We propose Federated Generative Adversarial Network (FedGAN) for training a GAN across distributed sources of non-independent-and-identically-distributed data sources subject to communication and privacy constraints. Our algorithm uses local generators and discriminators which are periodically synced via an intermediary that averages and broadcasts the generator and discriminator parameters. We theoretically prove the convergence of FedGAN with both equal and two time-scale updates of generator and discriminator, under standard assumptions, using stochastic approximations and communication efficient stochastic gradient descents. We experiment FedGAN on toy examples (2D system, mixed Gaussian, and Swiss role), image datasets (MNIST, CIFAR-10, and CelebA), and time series datasets (household electricity consumption and electric vehicle charging sessions). We show FedGAN converges and has similar performance to general distributed GAN, while reduces communication complexity. We also show its robustness to reduced communications.

To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.

We provide a rigorous analysis of how implicit bias towards smooth interpolations leads to low generalization error in the overparameterized setting. We provide the first case study of this connection through a random Fourier series model and weighted least squares. We then argue through this model and numerical experiments that normalization methods in deep learning such as weight normalization improve generalization in overparameterized neural networks by implicitly encouraging smooth interpolants.

In a machine learning setup, the function F could be interpreted as the loss function associated with a sample ξ and the function f could represent the risk, which is defined as the expected loss. Such constrained stochastic optimization problems arise frequently in statistical machine learning applications. Conditional gradient algorithm, also called as Frank-Wolfe algorithm, is an efficient method for solving constrained optimization problems of the form in (1) due to their projection-free nature [Jag13, HJN15, FGM17, LPZZ17, BZK18, RDLS18]. In each step of the conditional gradient method, it is only required to minimize a linear objective over the set Ω. This operation could be implemented efficiently for a variety of sets arising in statistical machine learning, compared to the operation of projecting on to the set Ω, which is required for example by the projected gradient method. Hence, conditional gradient method has regained popularity in the last decade in the optimization and machine learning community.

As deep learning models become tasked with more and more decisions that impact human lives, such as hiring, criminal recidivism, and loan repayment, bias is becoming a growing concern. This has led to dozens of definitions of fairness and numerous algorithmic techniques to improve the fairness of neural networks. Most debiasing algorithms require retraining a neural network from scratch, however, this is not feasible in many applications, especially when the model takes days to train or when the full training dataset is no longer available. In this work, we present a study on post-hoc methods for debiasing neural networks. First we study the nature of the problem, showing that the difficulty of post-hoc debiasing is highly dependent on the initial conditions of the original model. Then we define three new fine-tuning techniques: random perturbation, layer-wise optimization, and adversarial fine-tuning. All three techniques work for any group fairness constraint. We give a comparison with six algorithms - three popular post-processing debiasing algorithms and our three proposed methods - across three datasets and three popular bias measures. We show that no post-hoc debiasing technique dominates all others, and we identify settings in which each algorithm performs the best. Our code is available at https://github.com/realityengines/post_hoc_debiasing.

We propose a robust variational autoencoder with $\beta$ divergence for tabular data (RTVAE) with mixed categorical and continuous features. Variational autoencoders (VAE) and their variations are popular frameworks for anomaly detection problems. The primary assumption is that we can learn representations for normal patterns via VAEs and any deviation from that can indicate anomalies. However, the training data itself can contain outliers. The source of outliers in training data include the data collection process itself (random noise) or a malicious attacker (data poisoning) who may target to degrade the performance of the machine learning model. In either case, these outliers can disproportionately affect the training process of VAEs and may lead to wrong conclusions about what the normal behavior is. In this work, we derive a novel form of a variational autoencoder for tabular data sets with categorical and continuous features that is robust to outliers in training data. Our results on the anomaly detection application for network traffic datasets demonstrate the effectiveness of our approach.

Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6 and Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec (Québec), Canada G1V 0A6 (Dated: June 16, 2020) Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically and/or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where the effective local mechanisms governing a dynamic are learned automatically from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using stochastic contagion dynamics of increasing complexity on static and temporal networks. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks. Our capacity to prevent or contain outbreaks of infectious tasks, making them prime candidates to tackle several diseases is directly linked to our ability to accurately model challenges of contagion dynamics modeling. Since the seminal work of Kermack and Here, we demonstrate how deep learning can be used to McKendrick almost a century ago [1], a variety of models build effective models of stochastic contagion dynamics taking incorporating ever more sophisticated contagion mechanisms place on complex networks. Instead of constructing a have been proposed, studied and used [2-5].

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions on the boundedness of gradients, strong smoothness and convexity of loss functions. In this paper, we provide a fine-grained analysis of stability and generalization for SGD by substantially relaxing these assumptions. Firstly, we establish stability and generalization for SGD by removing the existing bounded gradient assumptions. The key idea is the introduction of a new stability measure called on-average model stability, for which we develop novel bounds controlled by the risks of SGD iterates. This yields generalization bounds depending on the behavior of the best model, and leads to the first-ever-known fast bounds in the low-noise setting using stability approach. Secondly, the smoothness assumption is relaxed by considering loss functions with Holder continuous (sub)gradients for which we show that optimal bounds are still achieved by balancing computation and stability. To our best knowledge, this gives the first-ever-known stability and generalization bounds for SGD with even non-differentiable loss functions. Finally, we study learning problems with (strongly) convex objectives but non-convex loss functions.

In this paper we introduce a new problem in the field of production planning which we call the Production Leveling Problem. The task is to assign orders to production periods such that the load in each period and on each production resource is balanced, capacity limits are not exceeded and the orders' priorities are taken into account. Production Leveling is an important intermediate step between long-term planning and the final scheduling of orders within a production period, as it is responsible for selecting good subsets of orders to be scheduled within each period. A formal model of the problem is proposed and NP-hardness is shown by reduction from Bin Backing. As an exact method for solving moderately sized instances we introduce a MIP formulation. For solving large problem instances, metaheuristic local search is investigated. A greedy heuristic and two neighborhood structures for local search are proposed, in order to apply them using Variable Neighborhood Descent and Simulated Annealing. Regarding exact techniques, the main question of research is, up to which size instances are solvable within a fixed amount of time. For the metaheuristic approaches the aim is to show that they produce near-optimal solutions for smaller instances, but also scale well to very large instances. A set of realistic problem instances from an industrial partner is contributed to the literature, as well as random instance generators. The experimental evaluation conveys that the proposed MIP model works well for instances with up to 250 orders. Out of the investigated metaheuristic approaches, Simulated Annealing achieves the best results. It is shown to produce solutions with less than 3% average optimality gap on small instances and to scale well up to thousands of orders and dozens of periods and products. The presented metaheuristic methods are already being used in the industry.

Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder directly applying meta-learning techniques. Although the knowledge of governing partial differential equations (PDEs) of the data can be helpful for the fast adaptation to few observations, it is difficult to generalize to different or unknown dynamics. In this paper, we propose a framework, physics-aware modular meta-learning with auxiliary tasks (PiMetaL) whose spatial modules incorporate PDE-independent knowledge and temporal modules are rapidly adaptable to the limited data, respectively. The framework does not require the exact form of governing equations to model the observed spatiotemporal data. Furthermore, it mitigates the need for a large number of real-world tasks for meta-learning by leveraging simulated data. We apply the proposed framework to both synthetic and real-world spatiotemporal prediction tasks and demonstrate its superior performance with limited observations.