Related papers: NGS Based Haplotype Assembly Using Matrix Completi…
Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…
We propose a general method for optimally approximating an arbitrary matrix $\mathbf{M}$ by a structured matrix $\mathbf{T}$ (circulant, Toeplitz/Hankel, etc.) and examine its use for estimating the spectra of genomic linkage disequilibrium…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
The task of predicting missing entries of a matrix, from a subset of known entries, is known as \textit{matrix completion}. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step.…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
The prevalent fully-connected tensor network (FCTN) has achieved excellent success to compress data. However, the FCTN decomposition suffers from slow computational speed when facing higher-order and large-scale data. Naturally, there…
Computing haplotypes from sequencing data, i.e. haplotype assembly, is an important component of molecular and population genetics problems, including interpreting the effects of genetic variation on complex traits and reconstructing…
While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…
Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…
We study compute efficiency of LLM training when using different parameterizations, i.e., rules for adjusting model and optimizer hyperparameters (HPs) as model size changes. Some parameterizations fail to transfer optimal base HPs (such as…
Protein structure prediction (PSP) is computationally a very challenging problem. The challenge largely comes from the fact that the energy function that needs to be minimised in order to obtain the native structure of a given protein is…
We introduce gbpTrees: an algorithm for constructing merger trees from cosmological simulations, designed to identify and correct for pathological cases introduced by errors or ambiguities in the halo finding process. gbpTrees is built upon…
Accurate identification of haplotypes in sequenced human genomes can provide invaluable information about population demography and fine-scale correlations along the genome, thus empowering both population genomic and medical association…
Insufficient reference data is ubiquitous in data-driven computational fluid dynamics, as it is usually too expensive to compute or impossible to observe over long enough times needed for data-driven methods. The lack of data can…
Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
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…
We consider estimating the edge-probability matrix of a network generated from a graphon model when the full network is not observed---only some overlapping subgraphs are. We extend the neighbourhood smoothing (NBS) algorithm of Zhang et…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…