Scalable Robust Kidney Exchange

In barter exchanges, participants directly trade their endowed goods in a constrained economic setting without money. Transactions in barter exchanges are often facilitated via a central clearinghouse that must match participants even in the face of uncertainty---over participants, existence and quality of potential trades, and so on. Leveraging robust combinatorial optimization techniques, we address uncertainty in kidney exchange, a real-world barter market where patients swap (in)compatible paired donors. We provide two scalable robust methods to handle two distinct types of uncertainty in kidney exchange---over the quality and the existence of a potential match. The latter case directly addresses a weakness in all stochastic-optimization-based methods to the kidney exchange clearing problem, which all necessarily require explicit estimates of the probability of a transaction existing---a still-unsolved problem in this nascent market. We also propose a novel, scalable kidney exchange formulation that eliminates the need for an exponential-time constraint generation process in competing formulations, maintains provable optimality, and serves as a subsolver for our robust approach. For each type of uncertainty we demonstrate the benefits of robustness on real data from a large, fielded kidney exchange in the United States. We conclude by drawing parallels between robustness and notions of fairness in the kidney exchange setting.Comment: Presented at AAAI1

GP-SUM. Gaussian Processes Filtering of non-Gaussian Beliefs

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attribute of GP-SUM is that it does not rely on linearizations of the dynamic or observation models, or on unimodal Gaussian approximations of the belief, hence enables tracking complex state distributions. The algorithm can be seen as a combination of a sampling-based filter with a probabilistic Bayes filter. On the one hand, GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. On the other hand, it achieves effective sampling and accurate probabilistic propagation by relying on the GP form of the system, and the sum-of-Gaussian form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also demonstrate its use in a pushing task, predicting with experimental accuracy the naturally occurring non-Gaussian distributions.Comment: WAFR 2018, 16 pages, 7 figure

Unsupervised Learning of Visual Structure using Predictive Generative Networks

The ability to predict future states of the environment is a central pillar of intelligence. At its core, effective prediction requires an internal model of the world and an understanding of the rules by which the world changes. Here, we explore the internal models developed by deep neural networks trained using a loss based on predicting future frames in synthetic video sequences, using a CNN-LSTM-deCNN framework. We first show that this architecture can achieve excellent performance in visual sequence prediction tasks, including state-of-the-art performance in a standard 'bouncing balls' dataset (Sutskever et al., 2009). Using a weighted mean-squared error and adversarial loss (Goodfellow et al., 2014), the same architecture successfully extrapolates out-of-the-plane rotations of computer-generated faces. Furthermore, despite being trained end-to-end to predict only pixel-level information, our Predictive Generative Networks learn a representation of the latent structure of the underlying three-dimensional objects themselves. Importantly, we find that this representation is naturally tolerant to object transformations, and generalizes well to new tasks, such as classification of static images. Similar models trained solely with a reconstruction loss fail to generalize as effectively. We argue that prediction can serve as a powerful unsupervised loss for learning rich internal representations of high-level object features.Comment: under review as conference paper at ICLR 201