Related papers: Categories of Empirical Models
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less…
In this paper, following an elementary line of thought which somewhat differs from the usual one, we prove once more that any deterministic theory predictively equivalent to quantum mechanics unavoidably exhibits a contextual character. The…
The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph…
A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of…
This paper proposes a single form for statistical models that accommodates a broad range of models, from ordinary least squares to agent-based microsimulations. The definition makes it almost trivial to define morphisms to transform and…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Contextuality is the leading notion of nonclassicality for a single system. However, an experimental demonstration requires finding procedures that are operationally equivalent, which might seem impossible to achieve exactly. Here I focus…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory…
Causal inference is a science with multi-disciplinary evolution and applications. On the one hand, it measures effects of treatments in observational data based on experimental designs and rigorous statistical inference to draw causal…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to…
Recent zero-shot evaluations have highlighted important limitations in the abilities of language models (LMs) to perform meaning extraction. However, it is now well known that LMs can demonstrate radical improvements in the presence of…
This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices…
Psychology has had difficulty accounting for the creative, context-sensitive manner in which concepts are used. We believe this stems from the view of concepts as identifiers rather than bridges between mind and world that participate in…
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…