Related papers: Representation and Integration by Parts Formulas f…
Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Sophisticated inference algorithms, such as belief propagation (BP),…
We present new high order approximations schemes for the Cox-Ingersoll-Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021) for the approximation of semigroups. The idea consists in using a…
Integration-by-parts (IBP) reduction is one of the essential steps in evaluating Feynman integrals. A modern approach to IBP reduction uses modular arithmetic evaluations with parameters set to numerical values at sample points, followed by…
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which…
Inductive Conformal Prediction (ICP) is a set of distribution-free and model agnostic algorithms devised to predict with a user-defined confidence with coverage guarantee. Instead of having point predictions, i.e., a real number in the case…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
Piecewise diffusion Markov processes (PDifMPs) form a versatile class of stochastic hybrid systems that combine continuous diffusion processes with discrete event-driven dynamics, enabling flexible modelling of complex real-world hybrid…
Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on…
The logarithmic model offers new tools for image processing. An efficient method for image enhancement is to use an affine transformation with the logarithmic operations: addition and scalar multiplication. We define some criteria for…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…
We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and…
Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we…
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…
Learning representations with diversified information remains as an open problem. Towards learning diversified representations, a new approach, termed Information Competing Process (ICP), is proposed in this paper. Aiming to enrich the…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.