Metrics for Bayesian Optimal Experiment Design under Model Misspecification

The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint distribution of all unknown variables implied by the statistical model that will be used to analyze the collected data. The utility function defines the objective of the experiment where a common utility function is the information gain. This article introduces an expanded framework for this process, where we go beyond the traditional Expected Information Gain criteria and introduce the Expected General Information Gain which measures robustness to the model discrepancy and Expected Discriminatory Information as a criterion to quantify how well an experiment can detect model discrepancy. The functionality of the framework is showcased through its application to a scenario involving a linearized spring mass damper system and an F-16 model where the model discrepancy is taken into account while doing Bayesian optimal experiment design.

Variational Kalman Filtering with Hinf-Based Correction for Robust Bayesian Learning in High Dimensions

In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and Hinf-norm based correction for a linear Gaussian system. As the dimension of state or parameter space grows, performing the full Kalman update with the dense covariance matrix for a large scale system requires increased storage and computational complexity, making it impractical. The VIF approach, based on mean-field Gaussian variational inference, reduces this burden through the variational approximation to the covariance usually in the form of a diagonal covariance approximation. The challenge is to retain convergence and correct for biases introduced by the sequential VIF steps. We desire a framework that improves feasibility while still maintaining reasonable proximity to the optimal Kalman filter as data is assimilated. To accomplish this goal, a Hinf-norm based optimization perturbs the VIF covariance matrix to improve robustness. This yields a novel VIF- Hinf recursion that employs consecutive variational inference and Hinf based optimization steps. We explore the development of this method and investigate a numerical example to illustrate the effectiveness of the proposed filter.

Adaptive n-ary Activation Functions for Probabilistic Boolean Logic

Balancing model complexity against the information contained in observed data is the central challenge to learning. In order for complexity-efficient models to exist and be discoverable in high dimensions, we require a computational framework that relates a credible notion of complexity to simple parameter representations. Further, this framework must allow excess complexity to be gradually removed via gradient-based optimization. Our n-ary, or n-argument, activation functions fill this gap by approximating belief functions (probabilistic Boolean logic) using logit representations of probability. Just as Boolean logic determines the truth of a consequent claim from relationships among a set of antecedent propositions, probabilistic formulations generalize predictions when antecedents, truth tables, and consequents all retain uncertainty. Our activation functions demonstrate the ability to learn arbitrary logic, such as the binary exclusive disjunction (p xor q) and ternary conditioned disjunction ( c ? p : q ), in a single layer using an activation function of matching or greater arity. Further, we represent belief tables using a basis that directly associates the number of nonzero parameters to the effective arity of the belief function, thus capturing a concrete relationship between logical complexity and efficient parameter representations. This opens optimization approaches to reduce logical complexity by inducing parameter sparsity.

Optimal Sensor Precision for Multi-Rate Sensing for Bounded Estimation Error

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the l1 norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to a) determine redundant sensing architectures for linear time invariant systems, b) accurately estimate states with low-cost sensors, and c) optimally schedule sensors for linear time-varying systems.

Combining Visible and Infrared Spectrum Imagery using Machine Learning for Small Unmanned Aerial System Detection

Advances in machine learning and deep neural networks for object detection, coupled with lower cost and power requirements of cameras, led to promising vision-based solutions for sUAS detection. However, solely relying on the visible spectrum has previously led to reliability issues in low contrast scenarios such as sUAS flying below the treeline and against bright sources of light. Alternatively, due to the relatively high heat signatures emitted from sUAS during flight, a long-wave infrared (LWIR) sensor is able to produce images that clearly contrast the sUAS from its background. However, compared to widely available visible spectrum sensors, LWIR sensors have lower resolution and may produce more false positives when exposed to birds or other heat sources. This research work proposes combining the advantages of the LWIR and visible spectrum sensors using machine learning for vision-based detection of sUAS. Utilizing the heightened background contrast from the LWIR sensor combined and synchronized with the relatively increased resolution of the visible spectrum sensor, a deep learning model was trained to detect the sUAS through previously difficult environments. More specifically, the approach demonstrated effective detection of multiple sUAS flying above and below the treeline, in the presence of heat sources, and glare from the sun. Our approach achieved a detection rate of 71.2 +- 8.3%, improving by 69% when compared to LWIR and by 30.4% when visible spectrum alone, and achieved false alarm rate of 2.7 +- 2.6%, decreasing by 74.1% and by 47.1% when compared to LWIR and visible spectrum alone, respectively, on average, for single and multiple drone scenarios, controlled for the same confidence metric of the machine learning object detector of at least 50%. Videos of the solution's performance can be seen at https://sites.google.com/view/tamudrone-spie2020/.