Related papers: Product Distribution Field Theory
We propose Distributionally Balanced Designs (DBD), a new class of probability sampling designs that target representativeness at the level of the full auxiliary distribution rather than selected moments. In disciplines such as ecology,…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and…
We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete…
The auxiliary field diffusion Monte Carlo method uses imaginary-time projection techniques to accurately solve the ground-state wave function of atomic nuclei and infinite nuclear matter. In this work, we present a novel representation of…
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
This paper presents a distributed stochastic model predictive control (SMPC) approach for large-scale linear systems with private and common uncertainties in a plug-and-play framework. Using the so-called scenario approach, the centralized…
This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The…
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in…
We use Monte Carlo techniques to simulate an organized prediction competition between a group of a scientific experts acting under the influence of a ``self-governing'' prediction reward algorithm. Our aim is to illustrate the advantages of…
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field…
This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…