Related papers: What is Stochastic Supervenience?
Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
Triplet Markov chains are general generative models for sequential data which take into account three kinds of random variables: (noisy) observations, their associated discrete labels and latent variables which aim at strengthening the…
This paper proves a version for stochastic differential equations of the Lie-Scheffers Theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution…
Principles of cognitive economy would require that concepts about objects, properties and relations should be introduced only if they simplify the conceptualisation of a domain. Unexpectedly, classic logic conditionals, specifying…
The traditional approach of statistical physics to supervised learning routinely assumes unrealistic generative models for the data: usually inputs are independent random variables, uncorrelated with their labels. Only recently, statistical…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
Detecting anomalies in large sets of observations is crucial in various applications, such as epidemiological studies, gene expression studies, and systems monitoring. We consider settings where the units of interest result in multiple…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
We view sorites in terms of stimuli acting upon a system and evoking this system's responses. Supervenience of responses on stimuli implies that they either lack tolerance (i.e., they change in every vicinity of some of the stimuli), or…
This article presents a modern deterministic framework for the study of leading significant digit distributions in numerical data. Rather than relying on traditional probabilistic or mixture-based explanations, we demonstrate that the…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
We consider particles that are conditioned to initial and final states. The trajectory of these particles is uniquely shaped by the intricate interplay of internal and external sources of randomness. The internal randomness is aptly…
The ability to predict future events or patterns based on previous experience is crucial for many applications such as traffic control, weather forecasting, or supply chain management. While modern supervised Machine Learning approaches…
We introduce a novel framework for causal explanations of stochastic, sequential decision-making systems built on the well-studied structural causal model paradigm for causal reasoning. This single framework can identify multiple,…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…