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Non-asymptotic rate for Random Shuffling for Quadratic functions

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This article is in continuation of my previous blog, and discusses about a section of the work by Jeffery Z. HaoChen and Suvrit Sra 2018, in which the authors come up with a non-asymptotic rate of $\mathcal{O}\left(\frac{1}{T^2} + \frac{n^3}{T^3} \right)$ for Random Shuffling Stochastic algorithm which is strictly better than that of SGD. Read more

Bias-Variance Trade-offs for Averaged SGD in Least Mean Squares

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This article is on the work by Défossez and Bach 2014, in which the authors develop an operator view point for analyzing Averaged SGD updates to show the Bias-Variance Trade-off and provide tight convergence rates of Least Mean Squared problem. Read more

Random Reshuffling converges to a smaller neighborhood than SGD

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This article is on the recent work by Ying et. al. 2018, in which the authors show that SGD with Random Reshuffling outperforms independent sampling with replacement. Read more

Nesterov’s Acceleration

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This post contains a summary and survey of the Nesterov’s accelerated gradient descent method and some insightful implications that can be derived from it. We analyze the simple convex quadratic case and have a close look at the dynamics of the error vectors. Read more

Some resources to start with Fundamentals of Machine Learning

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With a number of courses, books and reading material out there here is a list of some which I personally find useful for building a fundamental understanding in Machine Learning. Read more

A survey on Large Scale Optimization

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This post contains a summary and survey of the theoretical understandings of Large Scale Optimization by referring some talks, papers, and lectures that I have come across in the recent. Read more

Mini Search Engine

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We used data structures like Hash Tables, Balanced Trees in order to design a text search engine that gives the frequency of the searched word in a given folder of files. Read more

Modelling Economic Policy Uncertainty Index using Text Classification

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Using Soft Margin Kernel Support Vector Machine to classify newspaper articles to model an Economic Policy Uncertainty Index for India. Read more

Some Approaches of Building Recommendation Systems

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The project aims at using different recommendation methods for different kinds of real world data like rating matrices, images and text, using Deep Learning and Optimization. Read more

A case study of Empirical Bayes in Recommendation system

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We provide a formulation of empirical bayes described by Atchadé (2011) to tune the hyperparameters of priors used in Bayesian set up of collaborative filter. Read more

Approximating Matrices for Recommendation

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The work is in submission at WSDM 2019. Visit this page in November 2018 for details. Read more

Sparse Regression and Support Recovery bounds for Orthogonal Matching Pursuit

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We study the problem of sparse regression where the goal is to learn a sparse vector that best optimizes a given objective function. Under the assumption that the objective function satisfies restricted strong convexity (RSC), we analyze Orthogonal Matching Pursuit (OMP) and obtain support recovery result as well as a tight generalization error bound for OMP. Furthermore, we obtain lower bounds for OMP, showing that both our results on support recovery and generalization error are tight up to logarithmic factors. To the best of our knowledge, these support recovery and generalization bounds are the first such matching upper and lower bounds (up to logarithmic factors) for any sparse regression algorithm under the RSC assumption. Read more

A case study of empirical Bayes in a user-movie recommendation system

Arabin Kumar Dey, Raghav Somani & Sreangsu Acharyya
Communications in Statistics: Case Studies, Data Analysis and Applications Volume 3, 2017 - Issue 1-2, 2017

We provide a formulation of empirical Bayes Atchadé to tune the hyperparameters of priors used in Bayesian set-up of collaborative filter. Read more

Links : [paper], [arXiv]

Support Recovery for Orthogonal Matching Pursuit: Upper and Lower bounds

Raghav Somani, Chirag Gupta, Prateek Jain & Praneeth Netrapalli
Neural Information Processing Systems (NIPS), 2018

The paper has been accepted for Spotlight presentation (168/4856 submissions ≈ 3.5% Acceptance Rate). Read more