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Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…
Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set.…
The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…
Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the…
The output distribution, when rate is above capacity, is investigated. It is shown that there is an asymptotic equipartition property (AEP) of the typical output sequences, independently of the specific codebook used, as long as the…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…
In this note, we prove a central limit theorem for smooth linear statistics of zeros of random polynomials which are linear combinations of orthogonal polynomials with iid standard complex Gaussian coefficients. Along the way, we obtain…
We give a characterization for the binary linear constant weight codes by using the symmetric difference of the supports of the codewords. This characterization gives a correspondence between the set of binary linear constant weight codes…
Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this…
In network data analysis, summary statistics of a network can provide us with meaningful insight into the structure of the network. The average clustering coefficient is one of the most popular and widely used network statistics. In this…
The problem of linear modulation classification using likelihood based methods is considered. Asymptotic properties of most commonly used classifiers in the literature are derived. These classifiers are based on hybrid likelihood ratio test…
The cluster-weighted model (CWM) is a mixture model with random covariates which allows for flexible clustering and density estimation of a random vector composed by a response variable and by a set of covariates. In this class of models,…
Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled…
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This…
Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input…
The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions $0\rightarrow 1$ and $1\rightarrow0$ differ substantially. In this paper, we introduce the notion of…