This paper shows that dropout training in generalized linear models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability $\delta$. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. The paper makes a concrete recommendation on how to select the tuning parameter $\delta$. The paper also provides a novel, parallelizable, unbiased multi-level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector.

Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability. We formulate a Distributionally Robust Optimization (DRO) problem which recovers popular estimators, such as Group Square Root Lasso (GSRL). Our DRO formulation allows us to interpret GSRL as a game, in which we learn a regression parameter while an adversary chooses a perturbation of the data. We wish to pick the parameter to minimize the expected loss under any plausible model chosen by the adversary - who, on the other hand, wishes to increase the expected loss. The regularization parameter turns out to be precisely determined by the amount of perturbation on the training data allowed by the adversary. In this paper, we introduce a data-driven (statistical) criterion for the optimal choice of regularization, which we evaluate asymptotically, in closed form, as the size of the training set increases. Our easy-to-evaluate regularization formula is compared against cross-validation, showing comparable performance.

Despite the huge market potential of Printed Electronics on Flexible substrates, the printed circuits and systems are yet to be manufacturable due to high cost fabrication processes, large process variations between devices, large and somewhat intractable variations when the devices and their substrates are bent, and lack of a comprehensive Process Development Kit (PDK). In this review paper, we review our Low-Cost Fully-Additive printing process with these four shortcomings addressed. To the best of our knowledge, this process is arguably the Fully-Additive printing process that is closest to being manufacturable and for the realization of practical intelligent printed electronics.

Class D amplifiers are routinely employed as audio amplifiers due to their high power efficiency. Total Harmonic Distortion (THD) is one of the most important parameters to qualify and quantify their performance. In this paper, THD of a commonly used Bridge-Tied-Load (BTL) Class D amplifier is investigated, including the derivation of the analytical expression for the THD of the BTL Class D amplifier. We show that in some cases, the THD of the BTL Class D amplifier is independent of the integrator gain of the amplifier - this is unlike other Class D amplifiers and linear amplifiers whose THD is largely determined by their integrator gain. Instead, the THD of the BTL Class D amplifier is largely determined by the feedback amplifier. Further, unlike the single-ended Class D amplifier whose THD increases as the modulation index increases, the THD of the BTL Class D amplifier is maximum at the modulation index = 0.5. The analysis herein provide good insight to the design of BTL Class D amplifiers, including how various parameters may be varied/optimized to meet a given THD specification.