Related papers: The Beta-Bernoulli process and algebraic effects
We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving…
Types-and-effects are type systems, which allow one to express general semantic properties and to statically reason about program's execution. They have been widely exploited to specify static analyses, for example to track computational…
In the research on computational effects, defined algebraically, effect symbols are often expected to obey certain equations. If we orient these equations, we get a rewrite system, which may be an effective way of transforming or optimizing…
We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way}. The themes are organized…
We perform differential expression analysis of high-throughput sequencing count data under a Bayesian nonparametric framework, removing sophisticated ad-hoc pre-processing steps commonly required in existing algorithms. We propose to use…
Model-checking is one of the most powerful techniques for verifying systems and programs, which since the pioneering results by Knapik et al., Ong, and Kobayashi, is known to be applicable to functional programs with higher-order types…
Compositionality is a key feature of process algebras which is often cited as one of their advantages as a modelling technique. It is certainly true that in biochemical systems, as in many other systems, model construction is made easier in…
Stochastic variational inference (SVI) is emerging as the most promising candidate for scaling inference in Bayesian probabilistic models to large datasets. However, the performance of these methods has been assessed primarily in the…
We present a novel method of computing the beta-normal eta-long form of a simply-typed lambda-term by constructing traversals over a variant abstract syntax tree of the term. In contrast to beta-reduction, which changes the term by…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $\beta$-numeration. A matrix decomposition of these measures is obtained in the case when $\beta$ is a PV number. We also determine their…