Instrumental variable regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which the convergence rate achieves the minimax optimal rate for unconfounded, one-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric instrumental variable regression.

We consider nonconvex-concave minimax problems, $\min_{x} \max_{y\in\mathcal{Y}} f(x, y)$, where $f$ is nonconvex in $x$ but concave in $y$. The standard algorithm for solving this problem is the celebrated gradient descent ascent (GDA) algorithm, which has been widely used in machine learning, control theory and economics. However, despite the solid theory for the convex-concave setting, GDA can converge to limit cycles or even diverge in a general setting. In this paper, we present a nonasymptotic analysis of GDA for solving nonconvex-concave minimax problems, showing that GDA can find a stationary point of the function $\Phi(\cdot) :=\max_{y\in\mathcal{Y} }f(\cdot, y)$ efficiently. To the best our knowledge, this is the first theoretical guarantee for GDA in this setting, shedding light on its practical performance in many real applications.

The increasing impact of algorithmic decisions on people's lives compels us to scrutinize their fairness and, in particular, the disparate impacts that ostensibly-color-blind algorithms can have on different groups. Examples include credit decisioning, hiring, advertising, criminal justice, personalized medicine, and targeted policymaking, where in some cases legislative or regulatory frameworks for fairness exist and define specific protected classes. In this paper we study a fundamental challenge to assessing disparate impacts in practice: protected class membership is often not observed in the data. This is particularly a problem in lending and healthcare. We consider the use of an auxiliary dataset, such as the US census, that includes class labels but not decisions or outcomes. We show that a variety of common disparity measures are generally unidentifiable aside for some unrealistic cases, providing a new perspective on the documented biases of popular proxy-based methods. We provide exact characterizations of the sharpest-possible partial identification set of disparities either under no assumptions or when we incorporate mild smoothness constraints. We further provide optimization-based algorithms for computing and visualizing these sets, which enables reliable and robust assessments -- an important tool when disparity assessment can have far-reaching policy implications. We demonstrate this in two case studies with real data: mortgage lending and personalized medicine dosing.

Multi-output Gaussian processes (GPs) are a flexible Bayesian nonparametric framework that has proven useful in jointly modeling the physiological states of patients in medical time series data. However, capturing the short-term effects of drugs and therapeutic interventions on patient physiological state remains challenging. We propose a novel approach that models the effect of interventions as a hybrid Gaussian process composed of a GP capturing patient physiology convolved with a latent force model capturing effects of treatments on specific physiological features. This convolution of a multi-output GP with a GP including a causal time-marked kernel leads to a well-characterized model of the patients' physiological state responding to interventions. We show that our model leads to analytically tractable cross-covariance functions, allowing scalable inference. Our hierarchical model includes estimates of patient-specific effects but allows sharing of support across patients. Our approach achieves competitive predictive performance on challenging hospital data, where we recover patient-specific response to the administration of three common drugs: one antihypertensive drug and two anticoagulants.

The family of f-divergences is ubiquitously applied to generative modeling in order to adapt the distribution of the model to that of the data. Well-definedness of f-divergences, however, requires the distributions of the data and model to overlap completely in every time step of training. As a result, as soon as the support of distributions of data and model contain non-overlapping portions, gradient based training of the corresponding model becomes hopeless. Recent advances in generative modeling are full of remedies for handling this support mismatch problem: key ideas include either modifying the objective function to integral probability measures (IPMs) that are well-behaved even on disjoint probabilities, or optimizing a well-behaved variational lower bound instead of the true objective. We, on the other hand, establish that a complete change of the objective function is unnecessary, and instead an augmentation of the base measure of the problematic divergence can resolve the issue. Based on this observation, we propose a generative model which leverages the class of Scaled Bregman Divergences and generalizes both f-divergences and Bregman divergences. We analyze this class of divergences and show that with the appropriate choice of base measure it can resolve the support mismatch problem and incorporate geometric information. Finally, we study the performance of the proposed method and demonstrate promising results on MNIST, CelebA and CIFAR-10 datasets.

There has been much discussion recently about how fairness should be measured or enforced in classification. Individual Fairness [Dwork, Hardt, Pitassi, Reingold, Zemel, 2012], which requires that similar individuals be treated similarly, is a highly appealing definition as it gives strong guarantees on treatment of individuals. Unfortunately, the need for a task-specific similarity metric has prevented its use in practice. In this work, we propose a solution to the problem of approximating a metric for Individual Fairness based on human judgments. Our model assumes that we have access to a human fairness arbiter, who can answer a limited set of queries concerning similarity of individuals for a particular task, is free of explicit biases and possesses sufficient domain knowledge to evaluate similarity. Our contributions include definitions for metric approximation relevant for Individual Fairness, constructions for approximations from a limited number of realistic queries to the arbiter on a sample of individuals, and learning procedures to construct hypotheses for metric approximations which generalize to unseen samples under certain assumptions of learnability of distance threshold functions.

Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inference task. We formalize deconditional kernel mean embeddings as a solution to this inverse problem, and show that it can be naturally viewed as a nonparametric Bayes' rule. Critically, we introduce the notion of task transformed Gaussian processes and establish deconditional kernel means as their posterior predictive mean. This connection provides Bayesian interpretations and uncertainty estimates for deconditional kernel mean embeddings, explains their regularization hyperparameters, and reveals a marginal likelihood for kernel hyperparameter learning. These revelations further enable practical applications such as likelihood-free inference and learning sparse representations for big data.

Several recent papers have examined generalization in reinforcement learning (RL), by proposing new environments or ways to add noise to existing environments, then benchmarking algorithms and model architectures on those environments. We discuss subtle conceptual properties of RL benchmarks that are not required in supervised learning (SL), and also properties that an RL benchmark should possess. Chief among them is one we call the principle of unchanged optimality: there should exist a single $\pi$ that is optimal across all train and test tasks. In this work, we argue why this principle is important, and ways it can be broken or satisfied due to subtle choices in state representation or model architecture. We conclude by discussing challenges and future lines of research in theoretically analyzing generalization benchmarks.

In this paper, we propose a novel method for generating a synthetic dataset obeying Gaussian distribution. Compared to the commonly used benchmark datasets with unknown distribution, the synthetic dataset has an explicit distribution, i.e., Gaussian distribution. Meanwhile, it has the same characteristics as the benchmark dataset MNIST. As a result, we can easily apply Deep Neural Networks (DNNs) on the synthetic dataset. This synthetic dataset provides a novel experimental tool to verify the proposed theories of deep learning.

Despite being first proposed about 60 years ago [1], only in the past few years have artificial neural networks (ANNs) become the de facto standard machine learning model [2] achieving accurate state-of-the-art results for a wide range of problems ranging from image classification [3]-[5], object detection [6], [7], semantic segmentation [8], [9], face recognition [10], [11], and text recognition [12], [13], to speech recognition [14]-[16], natural language processing problems such as machine translation [17], [18], language modeling [19], and question answering [20]. This has resulted in a huge industry-wide adoption from leading technology companies such as Google, Facebook, Microsoft, IBM, Yahoo!, Twitter, Adobe, and a quickly growing number of startups. One of the prominent reasons for this recent revival is that in order for ANNs to achieve such performance they need very large labeled datasets and huge computational power at a scale that only recently came into the hands of individual researchers in the form of GPUs [21], which kick-started the deep learning revolution in 2012 [3]. Since then, the trend for demanding more computation and more power consumption for such applications has largely increased. Despite being initially bio-inspired architectures, ANNs have significant differences from actual biological neurons in how computations are performed by neurons, their structure (connection patterns and topologies of neurons), learning (how neurons adapt themselves to new observations), and communication (how inter-neuron data is encoded and passed). One of the main differences of ANNs compared to biological neurons, is how communication is done. While biological neurons use asynchronous trains of spikes in an event-based, data-driven manner that adapts locally to its external stimulation pattern to communicate and encode data (though the specific encoding mechanism used by neurons is not totally understood), ANNs communicate in dense, continuous valued activations, which means that all ANN neurons are working at the same time, thus using lots of computation and energy to operate. Spiking neural networks leverage the benefit from biological neurons to communicate asynchronously in trains of spikes. Thus, spiking neural networks incorporate the concept of time, and instead of all neurons firing at the same time as the case with ANNs, in spiking neural networks neurons fire only when thier intrinsic potential (i.e.