Govinda M. Kamath

Vivek Bagaria, Govinda M. Kamath, Vasilis Ntranos et al.

Computing the medoid of a large number of points in high-dimensional space is an increasingly common operation in many data science problems. We present an algorithm Med-dit which uses O(n log n) distance evaluations to compute the medoid with high probability. Med-dit is based on a connection with the multi-armed bandit problem. We evaluate the performance of Med-dit empirically on the Netflix-prize and the single-cell RNA-Seq datasets, containing hundreds of thousands of points living in tens of thousands of dimensions, and observe a 5-10x improvement in performance over the current state of the art. Med-dit is available at https://github.com/bagavi/Meddit

Govinda M. Kamath, Tavor Z. Baharav, Ilan Shomorony

Pairwise alignment of DNA sequencing data is a ubiquitous task in bioinformatics and typically represents a heavy computational burden. State-of-the-art approaches to speed up this task use hashing to identify short segments (k-mers) that are shared by pairs of reads, which can then be used to estimate alignment scores. However, when the number of reads is large, accurately estimating alignment scores for all pairs is still very costly. Moreover, in practice, one is only interested in identifying pairs of reads with large alignment scores. In this work, we propose a new approach to pairwise alignment estimation based on two key new ingredients. The first ingredient is to cast the problem of pairwise alignment estimation under a general framework of rank-one crowdsourcing models, where the workers' responses correspond to k-mer hash collisions. These models can be accurately solved via a spectral decomposition of the response matrix. The second ingredient is to utilise a multi-armed bandit algorithm to adaptively refine this spectral estimator only for read pairs that are likely to have large alignments. The resulting algorithm iteratively performs a spectral decomposition of the response matrix for adaptively chosen subsets of the read pairs.

Vivek Bagaria, Tavor Z. Baharav, Govinda M. Kamath et al.

The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive random sampling. The technique converts an optimization problem into a statistical estimation problem which is then solved via multi-armed bandits. We apply this technique to solve the problem of high-dimensional $k$-nearest neighbors, developing an algorithm which we prove is able to identify exact nearest neighbors with high probability. We show that under regularity assumptions on a dataset of $n$ points in $d$-dimensional space, the complexity of our algorithm scales logarithmically with the dimension of the data as $O\left((n+d)\log^2 \left(\frac{nd}δ\right)\right)$ for error probability $δ$, rather than linearly as in exact computation requiring $O(nd)$. We corroborate our theoretical results with numerical simulations, showing that our algorithm outperforms both exact computation and state-of-the-art algorithms such as kGraph, NGT, and LSH on real datasets.