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Nesterov’s Acceleration

Published:

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

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

projects

Mini Search Engine

Published:

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

Sparse Regression and Support Recovery bounds for Orthogonal Matching Pursuit

Published:

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

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