We draw attention to an important, yet largely overlooked aspect of evaluating fairness for automated decision making systems--namely risk and welfare considerations. Our proposed family of measures corresponds to the long-established formulations of cardinal social welfare in economics, and is justified by the Rawlsian conception of fairness behind a veil of ignorance. The convex formulation of our welfare-based measures of fairness allows us to integrate them as a constraint into any convex loss minimization pipeline. Our empirical analysis reveals interesting trade-offs between our proposal and (a) prediction accuracy, (b) group discrimination, and (c) Dwork et al.'s notion of individual fairness. Furthermore and perhaps most importantly, our work provides both heuristic justification and empirical evidence suggesting that a lower-bound on our measures often leads to bounded inequality in algorithmic outcomes; hence presenting the first computationally feasible mechanism for bounding individual-level inequality.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We here focus on the task of learning Granger causality matrices for multivariate point processes. In order to accomplish this task, our work is the first to explore the use of Wold processes. By doing so, we are able to develop asymptotically fast MCMC learning algorithms. WithN being the total number of events andK the number of processes, our learning algorithm has aO(N(log(N) + log(K))) cost per iteration.

Neural Information Processing Systems http://nips.cc/

Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs.

We study the general problem of testing whether an unknown discrete distribution belongs to a specified family of distributions. More specifically, given a distribution family P and sample access to an unknown discrete distribution P, we want to distinguish (with high probability) between the case that P P and the case that P is ɛ-far, in total variation distance, from every distribution in P. This is the prototypical hypothesis testing problem that has received significant attention in statistics and, more recently, in computer science. The main contribution of this work is a simple and general testing technique that is applicable to all distribution families whose Fourier spectrum satisfies a certain approximate sparsity property. We apply our Fourier-based framework to obtain near sample-optimal and computationally efficient testers for the following fundamental distribution families: Sums of Independent Integer Random Variables (SIIRVs), Poisson Multinomial Distributions (PMDs), and Discrete Log-Concave Distributions. For the first two, ours are the first non-trivial testers in the literature, vastly generalizing previous work on testing Poisson Binomial Distributions. For the third, our tester improves on prior work in both sample and time complexity.

We study extensions to the streaming setting where entries of the matrix arrive in an arbitrary order and output is produced at the very end or continually.

In this paper we consider parallelization for applications whose objective can be expressed as maximizing a non-monotone submodular function under a cardinality constraint.

We study the contextual linear bandit problem, a version of the standard stochastic multi-armed bandit (MAB) problem where a learner sequentially selects actions to maximize a reward which depends also on a user provided per-round context. Though the context is chosen arbitrarily or adversarially, the reward is assumed to be a stochastic function of a feature vector that encodes the context and selected action. Our goal is to devise private learners for the contextual linear bandit problem.