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Recent research suggests that predictions made by machine-learning models can amplify biases present in the training data. When a model amplifies bias, it makes certain predictions at a higher rate for some groups than expected based on training-data statistics. Mitigating such bias amplification requires a deep understanding of the mechanics in modern machine learning that give rise to that amplification. We perform the first systematic, controlled study into when and how bias amplification occurs. To enable this study, we design a simple image-classification problem in which we can tightly control (synthetic) biases. Our study of this problem reveals that the strength of bias amplification is correlated to measures such as model accuracy, model capacity, model overconfidence, and amount of training data. We also find that bias amplification can vary greatly during training. Finally, we find that bias amplification may depend on the difficulty of the classification task relative to the difficulty of recognizing group membership: bias amplification appears to occur primarily when it is easier to recognize group membership than class membership. Our results suggest best practices for training machine-learning models that we hope will help pave the way for the development of better mitigation strategies.

Many applications affecting human lives rely on models that have come to be known under the umbrella of machine learning and artificial intelligence. These AI models are usually complicated mathematical functions that map from an input space to an output space. Stakeholders are interested to know the rationales behind models' decisions and functional behavior. We study this functional behavior in relation to the data used to create the models. On this topic, scholars have often assumed that models do not extrapolate, i.e., they learn from their training samples and process new input by interpolation. This assumption is questionable: we show that models extrapolate frequently; the extent of extrapolation varies and can be socially consequential. We demonstrate that extrapolation happens for a substantial portion of datasets more than one would consider reasonable. How can we trust models if we do not know whether they are extrapolating? Given a model trained to recommend clinical procedures for patients, can we trust the recommendation when the model considers a patient older or younger than all the samples in the training set? If the training set is mostly Whites, to what extent can we trust its recommendations about Black and Hispanic patients? Which dimension (race, gender, or age) does extrapolation happen? Even if a model is trained on people of all races, it still may extrapolate in significant ways related to race. The leading question is, to what extent can we trust AI models when they process inputs that fall outside their training set? This paper investigates several social applications of AI, showing how models extrapolate without notice. We also look at different sub-spaces of extrapolation for specific individuals subject to AI models and report how these extrapolations can be interpreted, not mathematically, but from a humanistic point of view.

We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev regular and data that are merely integrable. We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. We prove that on unstructured regular meshes the rate of convergence of approximate solutions generated by the upwind scheme towards the unique solution of the continuous model is at least one. The numerical error is estimated in terms of logarithmic Kantorovich-Rubinstein distances and provides thus a bound on the rate of weak convergence.

With the widespread use of AI systems and applications in our everyday lives, it is important to take fairness issues into consideration while designing and engineering these types of systems. Such systems can be used in many sensitive environments to make important and life-changing decisions; thus, it is crucial to ensure that the decisions do not reflect discriminatory behavior toward certain groups or populations. We have recently seen work in machine learning, natural language processing, and deep learning that addresses such challenges in different subdomains. With the commercialization of these systems, researchers are becoming aware of the biases that these applications can contain and have attempted to address them. In this survey we investigated different real-world applications that have shown biases in various ways, and we listed different sources of biases that can affect AI applications. We then created a taxonomy for fairness definitions that machine learning researchers have defined in order to avoid the existing bias in AI systems. In addition to that, we examined different domains and subdomains in AI showing what researchers have observed with regard to unfair outcomes in the state-of-the-art methods and how they have tried to address them. There are still many future directions and solutions that can be taken to mitigate the problem of bias in AI systems. We are hoping that this survey will motivate researchers to tackle these issues in the near future by observing existing work in their respective fields.

Recent work has proposed stochastic Plackett-Luce (PL) ranking models as a robust choice for optimizing relevance and fairness metrics. Unlike their deterministic counterparts that require heuristic optimization algorithms, PL models are fully differentiable. Theoretically, they can be used to optimize ranking metrics via stochastic gradient descent. However, in practice, the computation of the gradient is infeasible because it requires one to iterate over all possible permutations of items. Consequently, actual applications rely on approximating the gradient via sampling techniques. In this paper, we introduce a novel algorithm: PL-Rank, that estimates the gradient of a PL ranking model w.r.t. both relevance and fairness metrics. Unlike existing approaches that are based on policy gradients, PL-Rank makes use of the specific structure of PL models and ranking metrics. Our experimental analysis shows that PL-Rank has a greater sample-efficiency and is computationally less costly than existing policy gradients, resulting in faster convergence at higher performance. PL-Rank further enables the industry to apply PL models for more relevant and fairer real-world ranking systems.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works have focused on fairness with respect to a specific metric, modeled the corresponding fair classification problem as a constrained optimization problem, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which we do not have fair classifiers and many of the aforementioned algorithms do not come with theoretical guarantees; perhaps because the resulting optimization problem is non-convex. The main contribution of this paper is a new meta-algorithm for classification that takes as input a large class of fairness constraints, with respect to multiple non-disjoint sensitive attributes, and which comes with provable guarantees. This is achieved by first developing a meta-algorithm for a large family of classification problems with convex constraints, and then showing that classification problems with general types of fairness constraints can be reduced to those in this family. We present empirical results that show that our algorithm can achieve near-perfect fairness with respect to various fairness metrics, and that the loss in accuracy due to the imposed fairness constraints is often small. Overall, this work unifies several prior works on fair classification, presents a practical algorithm with theoretical guarantees, and can handle fairness metrics that were previously not possible.

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent work has shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al.~\cite{AroraGeLiMaZh17} suggests a dilemma about GANs' statistical properties: powerful discriminators cause overfitting, whereas weak discriminators cannot detect mode collapse. In contrast, we show in this paper that GANs can in principle learn distributions in Wasserstein distance (or KL-divergence in many cases) with polynomial sample complexity, if the discriminator class has strong distinguishing power against the particular generator class (instead of against all possible generators). For various generator classes such as mixture of Gaussians, exponential families, and invertible neural networks generators, we design corresponding discriminators (which are often neural nets of specific architectures) such that the Integral Probability Metric (IPM) induced by the discriminators can provably approximate the Wasserstein distance and/or KL-divergence. This implies that if the training is successful, then the learned distribution is close to the true distribution in Wasserstein distance or KL divergence, and thus cannot drop modes. Our preliminary experiments show that on synthetic datasets the test IPM is well correlated with KL divergence, indicating that the lack of diversity may be caused by the sub-optimality in optimization instead of statistical inefficiency.

The field of Multi-Agent System (MAS) is an active area of research within Artificial Intelligence, with an increasingly important impact in industrial and other real-world applications. Within a MAS, autonomous agents interact to pursue personal interests and/or to achieve common objectives. Distributed Constraint Optimization Problems (DCOPs) have emerged as one of the prominent agent architectures to govern the agents' autonomous behavior, where both algorithms and communication models are driven by the structure of the specific problem. During the last decade, several extensions to the DCOP model have enabled them to support MAS in complex, real-time, and uncertain environments. This survey aims at providing an overview of the DCOP model, giving a classification of its multiple extensions and addressing both resolution methods and applications that find a natural mapping within each class of DCOPs. The proposed classification suggests several future perspectives for DCOP extensions, and identifies challenges in the design of efficient resolution algorithms, possibly through the adaptation of strategies from different areas.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.