Related papers: On some properties of probability kernels

Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…

A Causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and the optimal reconstruction kernel is derived, which consists of a product of causal kernels. In the process, general abstract spaces…

Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…

The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…

Racks and quandles are algebraic structures with a single binary operation that is right self-distributive and right invertible, and additionally idempotent in the case of quandles. The invertibility condition is equivalent to the existence…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…

We consider the problem of modifying a quasi-probability kernel in order to improve its properties without changing the set of measures whose conditional probabilities it specifies.

The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems…

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…