Related papers: Complex Correntropy Function: properties, and appl…
This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…
How do we know if two systems - biological or artificial - process information in a similar way? Similarity measures such as linear regression, Centered Kernel Alignment (CKA), Normalized Bures Similarity (NBS), and angular Procrustes…
Based on the notion of maximal correlation, Kimeldorf, May and Sampson (1980) introduce a measure of correlation between two random variables, called the "concordant monotone correlation" (CMC). We revisit, generalize and prove new…
Among many current data processing systems, the objectives are often not the reproduction of data, but to compute some answers based on the data resulting from queries. The similarity identification task is to identify the items in a…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
We present a new similarity measure based on information theoretic measures which is superior than Normalized Compression Distance for clustering problems and inherits the useful properties of conditional Kolmogorov complexity. We show that…
Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal…
Measuring dataset similarity is fundamental in machine learning, particularly for transfer learning and domain adaptation. In the context of supervised learning, most existing approaches quantify similarity of two data sets based on their…
The Tanimoto coefficient is commonly used to measure the similarity between molecules represented as discrete fingerprints, either as a distance metric or a positive definite kernel. While many kernel methods can be accelerated using random…
Recent work has compared neural network representations via similarity-based analyses to improve model interpretation. The quality of a similarity measure is typically evaluated by its success in assigning a high score to representations…
For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined for this purpose. The proposed algorithm is derived and a kernel width…