Related papers: Convergence of the Population Dynamics algorithm i…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
Non-parametric and distribution-free two-sample tests have been the foundation of many change point detection algorithms. However, randomness in the test statistic as a function of time makes them susceptible to false positives and…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…
We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the…
Conformal prediction yields a prediction set with guaranteed $1-\alpha$ coverage of the true target under the i.i.d. assumption, which may not hold and lead to a gap between $1-\alpha$ and the actual coverage. Prior studies bound the gap…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be…
While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…
Let $X_t$ be the (reflecting) diffusion process generated by $L:=\Delta+\nabla V$ on a complete connected Riemannian manifold $M$ possibly with a boundary $\partial M$, where $V\in C^1(M)$ such that $\mu(d x):= e^{V(x)}d x$ is a probability…
1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…
The problem of estimating the probability distribution of labels has been widely studied as a label distribution learning (LDL) problem, whose applications include age estimation, emotion analysis, and semantic segmentation. We propose a…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…
Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modelling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…