Related papers: Threshold Rules for the Classical Prophet Inequali…
This paper studies the fundamental limits of availability and throughput for independent and heterogeneous demands of a limited resource. Availability is the probability that the demands are below the capacity of the resource. Throughput is…
This work introduces \emph{sharding} and \emph{Poissonization} as a unified framework for analyzing prophet inequalities. Sharding involves splitting a random variable into several independent random variables, shards, that collectively…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
The aim of this paper is to discuss various concentration inequalities for U-statistics and most recent results. A special focus will be on providing proofs for bounds on the U-statistics using classical concentration inequalities, which,…
We study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief…
In extracting predictions from theories that describe a multiverse, we face the difficulty that we must assess probability distributions over possible observations, prescribed not just by an underlying theory, but by a theory together with…
In general, the CHSH inequality $S \le 2$ is considered to provide an \textit{upper} bound for classical correlations. In this note it is shown that if incoming particles are allowed to be delayed ever so briefly, the inequality can be…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
In information theory, we often use intersection and union of the typical sets to analyze various communication problems. However, in the quantum setting it is not very clear how to construct a measurement which behaves analogously to…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
In this work we design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description, i.e. a description based on representative points in classical phase-spaces. This is obtained by relating…
The fundamental limits of channels with mismatched decoding are addressed. A general formula is established for the mismatch capacity of a general channel, defined as a sequence of conditional distributions with a general decoding metrics…
Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…
In this note we consider boundary point principles for partial differential inequalities of elliptic type. Firstly, we highlight the difference between conditions required to establish classical strong maximum principles and classical…
The problem of isometry for threshold-based sampling such as integrate-and-fire (IF) or send-on-delta (SOD) is addressed. While for uniform sampling the Parseval theorem provides isometry and makes the Euclidean metric canonical, there is…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
We propose thresholding as an approach to deal with class imbalance. We define the concept of thresholding as a process of determining a decision boundary in the presence of a tunable parameter. The threshold is the maximum value of this…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
Shaping gain is attained in schemes where a shaped subcode is chosen from a larger codebook by a codeword selection process. This includes the popular method of Trellis Shaping (TS), originally proposed by Forney for average power…