Related papers: The Beta-Bernoulli process and algebraic effects
Computational difficulties in the general application of Bretthorsts formalism to time-series problems, posed by the large number of possible models and the use of models with nonorthogonal base-functions are discussed. The specific problem…
Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…
Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured…
Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra,…
We introduce a process algebra that concerns the timed behaviour of distributed systems with a known spatial distribution. This process algebra provides a communication mechanism that deals with the fact that a datum sent at one point in…
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can…
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof…
Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor…
A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the…
Algebraic effects and handlers have emerged in the programming languages community as a convenient, modular abstraction for controlling computational effects. They have found several applications including concurrent programming, meta…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect…
Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…
When using Bayesian inference to support conservative software reliability assessments, it is useful to consider a collection of Bayesian inference problems, with the aim of determining the worst-case value (from this collection) for a…