Machine learning has seen in the last 5-10 years an explosion in its growth from a research centered area of computer science and mathematics to a driving force for innovation in every aspect of our lives [1, 2, 3]. This was driven mainly by the success of deep learning and the significant investment of big technology firms in open source machine learning research [4, 5, 6]. Real life machine learning based solutions often require a number of models to work together to achieve the business goal of the product(s) [7]. Such models can be trained independently or as part of an optimised training pipeline [8, 9]. Breaking down the product into multiple models has several advantages: I) It allows for parallel model development with model designers focused on solving relatively small and well-defined problems.

We present Deep Tensor Canonical Correlation Analysis (DTCCA), a method to learn complex nonlinear transformations of multiple views (more than two) of data such that the resulting representations are linearly correlated in high order. The high-order correlation of given multiple views is modeled by covariance tensor, which is different from most CCA formulations relying solely on the pairwise correlations. Parameters of transformations of each view are jointly learned by maximizing the high-order canonical correlation. To solve the resulting problem, we reformulate it as the best sum of rank-1 approximation, which can be efficiently solved by existing tensor decomposition method. DTCCA is a nonlinear extension of tensor CCA (TCCA) via deep networks. The transformations of DTCCA are parametric functions, which are very different from implicit mapping in the form of kernel function. Comparing with kernel TCCA, DTCCA not only can deal with arbitrary dimensions of the input data, but also does not need to maintain the training data for computing representations of any given data point. Hence, DTCCA as a unified model can efficiently overcome the scalable issue of TCCA for either high-dimensional multi-view data or a large amount of views, and it also naturally extends TCCA for learning nonlinear representation. Extensive experiments on three multi-view data sets demonstrate the effectiveness of the proposed method.

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations.

Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations (embeddings) of these networks for the prediction of missing relations or signs. Existing embedding methods for sign prediction generally enforce different notions of status or balance theories in their optimization function. These theories, however, are often inaccurate or incomplete, which negatively impacts method performance. In this context, we introduce conditional signed network embedding (CSNE). Our probabilistic approach models structural information about the signs in the network separately from fine-grained detail. Structural information is represented in the form of a prior, while the embedding itself is used for capturing fine-grained information. These components are then integrated in a rigorous manner. CSNE's accuracy depends on the existence of sufficiently powerful structural priors for modelling signed networks, currently unavailable in the literature. Thus, as a second main contribution, which we find to be highly valuable in its own right, we also introduce a novel approach to construct priors based on the Maximum Entropy (MaxEnt) principle. These priors can model the \emph{polarity} of nodes (degree to which their links are positive) as well as signed \emph{triangle counts} (a measure of the degree structural balance holds to in a network). Experiments on a variety of real-world networks confirm that CSNE outperforms the state-of-the-art on the task of sign prediction. Moreover, the MaxEnt priors on their own, while less accurate than full CSNE, achieve accuracies competitive with the state-of-the-art at very limited computational cost, thus providing an excellent runtime-accuracy trade-off in resource-constrained situations.

Contrastive learning (CL) is an emerging analysis approach that aims to discover unique patterns in one dataset relative to another. By applying this approach to network analysis, we can reveal unique characteristics in one network by contrasting with another. For example, with networks of protein interactions obtained from normal and cancer tissues, we can discover unique types of interactions in cancer tissues. However, existing CL methods cannot be directly applied to networks. To address this issue, we introduce a novel approach called contrastive network representation learning (cNRL). This approach embeds network nodes into a low-dimensional space that reveals the uniqueness of one network compared to another. Within this approach, we also design a method, named i-cNRL, that offers interpretability in the learned results, allowing for understanding which specific patterns are found in one network but not the other. We demonstrate the capability of i-cNRL with multiple network models and real-world datasets. Furthermore, we provide quantitative and qualitative comparisons across i-cNRL and other potential cNRL algorithm designs.

One of the major concerns of targeting interventions on individuals in social welfare programs is discrimination: individualized treatments may induce disparities on sensitive attributes such as age, gender, or race. This paper addresses the question of the design of fair and efficient treatment allocation rules. We adopt the non-maleficence perspective of "first do no harm": we propose to select the fairest allocation within the Pareto frontier. We provide envy-freeness justifications to novel counterfactual notions of fairness. We discuss easy-to-implement estimators of the policy function, by casting the optimization into a mixed-integer linear program formulation. We derive regret bounds on the unfairness of the estimated policy function, and small sample guarantees on the Pareto frontier. Finally, we illustrate our method using an application from education economics.

Clustering has long been a popular unsupervised learning approach to identify groups of similar objects and discover patterns from unlabeled data in many applications. Yet, coming up with meaningful interpretations of the estimated clusters has often been challenging precisely due to its unsupervised nature. Meanwhile, in many real-world scenarios, there are some noisy supervising auxiliary variables, for instance, subjective diagnostic opinions, that are related to the observed heterogeneity of the unlabeled data. By leveraging information from both supervising auxiliary variables and unlabeled data, we seek to uncover more scientifically interpretable group structures that may be hidden by completely unsupervised analyses. In this work, we propose and develop a new statistical pattern discovery method named Supervised Convex Clustering (SCC) that borrows strength from both information sources and guides towards finding more interpretable patterns via a joint convex fusion penalty. We develop several extensions of SCC to integrate different types of supervising auxiliary variables, to adjust for additional covariates, and to find biclusters. We demonstrate the practical advantages of SCC through simulations and a case study on Alzheimer's Disease genomics. Specifically, we discover new candidate genes as well as new subtypes of Alzheimer's Disease that can potentially lead to better understanding of the underlying genetic mechanisms responsible for the observed heterogeneity of cognitive decline in older adults.

Pattern recognition and machine learning techniques have been increasingly adopted in adversarial settings such as spam, intrusion and malware detection, although their security against well-crafted attacks that aim to evade detection by manipulating data at test time has not yet been thoroughly assessed. While previous work has been mainly focused on devising adversary-aware classification algorithms to counter evasion attempts, only few authors have considered the impact of using reduced feature sets on classifier security against the same attacks. An interesting, preliminary result is that classifier security to evasion may be even worsened by the application of feature selection. In this paper, we provide a more detailed investigation of this aspect, shedding some light on the security properties of feature selection against evasion attacks. Inspired by previous work on adversary-aware classifiers, we propose a novel adversary-aware feature selection model that can improve classifier security against evasion attacks, by incorporating specific assumptions on the adversary's data manipulation strategy. We focus on an efficient, wrapper-based implementation of our approach, and experimentally validate its soundness on different application examples, including spam and malware detection.

Multiclass classification problems are most often solved by either training a single centralized classifier on all $K$ classes, or by reducing the problem to multiple binary classification tasks. This paper explores the uncharted region between these two extremes: How can we solve the $K$-class classification problem by combining the predictions of smaller classifiers, each trained on an arbitrary number of classes $R \in \{2, 3, \ldots, K\}$? We present a mathematical framework for answering this question, and derive bounds on the number of classifiers (in terms of $K$ and $R$) needed to accurately predict the true class of an unlabeled sample under both adversarial and stochastic assumptions. By exploiting a connection to the classical set cover problem in combinatorics, we produce an efficient, near-optimal scheme (with respect to the number of classifiers) for designing such configurations of classifiers, which recovers the well-known one-vs.-one strategy as a special case when $R=2$. Experiments with the MNIST and CIFAR-10 datasets show that our scheme is capable of matching the performance of centralized classifiers in practice. The results suggest that our approach offers a promising direction for solving the problem of data heterogeneity which plagues current federated learning methods.

We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the simple model $X_i = z_i \theta + \varepsilon_i$, $z_i \in \{-1,1\}$, $\varepsilon_i \thicksim \mathcal{N}(0, I)$, which has two clusters with centres $\theta$ and $-\theta$. We provide a finite sample analysis of a new sparse clustering algorithm based on sparse PCA and show that it achieves the minimax optimal misclustering rate in the regime $\|\theta\| \rightarrow \infty$, matching asymptotically the Bayes error. Our results require the sparsity to grow slower than the square root of the sample size. Using a recent framework for computational lower bounds---the low-degree likelihood ratio---we give evidence that this condition is necessary for any polynomial-time clustering algorithm to succeed below the BBP threshold. This complements existing evidence based on reductions and statistical query lower bounds. Compared to these existing results, we cover a wider set of parameter regimes and give a more precise understanding of the runtime required and the misclustering error achievable. We also discuss extensions of our results to more than two clusters.