Publications

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This paper presents an assessment of electrical device measurements using functional data analysis (FDA) on a test case of Zener diode devices. We employ three techniques from FDA to quantify the variability in device behavior, primarily due to production lot and demonstrate that this has a significant effect in our data set. We also argue for the expanded use of FDA methods in providing principled, quantitative analysis of electrical device data.

Accurate characterization of electrical device behavior is a key component of developing accurate electrical models and assessing reliability. Measurements characterizing an electrical device can be produced from current-voltage (I-V) sweeps. We introduce the pairwise midpoint method (PMM) for estimating the mean of a functional data set and apply it to I-V sweeps from a Zener diode. Comparisons indicate that the PMM is a viable method for describing the mean behavior of a functional data set.

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Neural networks (NN) have become almost ubiquitous with image classification, but in their standard form produce point estimates, with no measure of confidence. Bayesian neural networks (BNN) provide uncertainty quantification (UQ) for NN predictions and estimates through the posterior distribution. As NN are applied in more high-consequence applications, UQ is becoming a requirement. Automating systems can save time and money, but only if the operator can trust what the system outputs. BNN provide a solution to this problem by not only giving accurate predictions and estimates, but also an interval that includes reasonable values within a desired probability. Despite their positive attributes, BNN are notoriously difficult and time consuming to train. Traditional Bayesian methods use Markov Chain Monte Carlo (MCMC), but this is often brushed aside as being too slow. The most common method is variational inference (VI) due to its fast computation, but there are multiple concerns with its efficacy. MCMC is the gold standard and given enough time, will produce the correct result. VI, alternatively, is an approximation that converges asymptotically. Unfortunately (or fortunately), high consequence problems often do not live in the land of asymtopia so solutions like MCMC are preferable to approximations. We apply and compare MCMC-and VI-trained BNN in the context of target detection in hyperspectral imagery (HSI), where materials of interest can be identified by their unique spectral signature. This is a challenging field, due to the numerous permuting effects practical collection of HSI has on measured spectra. Both models are trained using out-of-the-box tools on a high fidelity HSI target detection scene. Both MCMC-and VI-trained BNN perform well overall at target detection on a simulated HSI scene. Splitting the test set predictions into two classes, high confidence and low confidence predictions, presents a path to automation. For the MCMC-trained BNN, the high confidence predictions have a 0.95 probability of detection with a false alarm rate of 0.05 when considering pixels with target abundance of 0.2. VI-trained BNN have a 0.25 probability of detection for the same, but its performance on high confidence sets matched MCMC for abundances >0.4. However, the VI-trained BNN on this scene required significant expert tuning to get these results while MCMC worked immediately. On neither scene was MCMC prohibitively time consuming, as is often assumed, but the networks we used were relatively small. This paper provides an example of how to utilize the benefits of UQ, but also to increase awareness that different training methods can give different results for the same model. If sufficient computational resources are available, the best approach rather than the fastest or most efficient should be used, especially for high consequence problems.

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature due to their usefulness in decision making, particularly for high-consequence decisions. However, there has been little research done on how to evaluate the quality of such methods. We use statistical methods of frequentist interval coverage and interval width to evaluate the quality of credible intervals, and expected calibration error to evaluate classification predicted confidence. These metrics are evaluated on Bayesian neural networks (BNN) fit using Markov Chain Monte Carlo (MCMC) and variational inference (VI), bootstrapped neural networks (NN), Deep Ensembles (DE), and Monte Carlo (MC) dropout. We apply these different UQ for DL methods to a hyperspectral image target detection problem and show the inconsistency of the different methods' results and the necessity of a UQ quality metric. To reconcile these differences and choose a UQ method that appropriately quantifies the uncertainty, we create a simulated data set with fully parameterized probability distribution for a two-class classification problem. The gold standard MCMC performs the best overall, and the bootstrapped NN is a close second, requiring the same computational expense as DE. Through this comparison, we demonstrate that, for a given data set, different models can produce uncertainty estimates of markedly different quality. This in turn points to a great need for principled assessment methods of UQ quality in DL applications.

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Deep neural networks (NNs) typically outperform traditional machine learning (ML) approaches for complicated, non-linear tasks. It is expected that deep learning (DL) should offer superior performance for the important non-proliferation task of predicting explosive device configuration based upon observed optical signature, a task which human experts struggle with. However, supervised machine learning is difficult to apply in this mission space because most recorded signatures are not associated with the corresponding device description, or “truth labels.” This is challenging for NNs, which traditionally require many samples for strong performance. Semi-supervised learning (SSL), low-shot learning (LSL), and uncertainty quantification (UQ) for NNs are emerging approaches that could bridge the mission gaps of few labels and rare samples of importance. NN explainability techniques are important in gaining insight into the inferential feature importance of such a complex model. In this work, SSL, LSL, and UQ are merged into a single framework, a significant technical hurdle not previously demonstrated. Exponential Average Adversarial Training (EAAT) and Pairwise Neural Networks (PNNs) are chosen as the SSL and LSL methods of choice. Permutation feature importance (PFI) for functional data is used to provide explainability via the Variable importance Explainable Elastic Shape Analysis (VEESA) pipeline. A variety of uncertainty quantification approaches are explored: Bayesian Neural Networks (BNNs), ensemble methods, concrete dropout, and evidential deep learning. Two final approaches, one utilizing ensemble methods and one utilizing evidential learning, are constructed and compared using a well-quantified synthetic 2D dataset along with the DIRSIG Megascene.

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