Related papers: Representation and Integration by Parts Formulas f…
This paper discusses the computational resolution and presents numerical results for solving affine combinations of Heaviside composite optimization problems (abbreviated as A-HSCOPs) by a progressive integer programming (abbreviated as…
Factorized Information Criterion (FIC) is a recently developed information criterion, based on which a novel model selection methodology, namely Factorized Asymptotic Bayesian (FAB) Inference, has been developed and successfully applied to…
In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of…
Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which…
We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions,…
We consider the forward investment problem in market models where the stock prices are continuous semimartingales adapted to a Brownian filtration. We construct a broad class of forward performance processes with initial conditions of power…
Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all relevant Hurst indices, i.e. $H \in…
Current probabilistic programming languages and tools tightly couple model representations with specific inference algorithms, preventing experimentation with novel representations or mixed discrete-continuous models. We introduce a factor…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
It is shown that, under some mild technical conditions, representations of prime numbers by binary quadratic forms can be computed in polynomial complexity by exploiting Schoof's algorithm, which counts the number of $\mathbb F_q$-points of…
Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…
Due to the importance of the Cox-Ingersoll-Ross process in different areas of finance, a broad spectrum of studies and investigations on this model have been carried out. In case of ambiguity, we characterize it by applying the…
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
Given a process with independent increments $X$ (not necessarily a martingale) and a large class of square integrable r.v. $H=f(X_T)$, $f$ being the Fourier transform of a finite measure $\mu$, we provide explicit Kunita-Watanabe and…
We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some original pathwise estimates…
INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling…