The goal of two-sample tests is to assess whether two samples, $S_P \sim P^n$ and $S_Q \sim Q^m$, are drawn from the same distribution. Perhaps intriguingly, one relatively unexplored method to build two-sample tests is the use of binary classifiers. In particular, construct a dataset by pairing the $n$ examples in $S_P$ with a positive label, and by pairing the $m$ examples in $S_Q$ with a negative label. If the null hypothesis "$P = Q$" is true, then the classification accuracy of a binary classifier on a held-out subset of this dataset should remain near chance-level. As we will show, such Classifier Two-Sample Tests (C2ST) learn a suitable representation of the data on the fly, return test statistics in interpretable units, have a simple null distribution, and their predictive uncertainty allow to interpret where $P$ and $Q$ differ. The goal of this paper is to establish the properties, performance, and uses of C2ST. First, we analyze their main theoretical properties. Second, we compare their performance against a variety of state-of-the-art alternatives. Third, we propose their use to evaluate the sample quality of generative models with intractable likelihoods, such as Generative Adversarial Networks (GANs). Fourth, we showcase the novel application of GANs together with C2ST for causal discovery.

We present the Structural Agnostic Model (SAM), a framework to estimate end-to-end non-acyclic causal graphs from observational data. In a nutshell, SAM implements an adversarial game in which a separate model generates each variable, given real values from all others. In tandem, a discriminator attempts to distinguish between the joint distributions of real and generated samples. Finally, a sparsity penalty forces each generator to consider only a small subset of the variables, yielding a sparse causal graph. SAM scales easily to hundreds variables. Our experiments show the state-of-the-art performance of SAM on discovering causal structures and modeling interventions, in both acyclic and non-acyclic graphs.

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the $1$-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.

We present Causal Generative Neural Networks (CGNNs) to learn functional causal models from observational data. CGNNs leverage conditional independencies and distributional asymmetries to discover bivariate and multivariate causal structures. CGNNs make no assumption regarding the lack of confounders, and learn a differentiable generative model of the data by using backpropagation. Extensive experiments show their good performances comparatively to the state of the art in observational causal discovery on both simulated and real data, with respect to cause-effect inference, v-structure identification, and multivariate causal discovery.

Over the past four years, neural networks have proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when seen as a function of the inputs. For most current network architectures, we prove that the $\ell_1$-norm of these gradients grows as the square root of the input-size. These nets therefore become increasingly vulnerable with growing image size. Over the course of our analysis we rediscover and generalize double-backpropagation, a technique that penalizes large gradients in the loss surface to reduce adversarial vulnerability and increase generalization performance. We show that this regularization-scheme is equivalent at first order to training with adversarial noise. Finally, we demonstrate that replacing strided by average-pooling layers decreases adversarial vulnerability. Our proofs rely on the network's weight-distribution at initialization, but extensive experiments confirm their conclusions after training.

One major obstacle towards AI is the poor ability of models to solve new problems quicker, and without forgetting previously acquired knowledge. To better understand this issue, we study the problem of continual learning, where the model observes, once and one by one, examples concerning a sequence of tasks. First, we propose a set of metrics to evaluate models learning over a continuum of data. These metrics characterize models not only by their test accuracy, but also in terms of their ability to transfer knowledge across tasks. Second, we propose a model for continual learning, called Gradient Episodic Memory (GEM) that alleviates forgetting, while allowing beneficial transfer of knowledge to previous tasks. Our experiments on variants of the MNIST and CIFAR-100 datasets demonstrate the strong performance of GEM when compared to the state-of-the-art.

This paper establishes the existence of observable footprints that reveal the "causal dispositions" of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to observational causal discovery, and build a classifier that achieves state-of-the-art performance on finding the causal direction between pairs of random variables, given samples from their joint distribution. Second, we use our causal direction classifier to effectively distinguish between features of objects and features of their contexts in collections of static images. Our experiments demonstrate the existence of a relation between the direction of causality and the difference between objects and their contexts, and by the same token, the existence of observable signals that reveal the causal dispositions of objects.

Large deep neural networks are powerful, but exhibit undesirable behaviors such as memorization and sensitivity to adversarial examples. In this work, we propose mixup, a simple learning principle to alleviate these issues. In essence, mixup trains a neural network on convex combinations of pairs of examples and their labels. By doing so, mixup regularizes the neural network to favor simple linear behavior in-between training examples. Our experiments on the ImageNet-2012, CIFAR-10, CIFAR-100, Google commands and UCI datasets show that mixup improves the generalization of state-of-the-art neural network architectures. We also find that mixup reduces the memorization of corrupt labels, increases the robustness to adversarial examples, and stabilizes the training of generative adversarial networks.

The introduction of data analytics into medicine has changed the nature of patient treatment. In this, patients are asked to disclose personal information such as genetic markers, lifestyle habits, and clinical history. This data is then used by statistical models to predict personalized treatments. However, due to privacy concerns, patients often desire to withhold sensitive information. This self-censorship can impede proper diagnosis and treatment, which may lead to serious health complications and even death over time. In this paper, we present privacy distillation, a mechanism which allows patients to control the type and amount of information they wish to disclose to the healthcare providers for use in statistical models. Meanwhile, it retains the accuracy of models that have access to all patient data under a sufficient but not full set of privacy-relevant information. We validate privacy distillation using a corpus of patients prescribed to warfarin for a personalized dosage. We use a deep neural network to implement privacy distillation for training and making dose predictions. We find that privacy distillation with sufficient privacy-relevant information i) retains accuracy almost as good as having all patient data (only 3\% worse), and ii) is effective at preventing errors that introduce health-related risks (only 3.9\% worse under- or over-prescriptions).

We introduce a new approach to functional causal modeling from observational data. The approach, called Causal Generative Neural Networks (CGNN), leverages the power of neural networks to learn a generative model of the joint distribution of the observed variables, by minimizing the Maximum Mean Discrepancy between generated and observed data. An approximate learning criterion is proposed to scale the computational cost of the approach to linear complexity in the number of observations. The performance of CGNN is studied throughout three experiments. First, we apply CGNN to the problem of cause-effect inference, where two CGNNs model $P(Y|X,\textrm{noise})$ and $P(X|Y,\textrm{noise})$ identify the best causal hypothesis out of $X\rightarrow Y$ and $Y\rightarrow X$. Second, CGNN is applied to the problem of identifying v-structures and conditional independences. Third, we apply CGNN to problem of multivariate functional causal modeling: given a skeleton describing the dependences in a set of random variables $\{X_1, \ldots, X_d\}$, CGNN orients the edges in the skeleton to uncover the directed acyclic causal graph describing the causal structure of the random variables. On all three tasks, CGNN is extensively assessed on both artificial and real-world data, comparing favorably to the state-of-the-art. Finally, we extend CGNN to handle the case of confounders, where latent variables are involved in the overall causal model.