arXiv subjects

Laura Schultz

Publications and source records attributed to Laura Schultz.

4 recordsLinked to original sources

arXiv2022

Deep Learning Gaussian Processes For Computer Models with Heteroskedastic and High-Dimensional Outputs

Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications, including social-economic processes, agriculture, environmental, biology, engineering and physics problems. A deterministic transformation of inputs is performed by deep learning and predictions are calculated by traditional Gaussian Processes. We illustrate our methodology using a simulation of motorcycle accidents and simulations of an Ebola outbreak. Finally, we conclude with directions for future research.

stat.AP↗

arXiv2022

Bayesian Calibration for Activity Based Models

We consider the problem of calibration and uncertainty analysis for activity-based transportation simulators. Activity-Based Models (ABMs) rely on statistical modeling of individual travelers' behavior to predict higher-order travel patterns in metropolitan areas. Input parameters are typically estimated from traveler surveys using maximum likelihood. We develop an approach that uses a Gaussian Process emulator to calibrate those parameters using traffic flow data. Our approach extends traditional emulators to handle the high-dimensional and non-stationary nature of transportation simulators. We introduce a deep learning dimensionality reduction model that is jointly estimated with Gaussin Process model to approximate the simulator. We demonstrate the methodology using several simulated examples as well as by calibrating key parameters of the Bloomington, Illinois model.

stat.AP↗

arXiv2018

Practical Bayesian Optimization for Transportation Simulators

We provide a method to solve optimization problem when objective function is a complex stochastic simulator of an urban transportation system. To reach this goal, a Bayesian optimization framework is introduced. We show how the choice of prior and inference algorithm effect the outcome of our optimization procedure. We develop dimensionality reduction techniques that allow for our optimization techniques to be applicable for real-life problems. We develop a distributed, Gaussian Process Bayesian regression and active learning models that allow parallel execution of our algorithms and enable usage of high performance computing. We present a fully Bayesian approach that is more sample efficient and reduces computational budget. Our framework is supported by theoretical analysis and an empirical study. We demonstrate our framework on the problem of calibrating a multi-modal transportation network of city of Bloomington, Illinois. Finally, we discuss directions for further research.

stat.CO↗

arXiv2018

Deep Reinforcement Learning for Dynamic Urban Transportation Problems

We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in intelligent transportation systems and long term urban planning. Often transportation models used to represent dynamics of a transportation system involve large data sets with complex input-output interactions and are difficult to use in the context of optimization. Use of deep learning metamodels can produce a lower dimensional representation of those relations and allow to implement optimization and reinforcement learning algorithms in an efficient manner. In particular, we develop deep learning models for calibrating transportation simulators and for reinforcement learning to solve the problem of optimal scheduling of travelers on the network.

stat.ML↗