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Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
Reliable and low latency multicast communication is important for future vehicular communication. Sparse random linear network coding approach used to ensure the reliability of multicast communication has been widely investigated. A…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum…
Effective iterative decoding of short BCH codes faces two primary challenges: identifying an appropriate parity-check matrix and accelerating decoder convergence. To address these issues, we propose a systematic scheme to derive an…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
We consider near maximum-likelihood (ML) decoding of short linear block codes based on neural belief propagation (BP) decoding recently introduced by Nachmani et al.. While this method significantly outperforms conventional BP decoding, the…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and order statistic decoding (OSD) algorithms. Specifically, a modified BP…
We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of…
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…
A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and…
Low energy barrier magnet (LBM) technology has recently been proposed as a candidate for accelerating algorithms based on energy minimization and probabilistic graphs because their physical characteristics have a one-to-one mapping onto the…