Related papers: A Cartesian Closed Category for Random Variables
In this paper, we continue to explore the consistence and usability of Probability Bracket Notation (PBN) proposed in our previous articles. After a brief review of PBN with dimensional analysis, we investigate probability spaces in terms…
This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes place within a categorical setting for generalized functional…
In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic…
We develop the foundations of Algebraic Stochastic Calculus, with an aim to replacing what is typically referred to as Stochastic Calculus by a purely categorical version thereof. We first give a sheaf theoretic reinterpretation of…
Constrained counting is important in domains ranging from artificial intelligence to software analysis. There are already a few approaches for counting models over various types of constraints. Recently, hashing-based approaches achieve…
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…
This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain H\"older-type classes in which a random field is…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Probabilistic programming languages and modeling toolkits are two modular ways to build and reuse stochastic models and inference procedures. Combining strengths of both, we express models and inference as generalized coroutines in the same…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…