Related papers: A Generalized Typicality for Abstract Alphabets
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…
Algorithm- and data-dependent generalization bounds are required to explain the generalization behavior of modern machine learning algorithms. In this context, there exists information theoretic generalization bounds that involve (various…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
We describe a general framework for weighted parametric multiple test procedures based on the closure principle. We utilize general weighting strategies that can reflect complex study objectives and include many procedures in the literature…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…
We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…
We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…