Related papers: The Beta-Bernoulli process and algebraic effects
We give a geometry of interaction model for a typed lambda-calculus endowed with operators for sampling from a continuous uniform distribution and soft conditioning, namely a paradigmatic calculus for higher-order Bayesian programming. The…
As Large Language Models (LLMs) become increasingly integrated into our daily lives, the potential harms from deceptive behavior underlie the need for faithfully interpreting their decision-making. While traditional probing methods have…
The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
We introduce a sound and complete equational theory capturing equivalence of discrete probabilistic programs, that is, programs extended with primitives for Bernoulli distributions and conditioning, to model distributions over finite sets…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Variable environment is the time-honored way of making sense of free variables, used in programming language theory as well when writing interpreters and some compilers. Algebraic effects give another way, as was pointed already at HOPE…
Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…
We introduce an approach to topic modelling with document-level covariates that remains tractable in the face of large text corpora. This is achieved by de-emphasizing the role of parameter estimation in an underlying probabilistic model,…
Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…
Binary concepts are empirically used by humans to generalize efficiently. And they are based on Bernoulli distribution which is the building block of information. These concepts span both low-level and high-level features such as "large vs…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using data from…
Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…