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We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

This paper serves as a survey of recent advances in large margin training and its theoretical foundations, mostly for (nonlinear) deep neural networks (DNNs) that are probably the most prominent machine learning models for large-scale data in the community over the past decade. We generalize the formulation of classification margins from classical research to latest DNNs, summarize theoretical connections between the margin, network generalization, and robustness, and introduce recent efforts in enlarging the margins for DNNs comprehensively. Since the viewpoint of different methods is discrepant, we categorize them into groups for ease of comparison and discussion in the paper. Hopefully, our discussions and overview inspire new research work in the community that aim to improve the performance of DNNs, and we also point to directions where the large margin principle can be verified to provide theoretical evidence why certain regularizations for DNNs function well in practice. We managed to shorten the paper such that the crucial spirit of large margin learning and related methods are better emphasized.

The rapid advancements in machine learning, graphics processing technologies and availability of medical imaging data has led to a rapid increase in use of machine learning models in the medical domain. This was exacerbated by the rapid advancements in convolutional neural network (CNN) based architectures, which were adopted by the medical imaging community to assist clinicians in disease diagnosis. Since the grand success of AlexNet in 2012, CNNs have been increasingly used in medical image analysis to improve the efficiency of human clinicians. In recent years, three-dimensional (3D) CNNs have been employed for analysis of medical images. In this paper, we trace the history of how the 3D CNN was developed from its machine learning roots, brief mathematical description of 3D CNN and the preprocessing steps required for medical images before feeding them to 3D CNNs. We review the significant research in the field of 3D medical imaging analysis using 3D CNNs (and its variants) in different medical areas such as classification, segmentation, detection, and localization. We conclude by discussing the challenges associated with the use of 3D CNNs in the medical imaging domain (and the use of deep learning models, in general) and possible future trends in the field.

Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc anomaly detection techniques to detect (and discard) these anomalous samples have been proposed in the recent past. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection for DL based applications. We provide a taxonomy for existing techniques based on their underlying assumptions and adopted approaches. We discuss various techniques in each of the categories and provide the relative strengths and weaknesses of the approaches. Our goal in this survey is to provide an easier yet better understanding of the techniques belonging to different categories in which research has been done on this topic. Finally, we highlight the unsolved research challenges while applying anomaly detection techniques in DL systems and present some high-impact future research directions.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.

Thoracic diseases are very serious health problems that plague a large number of people. Chest X-ray is currently one of the most popular methods to diagnose thoracic diseases, playing an important role in the healthcare workflow. However, reading the chest X-ray images and giving an accurate diagnosis remain challenging tasks for expert radiologists. With the success of deep learning in computer vision, a growing number of deep neural network architectures were applied to chest X-ray image classification. However, most of the previous deep neural network classifiers were based on deterministic architectures which are usually very noise-sensitive and are likely to aggravate the overfitting issue. In this paper, to make a deep architecture more robust to noise and to reduce overfitting, we propose using deep generative classifiers to automatically diagnose thorax diseases from the chest X-ray images. Unlike the traditional deterministic classifier, a deep generative classifier has a distribution middle layer in the deep neural network. A sampling layer then draws a random sample from the distribution layer and input it to the following layer for classification. The classifier is generative because the class label is generated from samples of a related distribution. Through training the model with a certain amount of randomness, the deep generative classifiers are expected to be robust to noise and can reduce overfitting and then achieve good performances. We implemented our deep generative classifiers based on a number of well-known deterministic neural network architectures, and tested our models on the chest X-ray14 dataset. The results demonstrated the superiority of deep generative classifiers compared with the corresponding deep deterministic classifiers.

This paper introduces a deep-learning based efficient classifier for common dermatological conditions, aimed at people without easy access to skin specialists. We report approximately 80% accuracy, in a situation where primary care doctors have attained 57% success rate, according to recent literature. The rationale of its design is centered on deploying and updating it on handheld devices in near future. Dermatological diseases are common in every population and have a wide spectrum in severity. With a shortage of dermatological expertise being observed in several countries, machine learning solutions can augment medical services and advise regarding existence of common diseases. The paper implements supervised classification of nine distinct conditions which have high occurrence in East Asian countries. Our current attempt establishes that deep learning based techniques are viable avenues for preliminary information to aid patients.

Machine Learning is a widely-used method for prediction generation. These predictions are more accurate when the model is trained on a larger dataset. On the other hand, the data is usually divided amongst different entities. For privacy reasons, the training can be done locally and then the model can be safely aggregated amongst the participants. However, if there are only two participants in \textit{Collaborative Learning}, the safe aggregation loses its power since the output of the training already contains much information about the participants. To resolve this issue, they must employ privacy-preserving mechanisms, which inevitably affect the accuracy of the model. In this paper, we model the training process as a two-player game where each player aims to achieve a higher accuracy while preserving its privacy. We introduce the notion of \textit{Price of Privacy}, a novel approach to measure the effect of privacy protection on the accuracy of the model. We develop a theoretical model for different player types, and we either find or prove the existence of a Nash Equilibrium with some assumptions. Moreover, we confirm these assumptions via a Recommendation Systems use case: for a specific learning algorithm, we apply three privacy-preserving mechanisms on two real-world datasets. Finally, as a complementary work for the designed game, we interpolate the relationship between privacy and accuracy for this use case and present three other methods to approximate it in a real-world scenario.

We explore the use of deep learning hierarchical models for problems in financial prediction and classification. Financial prediction problems -- such as those presented in designing and pricing securities, constructing portfolios, and risk management -- often involve large data sets with complex data interactions that currently are difficult or impossible to specify in a full economic model. Applying deep learning methods to these problems can produce more useful results than standard methods in finance. In particular, deep learning can detect and exploit interactions in the data that are, at least currently, invisible to any existing financial economic theory.