arXiv subjects

Haris Vikalo

Publications and source records attributed to Haris Vikalo.

62 records · Page 4Linked to original sources

arXiv2016

Sparse recovery via Orthogonal Least-Squares under presence of Noise

We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result also improves the existing guarantees for Orthogonal Matching Pursuit (OMP) algorithm. In addition, This framework is employed to provide probabilistic guarantees for the case that the coefficient matrix is drawn at random according to Gaussian or Bernoulli distribution where we exploit some concentration properties. It is shown that under certain conditions, OLS recovers the true support in $k$ iterations with high probability. This in turn demonstrates that ${\cal O}\left(k\log m\right)$ measurements is sufficient for exact recovery of sparse signals via OLS.

stat.ML↗

arXiv2016

Sparse Linear Regression via Generalized Orthogonal Least-Squares

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedily find an approximate sparse solution. In this paper, a generalization of Orthogonal Least-Squares which relies on a recursive relation between the components of the optimal solution to select L features at each step and solve the resulting overdetermined system of equations is proposed. Simulation results demonstrate that the generalized OLS algorithm is computationally efficient and achieves performance superior to that of existing greedy algorithms broadly used in the literature.

stat.ML↗

arXiv2015

End-to-End Optimization of High Throughput DNA Sequencing

At the core of high throughput DNA sequencing platforms lies a bio-physical surface process that results in a random geometry of clusters of homogenous short DNA fragments typically hundreds of base pairs long - bridge amplification. The statistical properties of this random process and length of the fragments are critical as they affect the information that can be subsequently extracted, i.e., density of successfully inferred DNA fragment reads. The ensemble of overlapping DNA fragment reads are then used to computationally reconstruct the much longer target genome sequence, e.g, ranging from hundreds of thousands to billions of base pairs. The success of the reconstruction in turn depends on having a sufficiently large ensemble of DNA fragments that are sufficiently long. In this paper using stochastic geometry we model and optimize the end-to-end process linking and partially controlling the statistics of the physical processes to the success of the computational step. This provides, for the first time, a framework capturing salient features of such sequencing platforms that can be used to study cost, performance or sensitivity of the sequencing process.

q-bio.GN↗

arXiv2015

A Perspective on Future Research Directions in Information Theory

Information theory is rapidly approaching its 70th birthday. What are promising future directions for research in information theory? Where will information theory be having the most impact in 10-20 years? What new and emerging areas are ripe for the most impact, of the sort that information theory has had on the telecommunications industry over the last 60 years? How should the IEEE Information Theory Society promote high-risk new research directions and broaden the reach of information theory, while continuing to be true to its ideals and insisting on the intellectual rigor that makes its breakthroughs so powerful? These are some of the questions that an ad hoc committee (composed of the present authors) explored over the past two years. We have discussed and debated these questions, and solicited detailed inputs from experts in fields including genomics, biology, economics, and neuroscience. This report is the result of these discussions.

cs.IT↗

arXiv2015

Designing Optimal Mortality Risk Prediction Scores that Preserve Clinical Knowledge

Many in-hospital mortality risk prediction scores dichotomize predictive variables to simplify the score calculation. However, hard thresholding in these additive stepwise scores of the form "add x points if variable v is above/below threshold t" may lead to critical failures. In this paper, we seek to develop risk prediction scores that preserve clinical knowledge embedded in features and structure of the existing additive stepwise scores while addressing limitations caused by variable dichotomization. To this end, we propose a novel score structure that relies on a transformation of predictive variables by means of nonlinear logistic functions facilitating smooth differentiation between critical and normal values of the variables. We develop an optimization framework for inferring parameters of the logistic functions for a given patient population via cyclic block coordinate descent. The parameters may readily be updated as the patient population and standards of care evolve. We tested the proposed methodology on two populations: (1) brain trauma patients admitted to the intensive care unit of the Dell Children's Medical Center of Central Texas between 2007 and 2012, and (2) adult ICU patient data from the MIMIC II database. The results are compared with those obtained by the widely used PRISM III and SOFA scores. The prediction power of a score is evaluated using area under ROC curve, Youden's index, and precision-recall balance in a cross-validation study. The results demonstrate that the new framework enables significant performance improvements over PRISM III and SOFA in terms of all three criteria.

stat.ML↗

arXiv2014

Haplotype Assembly: An Information Theoretic View

This paper studies the haplotype assembly problem from an information theoretic perspective. A haplotype is a sequence of nucleotide bases on a chromosome, often conveniently represented by a binary string, that differ from the bases in the corresponding positions on the other chromosome in a homologous pair. Information about the order of bases in a genome is readily inferred using short reads provided by high-throughput DNA sequencing technologies. In this paper, the recovery of the target pair of haplotype sequences using short reads is rephrased as a joint source-channel coding problem. Two messages, representing haplotypes and chromosome memberships of reads, are encoded and transmitted over a channel with erasures and errors, where the channel model reflects salient features of high-throughput sequencing. The focus of this paper is on the required number of reads for reliable haplotype reconstruction, and both the necessary and sufficient conditions are presented with order-wise optimal bounds.

cs.IT↗

arXiv2014

Iterative Learning for Reference-Guided DNA Sequence Assembly from Short Reads: Algorithms and Limits of Performance

Recent emergence of next-generation DNA sequencing technology has enabled acquisition of genetic information at unprecedented scales. In order to determine the genetic blueprint of an organism, sequencing platforms typically employ so-called shotgun sequencing strategy to oversample the target genome with a library of relatively short overlapping reads. The order of nucleotides in the reads is determined by processing the acquired noisy signals generated by the sequencing instrument. Assembly of a genome from potentially erroneous short reads is a computationally daunting task even in the scenario where a reference genome exists. Errors and gaps in the reference, and perfect repeat regions in the target, further render the assembly challenging and cause inaccuracies. In this paper, we formulate the reference-guided sequence assembly problem as the inference of the genome sequence on a bipartite graph and solve it using a message-passing algorithm. The proposed algorithm can be interpreted as the well-known classical belief propagation scheme under a certain prior. Unlike existing state-of-the-art methods, the proposed algorithm combines the information provided by the reads without needing to know reliability of the short reads (so-called quality scores). Relation of the message-passing algorithm to a provably convergent power iteration scheme is discussed. To evaluate and benchmark the performance of the proposed technique, we find an analytical expression for the probability of error of a genie-aided maximum a posteriori (MAP) decision scheme. Results on both simulated and experimental data demonstrate that the proposed message-passing algorithm outperforms commonly used state-of-the-art tools, and it nearly achieves the performance of the aforementioned MAP decision scheme.

q-bio.GN↗

arXiv2014

Sparsity-aware sphere decoding: Algorithms and complexity analysis

Integer least-squares problems, concerned with solving a system of equations where the components of the unknown vector are integer-valued, arise in a wide range of applications. In many scenarios the unknown vector is sparse, i.e., a large fraction of its entries are zero. Examples include applications in wireless communications, digital fingerprinting, and array-comparative genomic hybridization systems. Sphere decoding, commonly used for solving integer least-squares problems, can utilize the knowledge about sparsity of the unknown vector to perform computationally efficient search for the solution. In this paper, we formulate and analyze the sparsity-aware sphere decoding algorithm that imposes $\ell_0$-norm constraint on the admissible solution. Analytical expressions for the expected complexity of the algorithm for alphabets typical of sparse channel estimation and source allocation applications are derived and validated through extensive simulations. The results demonstrate superior performance and speed of sparsity-aware sphere decoder compared to the conventional sparsity-unaware sphere decoding algorithm. Moreover, variance of the complexity of the sparsity-aware sphere decoding algorithm for binary alphabets is derived. The search space of the proposed algorithm can be further reduced by imposing lower bounds on the value of the objective function. The algorithm is modified to allow for such a lower bounding technique and simulations illustrating efficacy of the method are presented. Performance of the algorithm is demonstrated in an application to sparse channel estimation, where it is shown that sparsity-aware sphere decoder performs close to theoretical lower limits.

cs.IT↗