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Variational approximation, such as mean-field (MF) and tree-reweighted (TRW), provide a computationally efficient approximation of the log-partition function for a generic graphical model. TRW provably provides an upper bound, but the…
In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly…
Asymmetric, non-Gaussian probability distributions are often observed in the analysis of natural and engineering datasets. The lognormal distribution is a standard model for data with skewed frequency histograms and fat tails. However, the…
Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…
We develop a neural-network framework for multi-period risk--reward stochastic control problems with constrained two-step feedback policies that may be discontinuous in the state. We allow a broad class of objectives built on a…
The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…
We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(\phi)$ of a Gaussian field $\phi$. A self similar renormalization group…
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…
The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…