Threshold tests have recently been proposed as a useful method for detecting bias in lending, hiring, and policing decisions. For example, in the case of credit extensions, these tests aim to estimate the bar for granting loans to white and minority applicants, with a higher inferred threshold for minorities indicative of discrimination. This technique, however, requires fitting a complex Bayesian latent variable model for which inference is often computationally challenging. Here we develop a method for fitting threshold tests that is two orders of magnitude faster than the existing approach, reducing computation from hours to minutes. To achieve these performance gains, we introduce and analyze a flexible family of probability distributions on the interval [0, 1] -- which we call discriminant distributions -- that is computationally efficient to work with. We demonstrate our technique by analyzing 2.7 million police stops of pedestrians in New York City.

The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then perform analysis on the representative data set. In this paper, we present efficient algorithms for constructing finite sample confidence intervals for each algorithmic leveraging estimated regression coefficient, with asymptotic coverage guarantees. In simulations, we confirm empirically that the confidence intervals have the desired coverage probabilities, while bootstrap confidence intervals may not.

We present a new machine learning approach to estimate personalized treatment effects in the classical potential outcomes framework with binary outcomes. To overcome the problem that both treatment and control outcomes for the same unit are required for supervised learning, we propose surrogate loss functions that incorporate both treatment and control data. The new surrogates yield tighter bounds than the sum of losses for treatment and control groups. A specific choice of loss function, namely a type of hinge loss, yields a minimax support vector machine formulation. The resulting optimization problem requires the solution to only a single convex optimization problem, incorporating both treatment and control units, and it enables the kernel trick to be used to handle nonlinear (also non-parametric) estimation. Statistical learning bounds are also presented for the framework, and experimental results.

TL;DR I cover how cross-validation is a somewhat tricky problem for matrix factorization models (including PCA & clustering as special cases) and provide some Python code snippets for fitting these models with held out data. Cross-validation is a fundamental paradigm in modern data analysis. However, it is largely applied to supervised settings, such as regression and classification. Here, the procedure is simple: fit your model on, say, 90% of the data (the training set), and evaluate its performance on the remaining 10% (the test set). However, this idea does not easily extend to other unsupervised methods, such as dimensionality reduction methods or clustering.

There is growing evidence regarding the importance of spike timing in neural information processing, with even a small number of spikes carrying information, but computational models lag significantly behind those for rate coding. Experimental evidence on neuronal behavior is consistent with the dynamical and state dependent behavior provided by recurrent connections. This motivates the minimalistic abstraction investigated in this paper, aimed at providing insight into information encoding in spike timing via recurrent connections. We employ information-theoretic techniques for a simple reservoir model which encodes input spatiotemporal patterns into a sparse neural code, translating the polychronous groups introduced by Izhikevich into codewords on which we can perform standard vector operations. We show that the distance properties of the code are similar to those for (optimal) random codes. In particular, the code meets benchmarks associated with both linear classification and capacity, with the latter scaling exponentially with reservoir size.

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short-ranged, the kernel matrix inversion can be replaced by analytic diagonalization using the SWD. We show that this approach applies to uni- and multi-dimensional input data, extends to include longer-range correlations, and the grid can be in a latent space and used as inducing points. Through simulations, we show that our approximate method outperforms existing methods in predictive accuracy per unit time in the regime where data are plentiful. Our SWD-GP is recommended for regression analyses where there is a relatively large amount of data and/or there are constraints on computation time.

With the increasing penetration of solar power into power systems, forecasting becomes critical in power system operations. In this paper, an hourly-similarity (HS) based method is developed for 1-hour-ahead (1HA) global horizontal irradiance (GHI) forecasting. This developed method utilizes diurnal patterns, statistical distinctions between different hours, and hourly similarities in solar data to improve the forecasting accuracy. The HS-based method is built by training multiple two-layer multi-model forecasting framework (MMFF) models independently with the same-hour subsets. The final optimal model is a combination of MMFF models with the best-performed blending algorithm at every hour. At the forecasting stage, the most suitable model is selected to perform the forecasting subtask of a certain hour. The HS-based method is validated by 1-year data with six solar features collected by the National Renewable Energy Laboratory (NREL). Results show that the HS-based method outperforms the non-HS (all-in-one) method significantly with the same MMFF architecture, wherein the optimal HS- based method outperforms the best all-in-one method by 10.94% and 7.74% based on the normalized mean absolute error and normalized root mean square error, respectively.

From a public-health perspective, the occurrence of drug-drug-interactions (DDI) from multiple drug prescriptions is a serious problem, especially in the elderly population. This is true both for individuals and the system itself since patients with complications due to DDI will likely re-enter the system at a costlier level. We conducted an 18-month study of DDI occurrence in Blumenau (Brazil; pop. 340,000) using city-wide drug dispensing data from both primary and secondary-care level. Our goal is also to identify possible risk factors in a large population, ultimately characterizing the burden of DDI for patients, doctors and the public system itself. We found 181 distinct DDI being prescribed concomitantly to almost 5% of the city population. We also discovered that women are at a 60% risk increase of DDI when compared to men, while only having a 6% co-administration risk increase. Analysis of the DDI co-occurrence network reveals which DDI pairs are most associated with the observed greater DDI risk for females, demonstrating that contraception and hormone therapy are not the main culprits of the gender disparity, which is maximized after the reproductive years. Furthermore, DDI risk increases dramatically with age, with patients age 70-79 having a 50-fold risk increase in comparison to patients aged 0-19. Interestingly, several null models demonstrate that this risk increase is not due to increased polypharmacy with age. Finally, we demonstrate that while the number of drugs and co-administrations help predict a patient's number of DDI ($R^2=.413$), they are not sufficient to flag these patients accurately, which we achieve by training classifiers with additional data (MCC=.83,F1=.72). These results demonstrate that accurate warning systems for known DDI can be devised for public and private systems alike, resulting in substantial prevention of DDI-related ADR and savings.

Machine-learning models have been recently used for detecting malicious Android applications, reporting impressive performances on benchmark datasets, even when trained only on features statically extracted from the application, such as system calls and permissions. However, recent findings have highlighted the fragility of such in-vitro evaluations with benchmark datasets, showing that very few changes to the content of Android malware may suffice to evade detection. How can we thus trust that a malware detector performing well on benchmark data will continue to do so when deployed in an operating environment? To mitigate this issue, the most popular Android malware detectors use linear, explainable machine-learning models to easily identify the most influential features contributing to each decision. In this work, we generalize this approach to any black-box machine- learning model, by leveraging a gradient-based approach to identify the most influential local features. This enables using nonlinear models to potentially increase accuracy without sacrificing interpretability of decisions. Our approach also highlights the global characteristics learned by the model to discriminate between benign and malware applications. Finally, as shown by our empirical analysis on a popular Android malware detection task, it also helps identifying potential vulnerabilities of linear and nonlinear models against adversarial manipulations.