ppsds 0.0.3-alpha released: an open-source library for probabilistic prediction of stochastic dynamical systems
ppsds 0.0.3-alpha is now on PyPI. The MIT-licensed library answers one question from both
sides: how predictably a system you know exactly behaves at best, and what a predictor can
still guarantee when you only partly know the system.
If that sounds abstract, the one-minute game in the card below is the shortest way in. Place a few bets on where a puck lands, watch the system move, and see what a probabilistic prediction is before reading a definition of it: the puck is the system, the stacks are the predictor, and the payout is the score. Click the demo to play — no install, no server, nothing kept.
Install it with pip install ppsds==0.0.3a0; the documentation and the game are public.
ppsds
Tao Xu, Jianping He
TL;DR How probabilistically predictable is a system you only partly know? ppsds answers from both sides: the ceiling any probabilistic prediction could reach on a system you know exactly, and a probabilistic predictor that comes with a floor over every system you are willing to admit.
pip install ppsds==0.0.3a0
Related publications (2)
Probabilistic Predictability of Stochastic Dynamical Systems
Automatica
TL;DR Quantifies how predictably a stochastic system behaves via an -logarithm score, tied to differential entropy and system dimension.
Abstract & PDF
To assess the quality of a probabilistic prediction for stochastic dynamical systems (SDSs), scoring rules assign a numerical score based on the predictive distribution and the measured state. We propose an -logarithm score that generalizes the logarithm score by considering a neighborhood of radius . We characterize the probabilistic predictability of an SDS by optimizing the expected score over the space of probability measures, and show how predictability is quantitatively determined by the neighborhood radius, the differential entropies of process noises, and the system dimension. For any predictor, we provide approximations of the expected score with error . We also analyze the asymptotic behaviors of the score on individual trajectories, proving convergence to the expected score for i.i.d. process noises with speed in probability. Numerical examples elaborate the results.
Distributionally Robust Probabilistic Prediction for Stochastic Dynamical Systems
IEEE Transactions on Automatic Control
TL;DR A distributionally robust probabilistic prediction framework that certifies worst-case predictive performance over an ambiguity set of dynamics.
Abstract & PDF
Probabilistic prediction of stochastic dynamical systems (SDSs) aims to accurately predict the conditional probability distributions of future states. However, accurate probabilistic predictions hinge on accurate distributional information from a nominal model, which is rarely available in practice. We propose a novel functional-maximin-based distributionally robust probabilistic prediction (DRPP) framework, in which one can design probabilistic predictors with worst-case performance guarantees over a pre-defined ambiguity set of SDSs. Although DRPP requires optimizing over the space of probability measures — generally intractable — we develop a methodology that equivalently transforms the maximin problem from function spaces to Euclidean spaces. Two suboptimal solutions are derived: Noise-DRPP (relaxing constraints on the ambiguity set) and Eig-DRPP (relaxing constraints on the predictor), together with their optimality gaps against the global optimum. Numerical simulations compare the performance of the predictors under different SDSs.