Related papers: On the Reliability Function of Distributed Hypothe…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and {unanimous…
In distributed detection, there does not exist an automatic way of generating optimal decision strategies for non-affine decision functions. Consequently, in a detection problem based on a non-affine decision function, establishing…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel (BSC)…
Minimax decentralized detection is studied under two scenarios: with and without a fusion center when the source of uncertainty is the Bayesian prior. When there is no fusion center, the constraints in the network design are determined.…
Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size $L$. Two asymptotic regimes are considered, the fixed list-size regime, where $L$ is fixed…
We study a variant of the simple hypothesis testing problem where observed samples do not necessarily come from either of the specified distributions, but rather from a close variant of them. In this setting, we require a test that is…
We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent--also called reliability function--is…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
We derive upper and lower bounds on the reliability function for the common-message discrete memoryless broadcast channel with variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically…
A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new…
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…