Related papers: A Convenient Category for Higher-Order Probability…
Deep probabilistic programming languages try to combine the advantages of deep learning with those of probabilistic programming languages. If successful, this would be a big step forward in machine learning and programming languages.…
We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert…
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
Probabilistic programming languages, which exist in abundance, are languages that allow users to calculate probability distributions defined by probabilistic programs, by using inference algorithms. However, the underlying inference…
In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…
Motivated by statistical practice, category theory terminology is used to introduce Borel data structures and study exchangeability in an abstract framework. A generalization of de Finetti's theorem is shown and natural transformations are…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is…
We present a categorical viewpoint of probability measures by showing that a probability measure can be viewed as a weakly averaging affine measurable functional taking values in the unit interval which preserves limits. The probability…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
We study termination of higher-order probabilistic functional programs with recursion, stochastic conditioning and sampling from continuous distributions. Reasoning about the termination probability of programs with continuous distributions…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
We consider the problem of quantifying the uncertainty on theoretical predictions based on perturbation theory due to missing higher orders. The most widely used approach, scale variation, is largely arbitrary and it has no probabilistic…
We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $\mathrm{Tr}\big[M(X\otimes Y)\big]$, maximized with respect to semidefinite constraints on $X$ and $Y$. Applied to the…
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However,…
Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy…
The estimation of the guessing probability has paramount importance in quantum cryptographic processes. It can also be used as a witness for nonlocal correlations. In most of the studied scenarios, estimating the guessing probability…