Algorithms For Sparse And Structurally Constrained Discrete Optimization Problems In Bioinformatics And Communications
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Algorithms for Sparse and Structurally Constrained Discrete Optimization Problems in Bioinformatics and Communications
Inference from high-dimensional noisy data, the task encountered in a wide range of applications including those in wireless communications and bioinformatics, is often computationally challenging. Structural constraints that sometimes restrict the space of possible solutions may adversely affect performance of the existing algorithms. Furthermore, when problem variables come from a finite alphabet, such inference problems are often NP-hard. However, one can exploit auxiliary information about the problem's structure to improve accuracy and reduce computational cost of finding a solution to such inference problems. In the first part of this dissertation, we study the setting where an l0-norm constraint is imposed on the solution to the integer least-square problem. We propose the sparsity-aware sphere decoding algorithm for finding a near-optimal solution to this problem, analyze its computational complexity for commonly used alphabets, and propose its fast variant. These algorithms can be successfully applied to a variety of settings, as demonstrated in the application to sparse channel estimation. In the second part, we focus on discrete valued data clustering problems, with observations that have non-zero representation on subsets of features, leading to sparsity in the object-to-object similarity space. Clustering objects with such structural constraints is computationally hard; however, one can leverage inherent sparsity to reduce the computational burden of sub-optimal heuristics. We study the problems of Single Individual Haplotyping (SIH) and Quasispecies Reconstruction (QSR), which involve determination of genetic variations causing disease susceptibility in humans and evolutionary fitness in RNA viruses, respectively. These problems require reconstruction of finite alphabet parental sequences using a library of sparse random samples of their mixtures. Our contribution here is two-fold: (i) development of a binary-constrained alternating minimization approach for SIH and providing first theoretical guarantee on the error performance, and (iii) design of an end-to-end clustering framework for QSR which estimates the number, composition and proportions of the distinct viral sequences. Experimental results with synthetic and biological datasets from state-of-the-art libraries demonstrate efficacy of the proposed algorithms. Respective software implementations, called HapAltMin and QSdpR, have been made available for use to bioinformatics community.
Beyond the Worst-Case Analysis of Algorithms
Author: Tim Roughgarden
language: en
Publisher: Cambridge University Press
Release Date: 2021-01-14
Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.
Encyclopedia of Bioinformatics and Computational Biology
Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases