Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise naturally in many contexts including biological and social networks. Clustering is a fundamental problem in network analysis where the goal is to regroup nodes with similar connectivity profiles. In the past decade, various clustering methods have been extended from the unilayer setting to multilayer graphs in order to incorporate the information provided by each layer. While most existing works assume - rather restrictively - that all layers share the same set of nodes, we propose a new framework that allows for layers to be defined on different sets of nodes. In particular, the nodes not recorded in a layer are treated as missing. Within this paradigm, we investigate several generalizations of well-known clustering methods in the complete setting to the incomplete one and prove some consistency results under the Multi-Layer Stochastic Block Model assumption. Our theoretical results are complemented by thorough numerical comparisons between our proposed algorithms on synthetic data, and also on real datasets, thus highlighting the promising behaviour of our methods in various settings.

The outbreak of the COVID-19 (Coronavirus disease 2019) pandemic has changed the world. According to the World Health Organization (WHO), there have been more than 100 million confirmed cases of COVID-19, including more than 2.4 million deaths. It is extremely important the early detection of the disease, and the use of medical imaging such as chest X-ray (CXR) and chest Computed Tomography (CCT) have proved to be an excellent solution. However, this process requires clinicians to do it within a manual and time-consuming task, which is not ideal when trying to speed up the diagnosis. In this work, we propose an ensemble classifier based on probabilistic Support Vector Machine (SVM) in order to identify pneumonia patterns while providing information about the reliability of the classification. Specifically, each CCT scan is divided into cubic patches and features contained in each one of them are extracted by applying kernel PCA. The use of base classifiers within an ensemble allows our system to identify the pneumonia patterns regardless of their size or location. Decisions of each individual patch are then combined into a global one according to the reliability of each individual classification: the lower the uncertainty, the higher the contribution. Performance is evaluated in a real scenario, yielding an accuracy of 97.86%. The large performance obtained and the simplicity of the system (use of deep learning in CCT images would result in a huge computational cost) evidence the applicability of our proposal in a real-world environment.

In many supervised learning applications, it is not sufficient to know the most probable class y for a certain data point x. Instead, a well-calibrated probabilistic prediction p(y x) is required. For instance, in clinical applications, class probabilities are important for confidence in model predictions (Challis et al., 2015). Some classifiers intrinsically provide such a posterior probability, e. g. logistic regression or Gaussian process classification (GPC) as described in Rasmussen and Williams (2006). There are also various methods to install or improve such a calibration for a given classification approach (Niculescu-Mizil and Caruana, 2005), like Platt scaling (Platt, 2000) or isotonic regression (Zadrozny and Elkan, 2002).

Tensor decomposition is a fundamentally challenging problem. Even the simplest case of tensor decomposition, the rank-1 approximation in terms of the Least Squares (LS) error, is known to be NP-hard. Here, we show that, if we consider the KL divergence instead of the LS error, we can analytically derive a closed form solution for the rank-1 tensor that minimizes the KL divergence from a given positive tensor. Our key insight is to treat a positive tensor as a probability distribution and formulate the process of rank-1 approximation as a projection onto the set of rank-1 tensors. This enables us to solve rank-1 approximation by convex optimization. We empirically demonstrate that our algorithm is an order of magnitude faster than the existing rank-1 approximation methods and gives better approximation of given tensors, which supports our theoretical finding.

This paper develops an efficient distributed inference algorithm, which is robust against a moderate fraction of Byzantine nodes, namely arbitrary and possibly adversarial machines in a distributed learning system. In robust statistics, the median-of-means (MOM) has been a popular approach to hedge against Byzantine failures due to its ease of implementation and computational efficiency. However, the MOM estimator has the shortcoming in terms of statistical efficiency. The first main contribution of the paper is to propose a variance reduced median-of-means (VRMOM) estimator, which improves the statistical efficiency over the vanilla MOM estimator and is computationally as efficient as the MOM. Based on the proposed VRMOM estimator, we develop a general distributed inference algorithm that is robust against Byzantine failures. Theoretically, our distributed algorithm achieves a fast convergence rate with only a constant number of rounds of communications. We also provide the asymptotic normality result for the purpose of statistical inference. To the best of our knowledge, this is the first normality result in the setting of Byzantine-robust distributed learning. The simulation results are also presented to illustrate the effectiveness of our method.

It is important for a broad range of applications, including policy making [136], medical imaging [30], advertisement [22], the development of medical treatments [189], the evaluation of evidence within legal frameworks [183, 218], social science [82, 96, 246], biology [235], and many others. It is also a burgeoning topic in machine learning and artificial intelligence [17, 66, 76, 144, 210, 247, 255], where it has been argued that a consideration for causality is crucial for reasoning about the world. In order to discover causal relations, and thereby gain causal understanding, one may perform interventions and manipulations as part of a randomized experiment. These experiments may not only allow researchers or agents to identify causal relationships, but also to estimate the magnitude of these relationships. Unfortunately, in many cases, it may not be possible to undertake such experiments due to prohibitive cost, ethical concerns, or impracticality.

The rise of algorithmic decision-making has spawned much research on fair machine learning (ML). Financial institutions use ML for building risk scorecards that support a range of credit-related decisions. Yet, the literature on fair ML in credit scoring is scarce. The paper makes two contributions. First, we provide a systematic overview of algorithmic options for incorporating fairness goals in the ML model development pipeline. In this scope, we also consolidate the space of statistical fairness criteria and examine their adequacy for credit scoring. Second, we perform an empirical study of different fairness processors in a profit-oriented credit scoring setup using seven real-world data sets. The empirical results substantiate the evaluation of fairness measures, identify more and less suitable options to implement fair credit scoring, and clarify the profit-fairness trade-off in lending decisions. Specifically, we find that multiple fairness criteria can be approximately satisfied at once and identify separation as a proper criterion for measuring the fairness of a scorecard. We also find fair in-processors to deliver a good balance between profit and fairness. More generally, we show that algorithmic discrimination can be reduced to a reasonable level at a relatively low cost.

Data privacy concerns often prevent the use of cloud-based machine learning services for sensitive personal data. While homomorphic encryption (HE) offers a potential solution by enabling computations on encrypted data, the challenge is to obtain accurate machine learning models that work within the multiplicative depth constraints of a leveled HE scheme. Existing approaches for encrypted inference either make ad-hoc simplifications to a pre-trained model (e.g., replace hard comparisons in a decision tree with soft comparators) at the cost of accuracy or directly train a new depth-constrained model using the original training set. In this work, we propose a framework to transfer knowledge extracted by complex decision tree ensembles to shallow neural networks (referred to as DTNets) that are highly conducive to encrypted inference. Our approach minimizes the accuracy loss by searching for the best DTNet architecture that operates within the given depth constraints and training this DTNet using only synthetic data sampled from the training data distribution. Extensive experiments on real-world datasets demonstrate that these characteristics are critical in ensuring that DTNet accuracy approaches that of the original tree ensemble. Our system is highly scalable and can perform efficient inference on batched encrypted (134 bits of security) data with amortized time in milliseconds. This is approximately three orders of magnitude faster than the standard approach of applying soft comparison at the internal nodes of the ensemble trees.

Kidney transplantation can significantly enhance living standards for people suffering from end-stage renal disease. A significant factor that affects graft survival time (the time until the transplant fails and the patient requires another transplant) for kidney transplantation is the compatibility of the Human Leukocyte Antigens (HLAs) between the donor and recipient. In this paper, we propose new biologically-relevant feature representations for incorporating HLA information into machine learning-based survival analysis algorithms. We evaluate our proposed HLA feature representations on a database of over 100,000 transplants and find that they improve prediction accuracy by about 1%, modest at the patient level but potentially significant at a societal level. Accurate prediction of survival times can improve transplant survival outcomes, enabling better allocation of donors to recipients and reducing the number of re-transplants due to graft failure with poorly matched donors.

Self-supervised learning (SSL) is rapidly closing the gap with supervised methods on large computer vision benchmarks. A successful approach to SSL is to learn representations which are invariant to distortions of the input sample. However, a recurring issue with this approach is the existence of trivial constant representations. Most current methods avoid such collapsed solutions by careful implementation details. We propose an objective function that naturally avoids such collapse by measuring the cross-correlation matrix between the outputs of two identical networks fed with distorted versions of a sample, and making it as close to the identity matrix as possible. This causes the representation vectors of distorted versions of a sample to be similar, while minimizing the redundancy between the components of these vectors. The method is called Barlow Twins, owing to neuroscientist H. Barlow's redundancy-reduction principle applied to a pair of identical networks. Barlow Twins does not require large batches nor asymmetry between the network twins such as a predictor network, gradient stopping, or a moving average on the weight updates. It allows the use of very high-dimensional output vectors. Barlow Twins outperforms previous methods on ImageNet for semi-supervised classification in the low-data regime, and is on par with current state of the art for ImageNet classification with a linear classifier head, and for transfer tasks of classification and object detection.