Related papers: Differentials and distances in probabilistic coher…
Probabilistic context-free grammars (PCFGs) are used to define distributions over strings, and are powerful modelling tools in a number of areas, including natural language processing, software engineering, model checking, bio-informatics,…
Computing derivatives is a crucial subroutine in computer science and related fields as it provides a local characterization of a function's steepest directions of ascent or descent. In this work, we recognize that derivatives are often not…
Fractional order derivatives and integrals (differintegrals) are viewed from a frequency-domain perspective using the formalism of Riesz, providing a computational tool as well as a way to interpret the operations in the frequency domain.…
We show that a variant of the continuous Frechet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming…
In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…
We present a theory for slicing probabilistic imperative programs -- containing random assignments, and ``observe'' statements (for conditioning) -- represented as probabilistic control-flow graphs (pCFGs) whose nodes modify probability…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
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…
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…
We construct a differentiable locally Lipschitz function $f$ in $\mathbb{R}^{N}$ with the property that for every convex body $K\subset \mathbb{R}^N$ there exists $\bar x \in \mathbb{R}^N$ such that $K$ coincides with the set $\partial_L…
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…
The performance of distance-based classifiers heavily depends on the underlying distance metric, so it is valuable to learn a suitable metric from the data. To address the problem of multimodality, it is desirable to learn local metrics. In…
The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic…
Probabilistic programming languages (PPLs) are an expressive means of representing and reasoning about probabilistic models. The computational challenge of probabilistic inference remains the primary roadblock for applying PPLs in practice.…
In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of…
This paper introduces a new derivative parsing algorithm for recognition of parsing expression grammars. Derivative parsing is shown to have a polynomial worst-case time bound, an improvement on the exponential bound of the recursive…