Re: Chandra's PhD defense

[Devansh Gupta]

Hi all,

A kind reminder for Chandra’s defense on March 26th!

Best,

Devansh

On Thu, Mar 19, 2026 at 3:10 PM Chandrasekhar Mukherjee <chandrasekha...@gmail.com> wrote:

Hey everyone, I just wanted to share that my defense will take place next Thursday (March 26) at 12: 00-1: 30 pm in GCS 302C at the theory lunch and your presence will be deeply appreciated! I am truly grateful to all your support throughout my

Hey everyone, 

I just wanted to share that my defense will take place next Thursday (March 26) at 12:00-1:30 pm in GCS 302C at the theory lunch and your presence will be deeply appreciated! I am truly grateful to all your support throughout my PhD journey. 

Please find the title and the abstract of the presentation below. 

Best regards,

Chandra

Title: On the Interplay of Structure and Learnability in Unsupervised Learning

Abstract: 

A central problem in unsupervised learning is recovering latent group structure from unlabeled data — a task that is information-theoretically impossible without structural assumptions relating the data to its hidden groups (clusters). This thesis advances the state of the art on two fronts: resolving open algorithmic questions within well-established structural assumptions, and proposing new assumptions for data modalities that existing frameworks fail to adequately capture.

In the first part, we study community recovery in the stochastic block model (SBM), one of the most well-studied random graph models with latent clusters. Motivated by real-world networks, we focus on recovering large clusters in the presence of arbitrarily small clusters. We achieve the best known guarantee on this problem, with matching lower bounds in some regimes, and also design the first completely parameter-free algorithm to accomplish this task. To achieve this goal, we design simple spectral algorithms motivated by conjectures of Van Vu and Emmanuel Abbe that several auxiliary steps in existing spectral algorithms are artifacts of proof techniques. Our results partially resolve these conjectures.

In the second part, we observe the existence of multi-layered structures in real-world data with latent clusters. On a high level, we observe that each latent cluster consists of central regions that are both dense and well-separable, surrounded by sparser regions that cause cluster overlaps and impede the performance of clustering algorithms. Our observations lead to two applications. 

i) A balanced ranking framework called relative centrality that is able to extract easily separable parts of similarity graphs of genomics data with latent clusters, thereby facilitating higher-quality clustering.

ii) A generic clustering enhancement framework CoreSPECT that boosts the performance of simple algorithms like K-Means to match that of state-of-the-art manifold clustering algorithms, while requiring only 2--5\% of the runtime on a wide range of genomics and vision datasets. The framework also boosts the performance of HDBSCAN to be competitive with the state-of-the-art, without requiring information about true number of clusters and any hyperparameter tuning. 

We further support the frameworks with extensive simulation as well as theoretical guarantees.

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[Devansh Gupta]

Hi all,

Please find the link attached below: https://usc.zoom.us/j/6555952212.

Best,

Devansh