We propose a nested reduced-rank regression (NRRR) approach in fitting regression model with multivariate functional responses and predictors, to achieve tailored dimension reduction and facilitate interpretation/visualization of the resulting functional model. Our approach is based on a two-level low-rank structure imposed on the functional regression surfaces. A global low-rank structure identifies a small set of latent principal functional responses and predictors that drives the underlying regression association. A local low-rank structure then controls the complexity and smoothness of the association between the principal functional responses and predictors. Through a basis expansion approach, the functional problem boils down to an interesting integrated matrix approximation task, where the blocks or submatrices of an integrated low-rank matrix share some common row space and/or column space. An iterative algorithm with convergence guarantee is developed. We establish the consistency of NRRR and also show through non-asymptotic analysis that it can achieve at least a comparable error rate to that of the reduced-rank regression. Simulation studies demonstrate the effectiveness of NRRR. We apply NRRR in an electricity demand problem, to relate the trajectories of the daily electricity consumption with those of the daily temperatures.

With the increase in population densities and environmental awareness, public transport has become an important aspect of urban life. Consequently, large quantities of transportation data are generated, and mining data from smart card use has become a standardized method to understand the travel habits of passengers. Public transport datasets, however, often may lack data integrity; boarding stop information may be missing due to either imperfect acquirement processes or inadequate reporting. As a result, large quantities of observations and even complete sections of cities might be absent from the smart card database. We have developed a machine (supervised) learning method to impute missing boarding stops based on ordinal classification. In addition, we present a new metric, Pareto Accuracy, to evaluate algorithms where classes have an ordinal nature. Results are based on a case study in the Israeli city of Beer Sheva for one month of data. We show that our proposed method significantly notably outperforms current imputation methods and can improve the accuracy and usefulness of large-scale transportation data.

We consider the task of auditing ML models for individual bias/unfairness. We formalize the task in an optimization problem and develop a suite of inferential tools for the optimal value. Our tools permit us to obtain asymptotic confidence intervals and hypothesis tests that cover the target/control the Type I error rate exactly. To demonstrate the utility of our tools, we use them to reveal the gender and racial biases in Northpointe's COMPAS recidivism prediction instrument.

In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach. However, a key practical difficulty of sketching an SVD is that the user does not know how far the sketched singular vectors/values are from the exact ones. Indeed, the user may be forced to rely on analytical worst-case error bounds, which do not account for the unique structure of a given problem. As a result, the lack of tools for error estimation often leads to much more computation than is really necessary. To overcome these challenges, this paper develops a fully data-driven bootstrap method that numerically estimates the actual error of sketched singular vectors/values. In particular, this allows the user to inspect the quality of a rough initial sketched SVD, and then adaptively predict how much extra work is needed to reach a given error tolerance. Furthermore, the method is computationally inexpensive, because it operates only on sketched objects, and it requires no passes over the full matrix being factored. Lastly, the method is supported by theoretical guarantees and a very encouraging set of experimental results.

The Fairness, Accountability, and Transparency in Machine Learning (FAT-ML) literature proposes a varied set of group fairness metrics to measure discrimination against socio-demographic groups that are characterized by a protected feature, such as gender or race. Such a system can be deemed as either fair or unfair depending on the choice of the metric. Several metrics have been proposed, some of them incompatible with each other. We present here a framework to navigate the tensions between various group-wise metrics and to study fairness in data-driven decision making without the constraint of choosing a single metric. We do so empirically, by observing that several of these metrics cluster together in two or three main clusters for the same groups and machine learning methods. In addition, we propose a robust way to visualize multidimensional fairness in two dimensions through a Principal Component Analysis (PCA) of the group fairness metrics. Experimental results on multiple datasets show that the PCA decomposition explains the variance between the metrics with one to three components.

Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at https://github.com/gitgiter/Graph-Adversarial-Learning.

Classification predictive modeling problems involve predicting a class label for a given set of inputs. It is a challenging problem in general, especially if little is known about the dataset, as there are tens, if not hundreds, of machine learning algorithms to choose from. The problem is made significantly more difficult if the distribution of examples across the classes is imbalanced. This requires the use of specialized methods to either change the dataset or change the learning algorithm to handle the skewed class distribution. A common way to deal with the overwhelm on a new classification project is to use a favorite machine learning algorithm like Random Forest or SMOTE. Another common approach is to scour the research literature for descriptions of vaguely similar problems and attempt to re-implement the algorithms and configurations that are described. These approaches can be effective, although they are hit-or-miss and time-consuming respectively.

Social media channels, such as Facebook, Twitter, and Instagram, have altered our world forever. People are now increasingly connected than ever and reveal a sort of digital persona. Although social media certainly has several remarkable features, the demerits are undeniable as well. Recent studies have indicated a correlation between high usage of social media sites and increased depression. The present study aims to exploit machine learning techniques for detecting a probable depressed Twitter user based on both, his/her network behavior and tweets. For this purpose, we trained and tested classifiers to distinguish whether a user is depressed or not using features extracted from his/ her activities in the network and tweets. The results showed that the more features are used, the higher are the accuracy and F-measure scores in detecting depressed users. This method is a data-driven, predictive approach for early detection of depression or other mental illnesses. This study's main contribution is the exploration part of the features and its impact on detecting the depression level.

The online analysis of multi-way data stored in a tensor $\mathcal{X} \in \mathbb{R} ^{I_1 \times \dots \times I_N} $ has become an essential tool for capturing the underlying structures and extracting the sensitive features which can be used to learn a predictive model. However, data distributions often evolve with time and a current predictive model may not be sufficiently representative in the future. Therefore, incrementally updating the tensor-based features and model coefficients are required in such situations. A new efficient tensor-based feature extraction, named NeSGD, is proposed for online $CANDECOMP/PARAFAC$ (CP) decomposition. According to the new features obtained from the resultant matrices of NeSGD, a new criteria is triggered for the updated process of the online predictive model. Experimental evaluation in the field of structural health monitoring using laboratory-based and real-life structural datasets show that our methods provide more accurate results compared with existing online tensor analysis and model learning. The results showed that the proposed methods significantly improved the classification error rates, were able to assimilate the changes in the positive data distribution over time, and maintained a high predictive accuracy in all case studies.

Although deep learning models have achieved state-of-the art performance on a number of vision tasks, generalization over high dimensional multi-modal data, and reliable predictive uncertainty estimation are still active areas of research. Bayesian approaches including Bayesian Neural Nets (BNNs) do not scale well to modern computer vision tasks, as they are difficult to train, and have poor generalization under dataset-shift [27,38]. This motivates the need for effective ensembles which can generalize and give reliable uncertainty estimates. In this paper, we target the problem of generating effective ensembles of neural networks by encouraging diversity in prediction. We explicitly optimize a diversity inducing adversarial loss for learning the stochastic latent variables and thereby obtain diversity in the output predictions necessary for modeling multi-modal data. We evaluate our method on benchmark datasets: MNIST, CIFAR100, TinyImageNet and MIT Places 2, and compared to the most competitive baselines show significant improvements in classification accuracy, under a shift in the data distribution and in out-of-distribution detection.