Taha

Taha

Hi, I am Taha.

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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

Pages

Posts

And god said let there be dijkstra

18 minute read

Published:

Alright, in this work I want to explain the seminal work of Jittat Fakcharoenphol and Satish Rao in 2006, devising the algorithm of FR-Dijkstra, which is so insightful and meaningful.

Dynamic Approximate Nearest-Neighbor Search in Doubling Metrics

18 minute read

Published:

Well, in this blog post we are going to review several papers and understand the techniques that are utilized in order to tackle several problems related to areas such as nearest neighbor problems, the facility location problem, and so on.

Lewis Weights, Leverage Scores, and Whitening — Chapter 2

12 minute read

Published:

This is the second chapter in my series on Sparsifying Sums of Norms. Chapter 1 set up the general problem and briefly mentioned Lewis weights. In the second post of this series on sparsification of the norm, I want to turn to the $\ell_p$ row sampling paper. I’ll be spending a few posts on this one, because I think it is genuinely revealing on the subject it is worth pondering carefully and going through in some detail. The paper relies heavily on the works of Milman and Talagrand(for example), so I may cover those seminal papers too at some point. At a high level, this paper is a vast generalization of the Johnson–Lindenstrauss lemma, with a few extremely technical steps, but the overall theme is clear and elegant. I especially like how they used Talagrand’s result and intuition, and the way they brought in Lewis weights to pull everything together.

Probabilistic Tree Embeddings and Hierarchical Cut Decompositions

10 minute read

Published:

As part of my effort to understand the broader literature surrounding the areas I hope to work on in the future, I am studying both foundational papers and contemporary developments. Alongside my primary focus on the work of James R. Lee, I plan to read a number of folklore and classical papers that have shaped the modern theory of metric embeddings.

Bukh’s Problem on Coloring Random Subgraphs

5 minute read

Published:

So, assume that we have a graph $G = (V, E)$. By $G_p$ for some $p \in (0,1)$ we mean a subgraph such that the probability of each edge appearing in that subgraph is independent with probability $p$.

publications

readinglist

Sparsifying Sums of Norms

The main theme I am interested in is sparsification and, more broadly, the discretization of continuous structures. One of the most beautiful and recent papers I have come across is the work of James R. Lee and his collaborators on the sparsification of sums of norms. To fully understand the technical aspects of this paper and the related unifying theories, I have designed a reading program consisting of papers and books that cover the history, background, and development of the subject.

Download Paper

$\ell_p$ Row Sampling by Lewis Weights

This paper studies row sampling in $\ell_p$ spaces through the notion of Lewis weights. I am interested in it because Lewis weights are one of the main tools behind several modern sparsification results, including the recent paper of James R. Lee and his collaborators on sparsifying sums of norms.

Download Paper

Future readings:

Metrical task systems on trees via mirror descent and unfair gluing

talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.