Related papers: Quantization Of Probability Measures In Maximum~Me…
This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
A common way to quantify the ,,distance'' between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are related to Sinkhorn divergences $S_\varepsilon$ with appropriate cost functions as…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Recently, a framework for application-oriented optimal experiment design has been introduced. In this context, the distance of the estimated system from the true one is measured in terms of a particular end-performance metric. This…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
The common approach of designing a communication device is to maximize a well-defined objective function, e.g., the channel capacity and the cut-off rate. We propose easy-to-implement solutions for Gaussian channels that approximate the…
Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and…