31,152 research outputs found
Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization
This paper introduces an optimization problem (P) and a solution strategy to
design variable-speed-limit controls for a highway that is subject to traffic
congestion and uncertain vehicle arrival and departure. By employing a finite
data-set of samples of the uncertain variables, we aim to find a data-driven
solution that has a guaranteed out-of-sample performance. In principle, such
formulation leads to an intractable problem (P) as the distribution of the
uncertainty variable is unknown. By adopting a distributionally robust
optimization approach, this work presents a tractable reformulation of (P) and
an efficient algorithm that provides a suboptimal solution that retains the
out-of-sample performance guarantee. A simulation illustrates the effectiveness
of this method.Comment: 10 pages, 2 figures, submitted to ECC 201
Automatic Differentiation Variational Inference
Probabilistic modeling is iterative. A scientist posits a simple model, fits
it to her data, refines it according to her analysis, and repeats. However,
fitting complex models to large data is a bottleneck in this process. Deriving
algorithms for new models can be both mathematically and computationally
challenging, which makes it difficult to efficiently cycle through the steps.
To this end, we develop automatic differentiation variational inference (ADVI).
Using our method, the scientist only provides a probabilistic model and a
dataset, nothing else. ADVI automatically derives an efficient variational
inference algorithm, freeing the scientist to refine and explore many models.
ADVI supports a broad class of models-no conjugacy assumptions are required. We
study ADVI across ten different models and apply it to a dataset with millions
of observations. ADVI is integrated into Stan, a probabilistic programming
system; it is available for immediate use
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