Related papers: Low coordinate degree algorithms I: Universality o…
This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression…
Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…
Tensor product function (TPF) approximations have been widely adopted in solving high-dimensional problems, such as partial differential equations and eigenvalue problems, achieving desirable accuracy with computational overhead that scales…
While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…
We study the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our main algorithmic result is a polynomial-time PAC learning algorithm for this…
In many practical applications of multiple hypothesis testing using the False Discovery Rate (FDR), the given hypotheses can be naturally partitioned into groups, and one may not only want to control the number of false discoveries (wrongly…
We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response…
This paper develops a fully discrete soft thresholding polynomial approximation over a general region, named Lasso hyperinterpolation. This approximation is an $\ell_1$-regularized discrete least squares approximation under the same…
A novel class of bit-flipping (BF) algorithms for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are called gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient…
In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…
In this paper, we present an efficient algorithm to sample random sparse matrices to be used as check matrices for quantum Low-Density Parity-Check (LDPC) codes. To ease the treatment, we mainly describe our algorithm as a technique to…
Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric…
In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among…
The "Divide and Concur'' (DC) algorithm, recently introduced by Gravel and Elser, can be considered a competitor to the belief propagation (BP) algorithm, in that both algorithms can be applied to a wide variety of constraint satisfaction,…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
We discuss error floor asympotics and present a method for improving the performance of low-density parity check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
In the first part of the paper we study absolute error of sampling discretization of the integral $L_p$-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for…