Related papers: Distance Correlation: A New Tool for Detecting Ass…
In this thesis I propose an algorithm to heuristically calculate different distance measures on uncertain graphs (i.e. graphs where edges only exist with a certain probability) and apply this to the heuristic calculation of harmonic…
Quantum correlations represent a fundamental tool for studies ranging from basic science to quantum technologies. Different non-classical correlations have been identified and studied, as entanglement and discord. In view of future…
The issue of distinguishing between the same-source and different-source hypotheses based on various types of traces is a generic problem in forensic science. This problem is often tackled with Bayesian approaches, which are able to provide…
The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of…
A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
The divergence of the correlation length $\xi$ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been…
Causality plays a central role in understanding interactions between variables in complex systems. These systems often exhibit state-dependent causal relationships, where both the strength and direction of causality vary with the value of…
Statisticians have warned us since the early days of their discipline that experimental correlation between two observations by no means implies the existence of a causal relation. The question about what clues exist in observational data…
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not),…
Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that…
In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…
We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause…
Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography,…
We propose a family of association measures for two-way contingency tables whose latent distribution can be assumed to be bivariate normal. When this assumption holds, the power-divergence measuring departure from independence can be…
According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here,…
The idea of spatial crosscorrelation was conceived of long ago. However, unlike the related spatial autocorrelation, the theory and method of spatial crosscorrelation analysis have remained undeveloped. This paper presents a set of models…
The interpretation of quantum mechanics (or, for that matter, of any physical theory) consists in answering the question: How can the world be for the theory to be true? That question is especially pressing in the case of the long-distance…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
Since the rise of fair machine learning as a critical field of inquiry, many different notions on how to quantify and measure discrimination have been proposed in the literature. Some of these notions, however, were shown to be mutually…