237 research outputs found
Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties
This paper proposes a statistical verification framework using Gaussian
processes (GPs) for simulation-based verification of stochastic nonlinear
systems with parametric uncertainties. Given a small number of stochastic
simulations, the proposed framework constructs a GP regression model and
predicts the system's performance over the entire set of possible
uncertainties. Included in the framework is a new metric to estimate the
confidence in those predictions based on the variance of the GP's cumulative
distribution function. This variance-based metric forms the basis of active
sampling algorithms that aim to minimize prediction error through careful
selection of simulations. In three case studies, the new active sampling
algorithms demonstrate up to a 35% improvement in prediction error over other
approaches and are able to correctly identify regions with low prediction
confidence through the variance metric.Comment: 8 pages, submitted to ACC 201
Active Mini-Batch Sampling using Repulsive Point Processes
The convergence speed of stochastic gradient descent (SGD) can be improved by
actively selecting mini-batches. We explore sampling schemes where similar data
points are less likely to be selected in the same mini-batch. In particular, we
prove that such repulsive sampling schemes lowers the variance of the gradient
estimator. This generalizes recent work on using Determinantal Point Processes
(DPPs) for mini-batch diversification (Zhang et al., 2017) to the broader class
of repulsive point processes. We first show that the phenomenon of variance
reduction by diversified sampling generalizes in particular to non-stationary
point processes. We then show that other point processes may be computationally
much more efficient than DPPs. In particular, we propose and investigate
Poisson Disk sampling---frequently encountered in the computer graphics
community---for this task. We show empirically that our approach improves over
standard SGD both in terms of convergence speed as well as final model
performance
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