Related papers: Estimation of mutual information via quantum kerne…

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations…

Information theoretic measures have helped to sharpen our understanding of many-body quantum states. As perhaps the most well-known example, the entanglement entropy (or more generally, the bipartite mutual information) has become a…

Basic quantum information measures involved in the information analysis of quantum systems are considered. It is shown that the main quantum information measurement methods depend on whether the corresponding quantum events are compatible…

Mutual Information (MI) is often used for feature selection when developing classifier models. Estimating the MI for a subset of features is often intractable. We demonstrate, that under the assumptions of conditional independence, MI…

We introduce the concept of mutual independence -- correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key -- it is a fully quantum and more…

We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…

The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…

Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…

Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding…

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…

Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…

Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial…

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…

This paper compares and evaluates a set of non-parametric mutual information estimators with the goal of providing a novel toolset to progress in the analysis of the capacity of the nonlinear optical channel, which is currently an open…

In this paper we focus on the estimation of mutual information from finite samples $(\mathcal{X}\times\mathcal{Y})$. The main concern with estimations of mutual information is their robustness under the class of transformations for which it…

Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…

We here propose a machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal…