arXiv subjects

Abishek Sankararaman

Publications and source records attributed to Abishek Sankararaman.

23 records · Page 2Linked to original sources

arXiv2019

ComHapDet: A Spatial Community Detection Algorithm for Haplotype Assembly

Background: Haplotypes, the ordered lists of single nucleotide variations that distinguish chromosomal sequences from their homologous pairs, may reveal an individual's susceptibility to hereditary and complex diseases and affect how our bodies respond to therapeutic drugs. Reconstructing haplotypes of an individual from short sequencing reads is an NP-hard problem that becomes even more challenging in the case of polyploids. While increasing lengths of sequencing reads and insert sizes {\color{black} helps improve accuracy of reconstruction}, it also exacerbates computational complexity of the haplotype assembly task. This has motivated the pursuit of algorithmic frameworks capable of accurate yet efficient assembly of haplotypes from high-throughput sequencing data. Results: We propose a novel graphical representation of sequencing reads and pose the haplotype assembly problem as an instance of community detection on a spatial random graph. To this end, we construct a graph where each read is a node with an unknown community label associating the read with the haplotype it samples. Haplotype reconstruction can then be thought of as a two-step procedure: first, one recovers the community labels on the nodes (i.e., the reads), and then uses the estimated labels to assemble the haplotypes. Based on this observation, we propose ComHapDet - a novel assembly algorithm for diploid and ployploid haplotypes which allows both bialleleic and multi-allelic variants. Conclusions: Performance of the proposed algorithm is benchmarked on simulated as well as experimental data obtained by sequencing Chromosome $5$ of tetraploid biallelic \emph{Solanum-Tuberosum} (Potato). The results demonstrate the efficacy of the proposed method and that it compares favorably with the existing techniques.

cs.SI↗

arXiv2019

Social Learning in Multi Agent Multi Armed Bandits

In this paper, we introduce a distributed version of the classical stochastic Multi-Arm Bandit (MAB) problem. Our setting consists of a large number of agents $n$ that collaboratively and simultaneously solve the same instance of $K$ armed MAB to minimize the average cumulative regret over all agents. The agents can communicate and collaborate among each other \emph{only} through a pairwise asynchronous gossip based protocol that exchange a limited number of bits. In our model, agents at each point decide on (i) which arm to play, (ii) whether to, and if so (iii) what and whom to communicate with. Agents in our model are decentralized, namely their actions only depend on their observed history in the past. We develop a novel algorithm in which agents, whenever they choose, communicate only arm-ids and not samples, with another agent chosen uniformly and independently at random. The per-agent regret scaling achieved by our algorithm is $O \left( \frac{\lceil\frac{K}{n}\rceil+\log(n)}Δ \log(T) + \frac{\log^3(n) \log \log(n)}{Δ^2} \right)$. Furthermore, any agent in our algorithm communicates only a total of $Θ(\log(T))$ times over a time interval of $T$. We compare our results to two benchmarks - one where there is no communication among agents and one corresponding to complete interaction. We show both theoretically and empirically, that our algorithm experiences a significant reduction both in per-agent regret when compared to the case when agents do not collaborate and in communication complexity when compared to the full interaction setting which requires $T$ communication attempts by an agent over $T$ arm pulls.

cs.LG↗

arXiv2019

Interference Queueing Networks on Grids

Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the processor sharing type,with the service rate in each queue slowed down, when the neighboring queues have a larger workload. The interactions are translation invariant in space and is neither of the Jackson Networks type, nor of the mean-field type. Coupling and percolation techniques are first used to show that this dynamics has well defined trajectories. Coupling from the past techniques are then proposed to build its minimal stationary regime. The rate conservation principle of Palm calculus is then used to identify the stability condition of this system, where the notion of stability is appropriately defined for an infinite dimensional process. We show that the identified condition is also necessary in certain special cases and conjecture it to be true in all cases. Remarkably, the rate conservation principle also provides a closed form expression for the mean queue size. When the stability condition holds, this minimal solution is the unique translation invariant stationary regime. In addition, there exists a range of small initial conditions for which the dynamics is attracted to the minimal regime. Nevertheless, there exists another range of larger though finite initial conditions for which the dynamics diverges, even though stability criterion holds.

math.PR↗

arXiv2016

Spatial Birth-Death Wireless Networks

We propose and study a novel continuous space-time model for wireless networks which takes into account the stochastic interactions in both space through interference and in time due to randomness in traffic. Our model consists of an interacting particle birth-death dynamics incorporating information-theoretic spectrum sharing. Roughly speaking, particles (or more generally wireless links) arrive according to a Poisson Point Process on space-time, and stay for a duration governed by the local configuration of points present and then exit the network after completion of a file transfer. We analyze this particle dynamics to derive an explicit condition for time ergodicity (i.e. stability) which is tight. We also prove that when the dynamics is ergodic, the steady-state point process of links (or particles) exhibits a form statistical clustering. Based on the clustering, we propose a conjecture which we leverage to derive approximations, bounds and asymptotics on performance characteristics such as delay and mean number of links per unit-space in the stationary regime. The mathematical analysis is combined with discrete event simulation to study the performance of this type of networks.

cs.IT↗

arXiv2016

Performance-Oriented Association in Large Cellular Networks with Technology Diversity

The development of mobile virtual network operators, where multiple wireless technologies (e.g. 3G and 4G) or operators with non-overlapping bandwidths are pooled and shared is expected to provide enhanced service with broader coverage, without incurring additional infrastructure cost. However, their emergence poses an unsolved question on how to harness such a technology and bandwidth diversity. This paper addresses one of the simplest questions in this class, namely, the issue of associating each mobile to one of those bandwidths. Intriguingly, this association issue is intrinsically distinct from those in traditional networks. We first propose a generic stochastic geometry model lending itself to analyzing a wide class of association policies exploiting various information on the network topology, e.g. received pilot powers and fading values. This model firstly paves the way for tailoring and designing an optimal association scheme to maximize any performance metric of interest (e.g. the probability of coverage) subject to the information known about the network. In this class of optimal association, we prove a result that the performance improves as the information known about the network increases. Secondly, this model is used to quantify the performance of any arbitrary association policy and not just the optimal association policy. We propose a simple policy called the Max-Ratio which is not-parametric, i.e. it dispenses with the statistical knowledge of base station deployments in stochastic geometry models. We also prove that this simple policy is optimal in a certain limiting regime of the wireless environment. Through simulations, we provide insights into (i) a practical compromise between performance gain and cost of estimating information and; (ii) the selection of association schemes under environments with different propagation models, i.e. path-loss exponents.

cs.IT↗