Ali Arab

Rozhin Eskandarpour, Amin Khodaei, Ali Arab

In this paper, in an attempt to improve power grid resilience, a machine learning model is proposed to predictively estimate the component states in response to extreme events. The proposed model is based on a multi-dimensional Support Vector Machine (SVM) considering the associated resilience index, i.e., the infrastructure quality level and the time duration that each component can withstand the event, as well as predicted path and intensity of the upcoming extreme event. The outcome of the proposed model is the classified component state data to two categories of outage and operational, which can be further used to schedule system resources in a predictive manner with the objective of maximizing its resilience. The proposed model is validated using Ä-fold cross-validation and model benchmarking techniques. The performance of the model is tested through numerical simulations and based on a well-defined and commonly-used performance measure.

Ali Arab, Dev Arora, Jialin Lu et al.

Subgroup discovery is a descriptive and exploratory data mining technique to identify subgroups in a population that exhibit interesting behavior with respect to a variable of interest. Subgroup discovery has numerous applications in knowledge discovery and hypothesis generation, yet it remains inapplicable for unstructured, high-dimensional data such as images. This is because subgroup discovery algorithms rely on defining descriptive rules based on (attribute, value) pairs, however, in unstructured data, an attribute is not well defined. Even in cases where the notion of attribute intuitively exists in the data, such as a pixel in an image, due to the high dimensionality of the data, these attributes are not informative enough to be used in a rule. In this paper, we introduce the subgroup-aware variational autoencoder, a novel variational autoencoder that learns a representation of unstructured data which leads to subgroups with higher quality. Our experimental results demonstrate the effectiveness of the method at learning subgroups with high quality while supporting the interpretability of the concepts.

Rozhin Eskandarpour, Amin Khodaei, Ali Arab

A machine learning model is proposed in this paper to help estimate potential nodal load curtailment in response to an extreme event. This is performed through identifying which grid components will fail as a result of an extreme event, and consequently, which parts of the power system will encounter a supply interruption. The proposed model to predict component outages is based on a Support Vector Machine (SVM) model. This model considers the category and the path of historical hurricanes, as the selected extreme event in this paper, and accordingly trains the SVM. Once trained, the model is capable of classifying the grid components into two categories of outage and operational in response to imminent hurricanes. The obtained component outages are then integrated into a load curtailment minimization model to estimate the nodal load curtailments. The merits and the effectiveness of the proposed models are demonstrated using the standard IEEE 30-bus system based on various hurricane path/intensity scenarios.

Nathan Wycoff, Ali Arab, Lisa O. Singh

In analyses with severe data-limitations, augmenting the target dataset with information from ancillary datasets in the application domain, called source datasets, can lead to significantly improved statistical procedures. However, existing methods for this transfer learning struggle to deal with situations where the source datasets are also limited and not guaranteed to be well-aligned with the target dataset. A typical strategy is to use the empirical loss minimizer on the source data as a prior mean for the target parameters, which places the estimation of source parameters outside of the Bayesian formalism. Our key conceptual contribution is to use a risk minimizer conditional on source parameters instead. This allows us to construct a single joint prior distribution for all parameters from the source datasets as well as the target dataset. As a consequence, we benefit from full Bayesian uncertainty quantification and can perform model averaging via Gibbs sampling over indicator variables governing the inclusion of each source dataset. We show how a particular instantiation of our prior leads to a Bayesian Lasso in a transformed coordinate system and discuss computational techniques to scale our approach to moderately sized datasets. We also demonstrate that recently proposed minimax-frequentist transfer learning techniques may be viewed as an approximate Maximum a Posteriori approach to our model. Finally, we demonstrate superior predictive performance relative to the frequentist baseline on a genetics application, especially when the source data are limited.

Nathan Wycoff, Lisa O. Singh, Ali Arab et al.

Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods. However, one drawback of the $\ell_1$ penalty is bias: nonzero parameters are underestimated in magnitude, motivating techniques such as the Adaptive Lasso which endow each parameter with its own penalty coefficient. But it's not clear how these parameter-specific penalties should be set in complex models. In this article, we study the approach of treating the penalty coefficients as additional decision variables to be learned in a \textit{Maximum a Posteriori} manner, developing a proximal gradient approach to joint optimization of these together with the parameters of any differentiable cost function. Beyond reducing bias in estimates, this procedure can also encourage arbitrary sparsity structure via a prior on the penalty coefficients. We compare our method to implementations of specific sparsity structures for non-Gaussian regression on synthetic and real datasets, finding our more general method to be competitive in terms of both speed and accuracy. We then consider nonlinear models for two case studies: COVID-19 vaccination behavior and international refugee movement, highlighting the applicability of this approach to complex problems and intricate sparsity structures.