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The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…
Probabilistic programming is a powerful abstraction for statistical machine learning. Applying static analysis methods to probabilistic programs could serve to optimize the learning process, automatically verify properties of models, and…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are…
The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Variety of machine learning problems can be formulated as an optimization task for some (surrogate) loss function. Calculation of loss function can be viewed in terms of stochastic computation graphs (SCG). We use this formalism to analyze…
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
When observational data is available from practical studies and a directed cyclic graph for how various variables affect each other is known based on substantive understanding of the process, we consider a problem in which a control plan of…
In branching simulation, a novel approach to simulation presented in this paper, a multiplicity of plausible scenarios are concurrently developed and implemented. In conventional simulations of complex systems, there arise from time to time…
This paper provides guidance to an analyst who wants to extract insight from a spreadsheet model. It discusses the terminology of spreadsheet analytics, how to prepare a spreadsheet model for analysis, and a hierarchy of analytical…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
We consider a sequential decision making process, such as renewable energy trading or electrical production scheduling, whose outcome depends on the future realization of a random factor, such as a meteorological variable. We assume that…
Recent work has demonstrated that water supply pumps in the drinking water distribution network can be leveraged to provide flexibility to the power network, but existing approaches are computationally demanding and/or overly conservative.…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…