Related papers: Low coordinate degree algorithms I: Universality o…
Lexicographic depth first search (LexDFS) is a graph search protocol which has already proved to be a powerful tool on cocomparability graphs. Cocomparability graphs have been well studied by investigating their complements (comparability…
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the…
In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the…
We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the…
We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard…
Universal hypothesis testing refers to the problem of deciding whether samples come from a nominal distribution or an unknown distribution that is different from the nominal distribution. Hoeffding's test, whose test statistic is equivalent…
In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of…
Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…
This work is a further study on the Generalized Constraint Neural Network (GCNN) model [1], [2]. Two challenges are encountered in the study, that is, to embed any type of prior information and to select its imposing schemes. The work…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
Deep Neural Networks (DNNs) became the standard tool for function approximation with most of the introduced architectures being developed for high-dimensional input data. However, many real-world problems have low-dimensional inputs for…
High-dimensional statistical learning (HDSL) has wide applications in data analysis, operations research, and decision-making. Despite the availability of multiple theoretical frameworks, most existing HDSL schemes stipulate the following…
Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have…
This paper outlines a three-step procedure for determining the low bit error rate performance curve of a wide class of LDPC codes of moderate length. The traditional method to estimate code performance in the higher SNR region is to use a…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local…