Related papers: Measures of distinguishability between stochastic …

We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context…

Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of…

Machine learning has been proven to be effective in various application areas, such as object and speech recognition on mobile systems. Since a critical key to machine learning success is the availability of large training data, many…

Given an iid sequence of pairs of stochastic processes on the unit interval we construct a measure of independence for the components of the pairs. We define distance covariance and distance correlation based on approximations of the…

Human evaluation of generated language through pairwise preference judgments is pervasive. However, under common scenarios, such as when generations from a model pair are very similar, or when stochastic decoding results in large variations…

The problem of identifying to which of a given set of classes objects belong is ubiquitous, occurring in many research domains and application areas, including medical diagnosis, financial decision making, online commerce, and national…

With growing applications of Machine Learning (ML) techniques in the real world, it is highly important to ensure that these models work in an equitable manner. One main step in ensuring fairness is to effectively measure fairness, and to…

The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number…

This review aims to draw attention to two issues of concern when we set out to make machine learning work in the chemical and materials domain, i.e., statistical loss function metrics for the validation and benchmarking of data-derived…

The comparison of local characteristics of two random processes can shed light on periods of time or space at which the processes differ the most. This paper proposes a method that learns about regions with a certain volume, where the…

Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…

We study stochastic choice across decision problems, each represented as a menu of action labels paired with observable outcome vectors. We propose a consistency condition for behavior in decision problems composed of two separable…

Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…

Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems…

We consider two different stationary random processes whose probability distributions are very close and indistinguishable by standard tests for large but limited statistics. Yet we demonstrate that these processes can be reliably…

Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $\alpha$-affinity, say $\alpha$-affinity of coherence for $\alpha \in (0, 1)$.…

It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between…

The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…

In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…

Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…