Techniques based on randomized response enable the collection of potentially sensitive data from clients in a privacy-preserving manner with strong local differential privacy guarantees. A recent such technology, RAPPOR [12], enables estimation of the marginal frequencies of a set of strings via privacy-preserving crowdsourcing. However, this original estimation process relies on a known dictionary of possible strings; in practice, this dictionary can be extremely large and/or unknown. In this paper, we propose a novel decoding algorithm for the RAPPOR mechanism that enables the estimation of "unknown unknowns," i.e., strings we do not know we should be estimating. To enable learning without explicit dictionary knowledge, we develop methodology for estimating the joint distribution of multiple variables collected with RAPPOR. Our contributions are not RAPPOR-specific, and can be generalized to other local differential privacy mechanisms for learning distributions of string-valued random variables.

Generative adversarial networks (GANs) are innovative techniques for learning generative models of complex data distributions from samples. Despite remarkable recent improvements in generating realistic images, one of their major shortcomings is the fact that in practice, they tend to produce samples with little diversity, even when trained on diverse datasets. This phenomenon, known as mode collapse, has been the main focus of several recent advances in GANs. Yet there is little understanding of why mode collapse happens and why recently proposed approaches are able to mitigate mode collapse. We propose a principled approach to handling mode collapse, which we call packing. The main idea is to modify the discriminator to make decisions based on multiple samples from the same class, either real or artificially generated. We borrow analysis tools from binary hypothesis testing-in particular the seminal result of Blackwell [6]-to prove a fundamental connection between packing and mode collapse. We show that packing naturally penalizes generators with mode collapse, thereby favoring generator distributions with less mode collapse during the training process. Numerical experiments on benchmark datasets suggests that packing provides significant improvements in practice as well.

Proof-of-stake (PoS) is a promising approach for designing efficient blockchains, where block proposers are randomly chosen with probability proportional to their stake. A primary concern with PoS systems is the "rich getting richer" phenomenon, whereby wealthier nodes are more likely to get elected, and hence reap the block reward, making them even wealthier. In this paper, we introduce the notion of equitability, which quantifies how much a proposer can amplify her stake compared to her initial investment. Even with everyone following protocol (i.e., honest behavior), we show that existing methods of allocating block rewards lead to poor equitability, as does initializing systems with small stake pools and/or large rewards relative to the stake pool. We identify a geometric reward function, which we prove is maximally equitable over all choices of reward functions under honest behavior and bound the deviation for strategic actions; the proofs involve the study of optimization problems and stochastic dominances of Pólya urn processes, and are of independent mathematical interest. These results allow us to provide a systematic framework to choose the parameters of a practical incentive system for PoS cryptocurrencies.

With the growing usage of Bitcoin and other cryptocurrencies, many scalability challenges have emerged. A promising scaling solution, exemplified by the Lightning Network, uses a network of bidirectional payment channels that allows fast transactions between two parties. However, routing payments on these networks efficiently is non-trivial, since payments require finding paths with sufficient funds, and channels can become unidirectional over time blocking further transactions through them. Today's payment channel networks exacerbate these problems by attempting to deliver all payments atomically. In this paper, we present the Spider network, a new packet-switched architecture for payment channel networks. Spider splits payments into transaction units and transmits them over time across different paths. Spider uses congestion control, payment scheduling, and imbalance-aware routing to optimize delivery of payments. Our results show that Spider improves the volume and number of successful payments on the network by 10-45% and 5-40% respectively compared to state-of-the-art approaches.

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