Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, gradient-free algorithm for finding a solution to these problems using ensemble Kalman inversion (EKI). Applications of our approach include offline and online supervised learning with deep neural networks, as well as graph-based semi-supervised learning. The essence of the EKI procedure is an ensemble based approximate gradient descent in which derivatives are replaced by differences from within the ensemble. We suggest several modifications to the basic method, derived from empirically successful heuristics developed in the context of SGD. Numerical results demonstrate wide applicability and robustness of the proposed algorithm.Comment: 41 pages, 14 figure

Adaptive and Neural Network-Based Aircraft Tracking Control with Synthetic Jet Actuators

Wing-embedded synthetic jet actuators (SJA) can be used to achieve maneuvering control in aircraft by delivering controllable airflow perturbations near the wing surface. Trajectory tracking control design for aircraft equipped with SJA is particularly challenging, since the controlling actuator itself has an uncertain dynamic model. These challenges necessitate advanced nonlinear control design methods to achieve desirable performance for SJA-based aircraft (e.g., micro air vehicles (MAVs)). In this research, adaptive and neural-network based control methods are investigated, which are specifically designed to compensate for the SJA dynamic model uncertainty and unpredictable operating conditions characters tic of real-world MAV applications. The control design methods discussed in this thesis are rigorously developed to achieve a prescribed level of trajectory tracking control performance, and numerical simulation results are presented to demonstrate the performance of the controllers in the presence of adversarial operating conditions

Rights Myopia in Child Welfare

For decades, legal scholars have debated the proper balance of parents\u27 rights and children\u27s rights in the child welfare system. This Article argues that the debate mistakenly privileges rights. Neither parents\u27 rights nor children\u27s rights serve families well because, as implemented, a solely rights-based model of child welfare does not protect the interests of parents or children. Additionally, even if well-implemented, the model still would not serve parents or children because it obscures the important role of poverty in child abuse and neglect and fosters conflict rather than collaboration between the state and families. In lieu of a solely rights-based model, this Article proposes a problem-solving model for child welfare and explores one embodiment of such a model, family group conferencing. This Article concludes that a problem-solving model holds significant potential to address many of the profound theoretical and practical shortcomings of the current child welfare system