We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased toward the training samples. Such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the out-of-sample performance. A classical cross validation strategy is the leave-one-out cross validation (LOOCV) where one sample is left out for validation and training is done on the rest of the samples that are presented to the learner, and this process is repeated on all of the samples. LOOCV is rarely used in practice due to the high computational complexity. In this paper, we first develop a computationally efficient approximate LOOCV (ALOOCV) and provide theoretical guarantees for its performance. Then we use ALOOCV to provide an optimization algorithm for finding the regularizer in the empirical risk minimization framework. In our numerical experiments, we illustrate the accuracy and efficiency of ALOOCV as well as our proposed framework for the optimization of the regularizer.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine whether $X \independent Y \vert Z$. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution $f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$ -- the joint distribution if and only if $X \independent Y \vert Z.$ -- when given access only to i.i.d. samples from the true joint distribution $f(x,y,z)$. To tackle this problem we propose a novel nearest neighbor bootstrap procedure and theoretically show that our generated samples are indeed close to $f^{CI}$ in terms of total variational distance. We then develop theoretical results regarding the generalization bounds for classification for our problem, which translate into error bounds for CI testing. We provide a novel analysis of Rademacher type classification bounds in the presence of non-i.i.d \textit{near-independent} samples. We empirically validate the performance of our algorithm on simulated and real datasets and show performance gains over previous methods.

We study fairness in collaborative-filtering recommender systems, which are sensitive to discrimination that exists in historical data. Biased data can lead collaborative-filtering methods to make unfair predictions for users from minority groups. We identify the insufficiency of existing fairness metrics and propose four new metrics that address different forms of unfairness. These fairness metrics can be optimized by adding fairness terms to the learning objective. Experiments on synthetic and real data show that our new metrics can better measure fairness than the baseline, and that the fairness objectives effectively help reduce unfairness.

Calcium imaging is a prominent technology in neuroscience research which allows for simultaneous recording of large numbers of neurons in awake animals. Automated extraction of neurons and their temporal activity from imaging datasets is an important step in the path to producing neuroscience results. However, nearly all imaging datasets contain gross contaminating sources which could originate from the technology used, or the underlying biological tissue. Although past work has considered the effects of contamination under limited circumstances, there has not been a general framework treating contamination and its effects on the statistical estimation of calcium signals. In this work, we proceed in a new direction and propose to extract cells and their activity using robust statistical estimation. Using the theory of M-estimation, we derive a minimax optimal robust loss, and also find a simple and practical optimization routine for this loss with provably fast convergence. We use our proposed robust loss in a matrix factorization framework to extract the neurons and their temporal activity in calcium imaging datasets. We demonstrate the superiority of our robust estimation approach over existing methods on both simulated and real datasets.

We present new practical local differentially private heavy hitters algorithms achieving optimal or near-optimal worst-case error -- TreeHist and Bitstogram. In both algorithms, server running time is $\tilde O(n)$ and user running time is $\tilde O(1)$, hence improving on the prior state-of-the-art result of Bassily and Smith [STOC 2015] requiring $\tilde O(n^{5/2})$ server time and $\tilde O(n^{3/2})$ user time. With a typically large number of participants in local algorithms ($n$ in the millions), this reduction in time complexity, in particular at the user side, is crucial for the use of such algorithms in practice. We implemented Algorithm TreeHist to verify our theoretical analysis and compared its performance with the performance of Google's RAPPOR code.

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of features specific to that hypothesis. For example, in genetic association studies, each hypothesis tests the correlation between a variant and the trait. We have a rich set of features for each variant (e.g. its location, conservation, epigenetics etc.) which could inform how likely the variant is to have a true association. However popular testing approaches, such as Benjamini-Hochberg's procedure (BH) and independent hypothesis weighting (IHW), either ignore these features or assume that the features are categorical. We propose a new algorithm, NeuralFDR, which automatically learns a discovery threshold as a function of all the hypothesis features. We parametrize the discovery threshold as a neural network, which enables flexible handling of multi-dimensional discrete and continuous features as well as efficient end-to-end optimization. We prove that NeuralFDR has strong false discovery rate (FDR) guarantees, and show that it makes substantially more discoveries in synthetic and real datasets. Moreover, we demonstrate that the learned discovery threshold is directly interpretable.

Brain connectivity analysis is a critical component of ongoing human connectome projects to decipher the healthy and diseased brain. Recent work has highlighted the power-law (multi-time scale) properties of brain signals; however, there remains a lack of methods to specifically quantify short- vs. long- time range brain connections. In this paper, using detrended partial cross-correlation analysis (DPCCA), we propose a novel functional connectivity measure to delineate brain interactions at multiple time scales, while controlling for covariates. We use a rich simulated fMRI dataset to validate the proposed method, and apply it to a real fMRI dataset in a cocaine dependence prediction task. We show that, compared to extant methods, the DPCCA-based approach not only distinguishes short and long memory functional connectivity but also improves feature extraction and enhances classification accuracy. Together, this paper contributes broadly to new computational methodologies in understanding neural information processing.

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein's method, meaning that it is not necessary to compute the normalising constant of the model. We analyse the asymptotic Bahadur efficiency of the new test, and prove that under a mean-shift alternative, our test always has greater relative efficiency than a previous linear-time kernel test, regardless of the choice of parameters for that test. In experiments, the performance of our method exceeds that of the earlier linear-time test, and matches or exceeds the power of a quadratic-time kernel test. In high dimensions and where model structure may be exploited, our goodness of fit test performs far better than a quadratic-time two-sample test based on the Maximum Mean Discrepancy, with samples drawn from the model.

Obtaining enough labeled data to robustly train complex discriminative models is a major bottleneck in the machine learning pipeline. A popular solution is combining multiple sources of weak supervision using generative models. The structure of these models affects the quality of the training labels, but is difficult to learn without any ground truth labels. We instead rely on weak supervision sources having some structure by virtue of being encoded programmatically. We present Coral, a paradigm that infers generative model structure by statically analyzing the code for these heuristics, thus significantly reducing the amount of data required to learn structure. We prove that Coral's sample complexity scales quasilinearly with the number of heuristics and number of relations identified, improving over the standard sample complexity, which is exponential in n for learning n-th degree relations. Empirically, Coral matches or outperforms traditional structure learning approaches by up to 3.81 F1 points. Using Coral to model dependencies instead of assuming independence results in better performance than a fully supervised model by 3.07 accuracy points when heuristics are used to label radiology data without ground truth labels.

Effective and efficient mitigation of malware is a long-time endeavor in the information security community. The development of an anti-malware system that can counteract an unknown malware is a prolific activity that may benefit several sectors. We envision an intelligent anti-malware system that utilizes the power of deep learning (DL) models. Using such models would enable the detection of newly-released malware through mathematical generalization. That is, finding the relationship between a given malware $x$ and its corresponding malware family $y$, $f: x \mapsto y$. To accomplish this feat, we used the Malimg dataset (Nataraj et al., 2011) which consists of malware images that were processed from malware binaries, and then we trained the following DL models 1 to classify each malware family: CNN-SVM (Tang, 2013), GRU-SVM (Agarap, 2017), and MLP-SVM. Empirical evidence has shown that the GRU-SVM stands out among the DL models with a predictive accuracy of ~84.92%. This stands to reason for the mentioned model had the relatively most sophisticated architecture design among the presented models. The exploration of an even more optimal DL-SVM model is the next stage towards the engineering of an intelligent anti-malware system.