Related papers: Optimal quantization for nonuniform Cantor distrib…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
We present a fully probabilistic approach for solving binary optimization problems with black-box objective functions and with budget constraints. In the probabilistic approach, the optimization variable is viewed as a random variable and…
Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and…
We apply algorithmic information theory to quantum mechanics in order to shed light on an algorithmic structure which inheres in quantum mechanics. There are two equivalent ways to define the (classical) Kolmogorov complexity K(s) of a…
We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are…
For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Levy, Kantorovich, and…
We show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto-homeomorphism, whenever the Cantor set is endowed with a suitable probability measure. This is valid both for the standard product…
We probabilistically analyze the performance of the arithmetic coding algorithm under a probability model for binary data in which a message is received by a coder from a source emitting independent equally distributed bits, with 1…
A probability measure in R^d is called a spectral measure if it has an orthonormal basis consisting of exponentials. In this paper we study spectral Cantor measures. We establish a large class of such measures and give a necessary and…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
For a collection of distributions over a countable support set, the worst case universal compression formulation by Shtarkov attempts to assign a universal distribution over the support set. The formulation aims to ensure that the universal…
For the four-state protocol of quantum key distribution, optimum sets of probe parameters are calculated for the most general unitary probe in which each individual transmitted photon is made to interact with the probe so that the signal…
The polarization measure is the probability that among 3 individuals chosen at random from a finite population exactly 2 come from the same class. This index is maximum at the midpoints of the edges of the probability simplex. We compute…
The dual attainment of the Monge--Kantorovich transport problem is analyzed in a general setting. The spaces $X, Y$ are assumed to be polish and equipped with Borel probability measures $\mu$ and $\nu$. The transport cost function $c:\XY…
In this paper we prove the S-inequality for certain product probability measures and ideals in R^n . As a result, for the Weibull and Gamma product distributions we derive concentration of measure type estimates as well as optimal…
In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input…
The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for…
The progressive censoring scheme has received considerable amount of attention in the last fifteen years. During the last few years joint progressive censoring scheme has gained some popularity. Recently, the authors Mondal and Kundu ("A…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…