Related papers: First- and Second-Order Hypothesis Testing for Mix…
We consider a multi-hop distributed hypothesis testing problem with multiple decision centers (DCs) for testing against independence and where the observations obey some Markov chain. For this system, we characterize the fundamental type-II…
In clinical studies upon which decisions are based there are two types of errors that can be made: a type I error arises when the decision is taken to declare a positive outcome when the truth is in fact negative, and a type II error arises…
The severity of type II errors is frequently ignored when deriving a multiple testing procedure, even though utilizing it properly can greatly help in making correct decisions. This paper puts forward a theory behind developing a multiple…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
We explore the fundamental limits of heterogeneous distributed detection in an anonymous sensor network with n sensors and a single fusion center. The fusion center collects the single observation from each of the n sensors to detect a…
The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation…
In this paper, an achievable error exponent for the multiple-access channel with two independent sources is derived. For each user, the source messages are partitioned into two classes and codebooks are generated by drawing codewords from…
We study optimal estimation when the likelihood may be misspecified. Building on tools from the theory of decision-making under uncertainty, we analyze a class of axiomatically grounded optimality criteria which nests several existing…
Second order asymptotics of fixed-length source coding and intrinsic randomness is discussed with a constant error constraint. There was a difference between optimal rates of fixed-length source coding and intrinsic randomness, which never…
A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
We servey a series of investigations of optimal testing of multiple hypotheses conserning various multiobject models. These studies are a bright instance of application of methods and technics developed in Shannon information theory to…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity. The alternatives are stationary self-exciting point processes. We…
We consider the fundamental problem of selecting $k$ out of $n$ random variables in a way that the expected highest or second-highest value is maximized. This question captures several applications where we have uncertainty about the…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
Consider the task of learning a hypothesis class $\mathcal{H}$ in the presence of an adversary that can replace up to an $\eta$ fraction of the examples in the training set with arbitrary adversarial examples. The adversary aims to fail the…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n +…
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test…