Related papers: Coalgebraic Behavioral Metrics
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
In data mining, it is usually to describe a set of individuals using some summaries (means, standard deviations, histograms, confidence intervals) that generalize individual descriptions into a typology description. In this case, data can…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Metric distortion in social choice is a framework for evaluating how well voting rules minimize social cost when both voters and candidates exist in a shared metric space, with a voter's cost defined by their distance to a candidate. Voters…
We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these…
Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by…
Citation and coauthor networks offer an insight into the dynamics of scientific progress. We can also view them as representations of a causal structure, a logical process captured in a graph. From a causal perspective, we can ask questions…
The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…
Research on human social interactions has traditionally relied on self-reports. Despite their widespread use, self-reported accounts of behaviour are prone to biases and necessarily reduce the range of behaviours, and the number of…
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…
The well-established methodology for the estimation of hidden semi-Markov models (HSMMs) as hidden Markov models (HMMs) with extended state spaces is further developed to incorporate covariate influences across all aspects of the state…
In contrast to the existing approaches to bisimulation for fuzzy systems, we introduce a behavioral distance to measure the behavioral similarity of states in a nondeterministic fuzzy-transition system. This behavioral distance is defined…
Behavioural metrics have been shown to be an effective mechanism for constructing representations in reinforcement learning. We present a novel perspective on behavioural metrics for Markov decision processes via the use of positive…
Discrete time random walks, in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$, are widely used models for stochastic processes. In the case of a correlated random walk, the next…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks…