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Navid Seidi, Ardhendu Tripathy, Sajal K. Das

Time elapsed till an event of interest is often modeled using the survival analysis methodology, which estimates a survival score based on the input features. There is a resurgence of interest in developing more accurate prediction models for time-to-event prediction in personalized healthcare using modern tools such as neural networks. Higher quality features and more frequent observations improve the predictions for a patient, however, the impact of including a patient's geographic location-based public health statistics on individual predictions has not been studied. This paper proposes a complementary improvement to survival analysis models by incorporating public health statistics in the input features. We show that including geographic location-based public health information results in a statistically significant improvement in the concordance index evaluated on the Surveillance, Epidemiology, and End Results (SEER) dataset containing nationwide cancer incidence data. The improvement holds for both the standard Cox proportional hazards model and the state-of-the-art Deep Survival Machines model. Our results indicate the utility of geographic location-based public health features in survival analysis.

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Blake Mason, Ardhendu Tripathy, Robert Nowak

Nearest Neighbor Search (NNS) is a central task in knowledge representation, learning, and reasoning. There is vast literature on efficient algorithms for constructing data structures and performing exact and approximate NNS. This paper studies NNS under Uncertainty (NNSU). Specifically, consider the setting in which an NNS algorithm has access only to a stochastic distance oracle that provides a noisy, unbiased estimate of the distance between any pair of points, rather than the exact distance. This models many situations of practical importance, including NNS based on human similarity judgements, physical measurements, or fast, randomized approximations to exact distances. A naive approach to NNSU could employ any standard NNS algorithm and repeatedly query and average results from the stochastic oracle (to reduce noise) whenever it needs a pairwise distance. The problem is that a sufficient number of repeated queries is unknown in advance; e.g., a point maybe distant from all but one other point (crude distance estimates suffice) or it may be close to a large number of other points (accurate estimates are necessary). This paper shows how ideas from cover trees and multi-armed bandits can be leveraged to develop an NNSU algorithm that has optimal dependence on the dataset size and the (unknown)geometry of the dataset.

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Subhojyoti Mukherjee, Ardhendu Tripathy, Robert Nowak

Active learning and structured stochastic bandit problems are intimately related to the classical problem of sequential experimental design. This paper studies active learning and best-arm identification in structured bandit settings from the viewpoint of active sequential hypothesis testing, a framework initiated by Chernoff (1959). We first characterize the sample complexity of Chernoff's original procedure by uncovering terms that reduce in significance as the allowed error probability $\delta \rightarrow 0$, but are nevertheless relevant at any fixed value of $\delta > 0$. While initially proposed for testing among finitely many hypotheses, we obtain the analogue of Chernoff sampling for the case when the hypotheses belong to a compact space. This makes it applicable to active learning and structured bandit problems, where the unknown parameter specifying the arm means is often assumed to be an element of Euclidean space. Empirically, we demonstrate the potential of our proposed approach for active learning of neural network models and in the linear bandit setting, where we observe that our general-purpose approach compares favorably to state-of-the-art methods.

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Blake Mason, Lalit Jain, Ardhendu Tripathy, Robert Nowak

The pure-exploration problem in stochastic multi-armed bandits aims to find one or more arms with the largest (or near largest) means. Examples include finding an {\epsilon}-good arm, best-arm identification, top-k arm identification, and finding all arms with means above a specified threshold. However, the problem of finding all {\epsilon}-good arms has been overlooked in past work, although arguably this may be the most natural objective in many applications. For example, a virologist may conduct preliminary laboratory experiments on a large candidate set of treatments and move all {\epsilon}-good treatments into more expensive clinical trials. Since the ultimate clinical efficacy is uncertain, it is important to identify all {\epsilon}-good candidates. Mathematically, the all-{\epsilon}-good arm identification problem presents significant new challenges and surprises that do not arise in the pure-exploration objectives studied in the past. We introduce two algorithms to overcome these and demonstrate their great empirical performance on a large-scale crowd-sourced dataset of 2.2M ratings collected by the New Yorker Caption Contest as well as a dataset testing hundreds of possible cancer drugs.

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Matthew L. Malloy, Ardhendu Tripathy, Robert D. Nowak

Construction of tight confidence regions and intervals is central to statistical inference and decision-making. Consider an empirical distribution $\widehat{\boldsymbol{p}}$ generated from $n$ iid realizations of a random variable that takes one of $k$ possible values according to an unknown distribution $\boldsymbol{p}$. This is analogous with a single draw from a multinomial distribution. A confidence region is a subset of the probability simplex that depends on $\widehat{\boldsymbol{p}}$ and contains the unknown $\boldsymbol{p}$ with a specified confidence. This paper shows how one can construct minimum average volume confidence regions, answering a long standing question. We also show the optimality of the regions directly translates to optimal confidence intervals of functionals, such as the mean, variance and median.

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Sumeet Katariya, Ardhendu Tripathy, Robert Nowak

This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. The key novelty of the MaxGap-bandit problem is that it aims to adaptively determine the natural partitioning of the distributions into a subset with larger means and a subset with smaller means, where the split is determined by the largest gap rather than a pre-specified rank or threshold. Estimating an arm's gap requires sampling its neighboring arms in addition to itself, and this dependence results in a novel hardness parameter that characterizes the sample complexity of the problem. We propose elimination and UCB-style algorithms and show that they are minimax optimal. Our experiments show that the UCB-style algorithms require 6-8x fewer samples than non-adaptive sampling to achieve the same error.

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Blake Mason, Ardhendu Tripathy, Robert Nowak

We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to problem domains where one wants to learn people's preferences from responses commonly modeled as noisy distance judgments. In this paper, we propose an active algorithm to find the graph with high probability and analyze its query complexity. In contrast to existing work that forces Euclidean structure, our method is valid for general metrics, assuming only symmetry and the triangle inequality. Furthermore, we demonstrate efficiency of our method empirically and theoretically, needing only O(n log(n)Delta^-2) queries in favorable settings, where Delta^-2 accounts for the effect of noise. Using crowd-sourced data collected for a subset of the UT Zappos50K dataset, we apply our algorithm to learn which shoes people believe are most similar and show that it beats both an active baseline and ordinal embedding.

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Ardhendu Tripathy, Ye Wang, Prakash Ishwar

We propose a data-driven framework for optimizing privacy-preserving data release mechanisms toward the information-theoretically optimal tradeoff between minimizing distortion of useful data and concealing sensitive information. Our approach employs adversarially-trained neural networks to implement randomized mechanisms and to perform a variational approximation of mutual information privacy. We empirically validate our Privacy-Preserving Adversarial Networks (PPAN) framework with experiments conducted on discrete and continuous synthetic data, as well as the MNIST handwritten digits dataset. With the synthetic data, we find that our model-agnostic PPAN approach achieves tradeoff points very close to the optimal tradeoffs that are analytically-derived from model knowledge. In experiments with the MNIST data, we visually demonstrate a learned tradeoff between minimizing the pixel-level distortion versus concealing the written digit.

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