Related papers: Categories of Empirical Models
We propose a novel approach for modeling semantic contextual relationships in videos. This graph-based model enables the learning and propagation of higher-level spatial-temporal contexts to facilitate the semantic labeling of local…
Causal inference is a central goal across many scientific disciplines. Over the past several decades, three major frameworks have emerged to formalize causal questions and guide their analysis: the potential outcomes framework, structural…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…
The basic concepts of category theory are developed and examples of them are presented to illustrate them using measurement theory and probability theory tools. Motivated by Perrone's workarXiv:1912.10642 where notes on category theory are…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…
We construct a categorical framework for nonlinear postquantum inference, with embeddings of convex closed sets of suitable reflexive Banach spaces as objects and pullbacks of Br\`egman quasi-nonexpansive mappings (in particular,…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological…
The object of contextuality analysis is a set of random variables each of which is uniquely labeled by a content and a context. In the measurement terminology, the content is that which the random variable measures, whereas the context…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
We investigate a possible category theoretical description for agent based modeling by outlining justifications for two main principles to describe the valuations in a realistic way in microeconomics: 1) It is assumed that the valuations…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
This paper investigates modal type theories by using a new categorical semantics called change-of-base semantics. Change-of-base semantics is novel in that it is based on (possibly infinitely) iterated enrichment and interpretation of…