Related papers: Universal Relationships in Measures of Unpredictab…
Intelligent agents must be able to articulate its own uncertainty. In this work, we show that pre-trained sequence models are naturally capable of probabilistic reasoning over exchangeable data points -- forming informed beliefs and…
Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
A new general procedure for a priori selection of more predictable events from a time series of observed variable is proposed. The procedure is applicable to time series which contains different types of events that feature significantly…
Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known,…
Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…
Sources of predictability in the basic laws of physics are described in the most general theoretical context -- the quantum theory of the universe as a whole. (To appear in the Proceedings of the conference on Fundamental Sources of…
In classical probability theory, the best predictor of a future observation of a random variable $X,$ is its expected value $E_P[X]$ when no other information is available When information consisting in the observation of another random…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
Prediction algorithms assign numbers to individuals that are popularly understood as individual "probabilities" -- what is the probability of 5-year survival after cancer diagnosis? -- and which increasingly form the basis for life-altering…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe…
We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…
Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…