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Pairwise alignment of DNA sequencing data is a ubiquitous task in bioinformatics and typically represents a heavy computational burden. A standard approach to speed up this task is to compute "sketches" of the DNA reads (typically via hashing-based techniques) that allow the efficient computation of pairwise alignment scores. We propose a rate-distortion framework to study the problem of computing sketches that achieve the optimal tradeoff between sketch size and alignment estimation distortion. We consider the simple setting of i.i.d. error-free sources of length $n$ and introduce a new sketching algorithm called "locational hashing." While standard approaches in the literature based on min-hashes require $B = (1/D) \cdot O\left( \log n \right)$ bits to achieve a distortion $D$, our proposed approach only requires $B = \log^2(1/D) \cdot O(1)$ bits. This can lead to significant computational savings in pairwise alignment estimation.

A popular approach to model compression is to train an inexpensive student model to mimic the class probabilities of a highly accurate but cumbersome teacher model. Surprisingly, this two-step knowledge distillation process often leads to higher accuracy than training the student directly on labeled data. To explain and enhance this phenomenon, we cast knowledge distillation as a semiparametric inference problem with the optimal student model as the target, the unknown Bayes class probabilities as nuisance, and the teacher probabilities as a plug-in nuisance estimate. By adapting modern semiparametric tools, we derive new guarantees for the prediction error of standard distillation and develop two enhancements -- cross-fitting and loss correction -- to mitigate the impact of teacher overfitting and underfitting on student performance. We validate our findings empirically on both tabular and image data and observe consistent improvements from our knowledge distillation enhancements.

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., Comment: NeurIPS 2020

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 $O\left((n+d)\log^2 \left(\frac{nd}{\delta}\right)\right)$ for error probability $\delta$, 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., Comment: Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT) - Special Issue on Sequential, Active, and Reinforcement Learning

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

Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is very often the case that the read data is not sufficiently rich to permit unambiguous reconstruction of the original sequence. While a natural generalization of the perfect assembly formulation to these cases would be to consider a rate-distortion framework, partial assemblies are usually represented in terms of an assembly graph, making the definition of a distortion measure challenging. In this work, we introduce a distortion function for assembly graphs that can be understood as the logarithm of the number of Eulerian cycles in the assembly graph, each of which correspond to a candidate assembly that could have generated the observed reads. We also introduce an algorithm for the construction of an assembly graph and analyze its performance on real genomes., Comment: To be published at ISIT-2016. 11 pages, 10 figures

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide polymorphisms (SNPs). A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes., Comment: 10 pages, 4 figures, Submitted to ISIT 2015

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously.

Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. In this paper, we provide several constructions for a class of vector codes with locality in which the local codes are regenerating codes, that enjoy both advantages. We derive an upper bound on the minimum distance of this class of codes and show that the proposed constructions achieve this bound. The constructions include both the cases where the local regenerating codes correspond to the MSR as well as the MBR point on the storage-repair-bandwidth tradeoff curve of regenerating codes. Also included is a performance comparison of various code constructions for fixed block length and minimum distance., Comment: 44 pages, 7 figures. A class of codes termed as Uniform Rank Accumulation (URA) codes is introduced and a minimum distance bound is derived when the local codes are URA codes. Also, the results of our earlier arXiv submssion(arXiv:1202:2414[cs.IT]) are included in Section 3 of this version

Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such "local" parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code., Comment: 13 pages, Shorter version submitted to ISIT 2012