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The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…
This paper presents a Bayesian model for unsupervised learning of verb selectional preferences. For each verb the model creates a Bayesian network whose architecture is determined by the lexical hierarchy of Wordnet and whose parameters are…
In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…
We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in…
Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…
We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…
We explore and formalize the task of synthesizing programs over noisy data, i.e., data that may contain corrupted input-output examples. By formalizing the concept of a Noise Source, an Input Source, and a prior distribution over programs,…
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…
Probabilistic programming languages aid developers performing Bayesian inference. These languages provide programming constructs and tools for probabilistic modeling and automated inference. Prior work introduced a probabilistic programming…
Automation is becoming ubiquitous in all laboratory activities, leading towards precisely defined and codified laboratory protocols. However, the integration between laboratory protocols and mathematical models is still lacking. Models…
We reflect on programming with complicated effects, recalling an undeservingly forgotten alternative to monadic programming and checking to see how well it can actually work in modern functional languages. We adopt and argue the position of…
Large Language Models (LLMs) are often evaluated against ideals of perfect Bayesian inference, yet growing evidence suggests that their in-context reasoning exhibits systematic forgetting of past information. Rather than viewing this…
The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…
Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…
We study the desiderata on a model for statistical probabilistic programming languages. We argue that they can be met by a combination of traditional tools, namely open bisimulation and probabilistic simulation.
This paper describes a new algorithm for exact Bayesian inference that is based on a recently proposed compositional semantics of Bayesian networks in terms of channels. The paper concentrates on the ideas behind this algorithm, involving a…
In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for…