Related papers: Data-driven Solution of Stochastic Differential Eq…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
We propose a method for transforming probability distributions so that parameters of interest are forced into a specified distribution. We prove that this approach is the maximum entropy choice, and provide a motivating example applicable…
Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
In this article we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy approach. Unlike standard procedures that require equating at zero the score function of the maximum-likelihood…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…