Feature selection can efficiently identify the most informative features with respect to the target feature used in training. However, state-of-the-art vector-based methods are unable to encapsulate the relationships between feature samples into the feature selection process, thus leading to significant information loss. To address this problem, we propose a new graph-based structurally interacting elastic net method for feature selection. Specifically, we commence by constructing feature graphs that can incorporate pairwise relationship between samples. With the feature graphs to hand, we propose a new information theoretic criterion to measure the joint relevance of different pairwise feature combinations with respect to the target feature graph representation. This measure is used to obtain a structural interaction matrix where the elements represent the proposed information theoretic measure between feature pairs. We then formulate a new optimization model through the combination of the structural interaction matrix and an elastic net regression model for the feature subset selection problem. This allows us to a) preserve the information of the original vectorial space, b) remedy the information loss of the original feature space caused by using graph representation, and c) promote a sparse solution and also encourage correlated features to be selected. Because the proposed optimization problem is non-convex, we develop an efficient alternating direction multiplier method (ADMM) to locate the optimal solutions. Extensive experiments on various datasets demonstrate the effectiveness of the proposed method. Keywords: Feature Selection; Graph; Interacting Elastic Net; Sparse; ADMM 1. Introduction There has recently been a rapid growth in both the size and dimension of the data encountered in many real world applications of pattern recognition including image processing, bioinformatics, and financial analysis. Finding useful information and building effective prediction models from such data presents new challenges for machine learning and pattern recognition [1]. One way to overcome this problem is to develop efficient spectral methods including stochastic neighbour embedding [2], elastic embedding methods [3] and feature selection [4] methods to reduce the dimensionality of the data.

Class imbalanced datasets are common in real-world applications that range from credit card fraud detection to rare disease diagnostics. Several popular classification algorithms assume that classes are approximately balanced, and hence build the accompanying objective function to maximize an overall accuracy rate. In these situations, optimizing the overall accuracy will lead to highly skewed predictions towards the majority class. Moreover, the negative business impact resulting from false positives (positive samples incorrectly classified as negative) can be detrimental. Many methods have been proposed to address the class imbalance problem, including methods such as over-sampling, under-sampling and cost-sensitive methods. In this paper, we consider the over-sampling method, where the aim is to augment the original dataset with synthetically created observations of the minority classes. In particular, inspired by the recent advances in generative modelling techniques (e.g., Variational Inference and Generative Adversarial Networks), we introduce a new oversampling technique based on variational autoencoders. Our experiments show that the new method is superior in augmenting datasets for downstream classification tasks when compared to traditional oversampling methods.

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients and obey application-specific constraints. In this paper, we present a new machine learning approach to learn risk scores. We formulate the risk score problem as a mixed integer nonlinear program, and present a new cutting plane algorithm for non-convex settings to efficiently recover its optimal solution. We improve our algorithm with specialized techniques to generate feasible solutions, narrow the optimality gap, and reduce data-related computation. Our approach can fit risk scores in a way that scales linearly in the number of samples, provides a certificate of optimality, and obeys real-world constraints without parameter tuning or post-processing. We illustrate the performance benefits of this approach through an extensive set of numerical experiments, where we compare risk scores built using our approach to those built using heuristic approaches. We also discuss the practical benefits of our approach through an application where we build a customized risk score for ICU seizure prediction in collaboration with the Massachusetts General Hospital.

Abstract--Increasingly fast development and update cycle of online course contents, and diverse demographics of students in each online classroom, make student performance prediction in real-time (before the course finishes) an interesting topic for both industrial research and practical needs. In that, we tackle the problem of real-time student performance prediction with ongoing courses in a domain adaptation framework, which is a system trained on students' labeled outcome from one previous coursework but is meant to be deployed on another. In particular, we first review recently-developed GritNet architecture [1] which is the current state of the art for student performance prediction problem, and introduce a new unsupervised domain adaptation method to transfer a GritNet trained on a past course to a new course without any (students' outcome) label. Our results for real Udacity students' graduation predictions show that the GritNet not only generalizes well from one course to another across different Nanodegree programs, but enhances real-time predictions explicitly in the first few weeks when accurate predictions are most challenging. With the growing need for people to keep learning throughout their careers, massive open online course (MOOCs) companies, such as Udacity and Coursera, not only aggressively design new courses that are relevant (e.g., self-driving cars and flying cars) but refresh existing courses' content frequently to keep them up-to-date.

This paper presents an efficient binarized algorithm for both learning and classification of human epileptic seizures from intracranial electroencephalography (iEEG). The algorithm combines local binary patterns with brain-inspired hyperdimensional computing to enable end-to-end learning and inference with binary operations. The algorithm first transforms iEEG time series from each electrode into local binary pattern codes. Then atomic high-dimensional binary vectors are used to construct composite representations of seizures across all electrodes. For the majority of our patients (10 out of 16), the algorithm quickly learns from one or two seizures (i.e., one-/few-shot learning) and perfectly generalizes on 27 further seizures. For other patients, the algorithm requires three to six seizures for learning. Overall, our algorithm surpasses the state-of-the-art methods for detecting 65 novel seizures with higher specificity and sensitivity, and lower memory footprint.

We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (actual positives). In addition, each distribution can be sequentially and repeatedly sampled. Inspired by the multi-armed bandit literature, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e. proportion of actual positives discovered) while giving anytime control of the false discovery proportion (nulls predicted as actual positives). Our sample complexity results match known information theoretic lower bounds and through simulations we show a substantial performance improvement over uniform sampling and an adaptive elimination style algorithm. Given the simplicity of the approach, and its sample efficiency, the method has promise for wide adoption in the biological sciences, clinical testing for drug discovery, and online A/B/n testing problems.

We mathematically compare three competing definitions of group-level nondiscrimination: demographic parity, equalized odds, and calibration. Using the theoretical framework of Friedler et al., we study the properties of each definition under various worldviews, which are assumptions about how, if at all, the observed data is biased. We prove that different worldviews call for different definitions of fairness, and we specify when it is appropriate to use demographic parity and equalized odds. In addition, we argue that calibration is unsuitable for the purpose of ensuring nondiscrimination. Finally, we define a worldview that is more realistic than the previously considered ones, and we introduce a new notion of fairness that is suitable for this worldview.

We consider the problem of inferring the directed, causal graph from observational data, assuming no hidden confounders. We take an information theoretic approach, and make three main contributions. First, we show how through algorithmic information theory we can obtain SCI, a highly robust, effective and computationally efficient test for conditional independence---and show it outperforms the state of the art when applied in constraint-based inference methods such as stable PC. Second, building upon on SCI, we show how to tell apart the parents and children of a given node based on the algorithmic Markov condition. We give the Climb algorithm to efficiently discover the directed, causal Markov blanket---and show it is at least as accurate as inferring the global network, while being much more efficient. Last, but not least, we detail how we can use the Climb score to direct those edges that state of the art causal discovery algorithms based on PC or GES leave undirected---and show this improves their precision, recall and F1 scores by up to 20%.

Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however, when the dimensionality is relatively large. To address this, we propose a novel procedure named DA-QDA for QDA in analyzing high-dimensional data. Formulated in a simple and coherent framework, DA-QDA aims to directly estimate the key quantities in the Bayes discriminant function including quadratic interactions and a linear index of the variables for classification. Under appropriate sparsity assumptions, we establish consistency results for estimating the interactions and the linear index, and further demonstrate that the misclassification rate of our procedure converges to the optimal Bayes risk, even when the dimensionality is exponentially high with respect to the sample size. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed for finding interactions, which is much faster than its competitor in the literature. The promising performance of DA-QDA is illustrated via extensive simulation studies and the analysis of four real datasets.

Health risks from cigarette smoking -- the leading cause of preventable death in the United States -- can be substantially reduced by quitting. Although most smokers are motivated to quit, the majority of quit attempts fail. A number of studies have explored the role of self-reported symptoms, physiologic measurements, and environmental context on smoking risk, but less work has focused on the temporal dynamics of smoking events, including daily patterns and related nicotine effects. In this work, we examine these dynamics and improve risk prediction by modeling smoking as a self-triggering process, in which previous smoking events modify current risk. Specifically, we fit smoking events self-reported by 42 smokers to a time-varying semi-parametric Hawkes process (TV-SPHP) developed for this purpose. Results show that the TV-SPHP achieves superior prediction performance compared to related and existing models, with the incorporation of time-varying predictors having greatest benefit over longer prediction windows. Moreover, the impact function illustrates previously unknown temporal dynamics of smoking, with possible connections to nicotine metabolism to be explored in future work through a randomized study design. By more effectively predicting smoking events and exploring a self-triggering component of smoking risk, this work supports development of novel or improved cessation interventions that aim to reduce death from smoking.