres; overlapping clusters are commonplace.

Clustering Topic Models

Convergence of Gradient EM on Multi-component Mixture of Gaussians

no code implementations NeurIPS 2017 Bowei Yan, Mingzhang Yin, Purnamrita Sarkar

In this paper, we study convergence properties of the gradient variant of Expectation-Maximization algorithm~\cite{lange1995gradient} for Gaussian Mixture Models for arbitrary number of clusters and mixing coefficients.

Learning Theory

Estimating Mixed Memberships with Sharp Eigenvector Deviations

no code implementations1 Sep 2017 Xueyu Mao, Purnamrita Sarkar, Deepayan Chakrabarti

We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community.

Community Detection

Network modelling of topological domains using Hi-C data

2 code implementations30 Jul 2017 Y. X. Rachel Wang, Purnamrita Sarkar, Oana Ursu, Anshul Kundaje, Peter J. Bickel

However, one of the drawbacks of community detection is that most methods take exchangeability of the nodes in the network for granted; whereas the nodes in this case, i. e. the positions on the chromosomes, are not exchangeable.

Applications Genomics

Provable Estimation of the Number of Blocks in Block Models

no code implementations24 May 2017 Bowei Yan, Purnamrita Sarkar, Xiuyuan Cheng

Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications.

Clustering Community Detection

Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture

no code implementations23 May 2017 Bowei Yan, Mingzhang Yin, Purnamrita Sarkar

In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients.

Learning Theory

Covariate Regularized Community Detection in Sparse Graphs

1 code implementation10 Jul 2016 Bowei Yan, Purnamrita Sarkar

In statistics, an emerging body of work has been focused on combining information from both the edges in the network and the node covariates to infer community memberships.

Clustering Community Detection

On clustering network-valued data

1 code implementation NeurIPS 2017 Soumendu Sundar Mukherjee, Purnamrita Sarkar, Lizhen Lin

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community.

Clustering Community Detection

On Robustness of Kernel Clustering

no code implementations NeurIPS 2016 Bowei Yan, Purnamrita Sarkar

Clustering is one of the most important unsupervised problems in machine learning and statistics.


Hypothesis Testing for Automated Community Detection in Networks

no code implementations12 Nov 2013 Peter J. Bickel, Purnamrita Sarkar

Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web.

Clustering Community Detection +1

Role of normalization in spectral clustering for stochastic blockmodels

no code implementations5 Oct 2013 Purnamrita Sarkar, Peter J. Bickel

The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors.


Active Learning for Crowd-Sourced Databases

no code implementations17 Sep 2012 Barzan Mozafari, Purnamrita Sarkar, Michael J. Franklin, Michael. I. Jordan, Samuel Madden

Based on this observation, we present two new active learning algorithms to combine humans and algorithms together in a crowd-sourced database.

Active Learning BIG-bench Machine Learning

Nonparametric Link Prediction in Dynamic Networks

no code implementations27 Jun 2012 Purnamrita Sarkar, Deepayan Chakrabarti, Michael Jordan

We propose a non-parametric link prediction algorithm for a sequence of graph snapshots over time.

Link Prediction

Nonparametric Link Prediction in Large Scale Dynamic Networks

no code implementations6 Sep 2011 Purnamrita Sarkar, Deepayan Chakrabarti, Michael Jordan

We propose a nonparametric approach to link prediction in large-scale dynamic networks.

Link Prediction

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