Related papers: Coalgebraic Behavioral Metrics
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
Liftings of endofunctors on sets to endofunctors on relations are commonly used to capture bisimulation of coalgebras. Lax versions have been used in those cases where strict lifting fails to capture bisimilarity, as well as in modeling…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
Supervised deep learning models require significant amount of labeled data to achieve an acceptable performance on a specific task. However, when tested on unseen data, the models may not perform well. Therefore, the models need to be…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…
In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally…
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore…
Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…
Comparing probability distributions is an indispensable and ubiquitous task in machine learning and statistics. The most common way to compare a pair of Borel probability measures is to compute a metric between them, and by far the most…
We seek to develop a Bures (minimal monotone/statistical distinguishability) metric-based series of formulas for the moments of probability distributions over the determinants $|\rho|$ and $|\rho^{PT}|$ of $4 \times 4$ density matrices,…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that…
Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize…
We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in $1$-codimensional closed linear subspaces implies in dimensions $\geq 2$ that the gauge is a norm, and in…