Related papers: Representation and Integration by Parts Formulas f…

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…

Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…

We outline a method to estimate the value of computation for a flexible algorithm using empirical data. To determine a reasonable trade-off between cost and value, we build an empirical model of the value obtained through computation, and…

We study triangulation schemes for the joint kernel of a diffusion process with uniformly continuous coefficients and an adapted, non-resonant Abelian process. The prototypical example of Abelian process to which our methods apply is given…

In this paper, we consider the Cox--Ingersoll--Ross (CIR) process in the regime where the process does not hit zero. We construct additive and multiplicative discrete approximation schemes for the price of asset that is modeled by the CIR…

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

We propose a novel implicit feature refinement module for high-quality instance segmentation. Existing image/video instance segmentation methods rely on explicitly stacked convolutions to refine instance features before the final…

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…

We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in…

In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and -- for each component process -- the number of points in each bin is counted. The distribution of…

We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, where the entries of the rows of the matrix…

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

We extend the theoretical results for any FOU(p) processes for the case in which the Hurst parameter is less than 1/2 and we show theoretically and by simulations that under some conditions on T and the sample size n it is possible to…

Parametric conditional copula models allow the copula parameters to vary with a set of covariates according to an unknown calibration function. Flexible Bayesian inference for the calibration function of a bivariate conditional copula is…

In this paper we address a practical aspect of differential barrier penalty functions in linear programming. In this respect we propose an affine scaling interior point algorithm based on a large classe of differential barrier functions.…

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…

We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we…