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We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The…
We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework…
We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by…
The authors present a Polynomial Chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-Profile Parametrization (KPP) within the MIT General Circulation Model (MITgcm) of the tropical pacific. The inference of…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…
Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
We study structural aspects of randomized parameterized computation. We introduce a new class ${\sf W[P]}$-${\sf PFPT}$ as a natural parameterized analogue of ${\sf PP}$. Our definition uses the machine based characterization of the…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
We examine the dependence of parton distribution functions (PDFs) on the value of the QCD coupling strength $\alpha_{s}(M_{Z})$. We explain a simple method that is rigorously valid in the quadratic approximation normally applied in PDF…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Container ships encounter large roll angles and high acceleration, and container loss remains a problem. This study proposes a method for calculating the probability density function~(PDF) of roll angular and cargo lateral accelerations.…
We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Compact and discriminative visual codebooks are preferred in many visual recognition tasks. In the literature, a number of works have taken the approach of hierarchically merging visual words of an initial large-sized codebook, but…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…
We present a probabilistic generalization of the Robinson--Schensted correspondence in which a permutation maps to several different pairs of standard Young tableaux with nonzero probability. The probabilities depend on two parameters $q$…