Eli Upfal

Alessio Mazzetto, Eli Upfal

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models, and generalizes previous results on agnostic learning under drift.

Alessio Mazzetto, Reza Esfandiarpoor, Akash Singirikonda et al.

We introduce an adaptive method with formal quality guarantees for weak supervision in a non-stationary setting. Our goal is to infer the unknown labels of a sequence of data by using weak supervision sources that provide independent noisy signals of the correct classification for each data point. This setting includes crowdsourcing and programmatic weak supervision. We focus on the non-stationary case, where the accuracy of the weak supervision sources can drift over time, e.g., because of changes in the underlying data distribution. Due to the drift, older data could provide misleading information to infer the label of the current data point. Previous work relied on a priori assumptions on the magnitude of the drift to decide how much data to use from the past. In contrast, our algorithm does not require any assumptions on the drift, and it adapts based on the input by dynamically varying its window size. In particular, at each step, our algorithm estimates the current accuracies of the weak supervision sources by identifying a window of past observations that guarantees a near-optimal minimization of the trade-off between the error due to the variance of the estimation and the error due to the drift. Experiments on synthetic and real-world labelers show that our approach adapts to the drift.

Alessio Mazzetto, Cristina Menghini, Andrew Yuan et al.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

Alessio Mazzetto, Eli Upfal

We develop and analyze a general technique for learning with an unknown distribution drift. Given a sequence of independent observations from the last $T$ steps of a drifting distribution, our algorithm agnostically learns a family of functions with respect to the current distribution at time $T$. Unlike previous work, our technique does not require prior knowledge about the magnitude of the drift. Instead, the algorithm adapts to the sample data. Without explicitly estimating the drift, the algorithm learns a family of functions with almost the same error as a learning algorithm that knows the magnitude of the drift in advance. Furthermore, since our algorithm adapts to the data, it can guarantee a better learning error than an algorithm that relies on loose bounds on the drift. We demonstrate the application of our technique in two fundamental learning scenarios: binary classification and linear regression.

Shahrzad Haddadan, Yue Zhuang, Cyrus Cousins et al.

We present a novel method for reducing the computational complexity of rigorously estimating the partition functions (normalizing constants) of Gibbs (Boltzmann) distributions, which arise ubiquitously in probabilistic graphical models. A major obstacle to practical applications of Gibbs distributions is the need to estimate their partition functions. The state of the art in addressing this problem is multi-stage algorithms, which consist of a cooling schedule, and a mean estimator in each step of the schedule. While the cooling schedule in these algorithms is adaptive, the mean estimation computations use MCMC as a black-box to draw approximate samples. We develop a doubly adaptive approach, combining the adaptive cooling schedule with an adaptive MCMC mean estimator, whose number of Markov chain steps adapts dynamically to the underlying chain. Through rigorous theoretical analysis, we prove that our method outperforms the state of the art algorithms in several factors: (1) The computational complexity of our method is smaller; (2) Our method is less sensitive to loose bounds on mixing times, an inherent component in these algorithms; and (3) The improvement obtained by our method is particularly significant in the most challenging regime of high-precision estimation. We demonstrate the advantage of our method in experiments run on classic factor graphs, such as voting models and Ising models.

Lorenzo De Stefani, Eli Upfal

While standard statistical inference techniques and machine learning generalization bounds assume that tests are run on data selected independently of the hypotheses, practical data analysis and machine learning are usually iterative and adaptive processes where the same holdout data is often used for testing a sequence of hypotheses (or models), which may each depend on the outcome of the previous tests on the same data. In this work, we present RadaBound a rigorous, efficient and practical procedure for controlling the generalization error when using a holdout sample for multiple adaptive testing. Our solution is based on a new application of the Rademacher Complexity generalization bounds, adapted to dependent tests. We demonstrate the statistical power and practicality of our method through extensive simulations and comparisons to alternative approaches.

Megumi Ando, Anna Lysyanskaya, Eli Upfal

Onion routing is the most widely used approach to anonymous communication online. The idea is that Alice wraps her message to Bob in layers of encryption to form an "onion," and routes it through a series of intermediaries. Each intermediary's job is to decrypt ("peel") the onion it receives to obtain instructions for where to send it next, and what to send. The intuition is that, by the time it gets to Bob, the onion will have mixed with so many other onions, that its origin will be hard to trace even for an adversary that observes the entire network and controls a fraction of the participants, possibly including Bob. In spite of its widespread use in practice, until now no onion routing protocol was known that simultaneously achieved, in the presence of an active adversary that observes all network traffic and controls a constant fraction of the participants, (a) fault-tolerance, where even if a few of the onions are dropped, the protocol still delivers the rest; (b) reasonable communication and computational complexity as a function of the security parameter and the number of participants; and (c) anonymity. In this paper, we give the first onion routing protocol that meets these goals: our protocol (a) tolerates a polylogarithmic (in the security parameter) number of dropped onions and still delivers the rest; (b) requires a polylogarithmic number of rounds and a polylogarithmic number of onions sent per participant per round; and (c) achieves anonymity. We also show that to achieve anonymity in a fault-tolerant fashion via onion routing, this number of onions and rounds is necessary. Of independent interest, our analysis introduces two new security properties of onion routing -- mixing and equalizing -- and we show that together they imply anonymity.

Clayton Sanford, Cyrus Cousins, Eli Upfal

We frame the problem of selecting an optimal audio encoding scheme as a supervised learning task. Through uniform convergence theory, we guarantee approximately optimal codec selection while controlling for selection bias. We present rigorous statistical guarantees for the codec selection problem that hold for arbitrary distributions over audio sequences and for arbitrary quality metrics. Our techniques can thus balance sound quality and compression ratio, and use audio samples from the distribution to select a codec that performs well on that particular type of data. The applications of our technique are immense, as it can be used to optimize for quality and bandwidth usage of streaming and other digital media, while significantly outperforming approaches that apply a fixed codec to all data sources.

Yeounoh Chung, Peter J. Haas, Eli Upfal et al.

Over the past decades, researchers and ML practitioners have come up with better and better ways to build, understand and improve the quality of ML models, but mostly under the key assumption that the training data is distributed identically to the testing data. In many real-world applications, however, some potential training examples are unknown to the modeler, due to sample selection bias or, more generally, covariate shift, i.e., a distribution shift between the training and deployment stage. The resulting discrepancy between training and testing distributions leads to poor generalization performance of the ML model and hence biased predictions. We provide novel algorithms that estimate the number and properties of these unknown training examples---unknown unknowns. This information can then be used to correct the training set, prior to seeing any test data. The key idea is to combine species-estimation techniques with data-driven methods for estimating the feature values for the unknown unknowns. Experiments on a variety of ML models and datasets indicate that taking the unknown examples into account can yield a more robust ML model that generalizes better.

Kim Albertsson, Piero Altoe, Dustin Anderson et al.

Machine learning has been applied to several problems in particle physics research, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications in particle and event identification and reconstruction in the 2010s. In this document we discuss promising future research and development areas for machine learning in particle physics. We detail a roadmap for their implementation, software and hardware resource requirements, collaborative initiatives with the data science community, academia and industry, and training the particle physics community in data science. The main objective of the document is to connect and motivate these areas of research and development with the physics drivers of the High-Luminosity Large Hadron Collider and future neutrino experiments and identify the resource needs for their implementation. Additionally we identify areas where collaboration with external communities will be of great benefit.

Megumi Ando, Anna Lysyanskaya, Eli Upfal

In an onion routing protocol, messages travel through several intermediaries before arriving at their destinations, they are wrapped in layers of encryption (hence they are called "onions"). The goal is to make it hard to establish who sent the message. It is a practical and widespread tool for creating anonymous channels. For the standard adversary models -- network, passive, and active -- we present practical and provably secure onion routing protocols. Akin to Tor, in our protocols each party independently chooses the routing paths for his onions. For security parameter $λ$, our differentially private solution for the active adversary takes $O(\log^2λ)$ rounds and requires every participant to transmit $O(\log^{4} λ)$ onions in every round.

Ahmad Mahmoody, Evgenios M. Kornaropoulos, Eli Upfal

We formulate and study a fundamental search and detection problem, Schedule Optimization, motivated by a variety of real-world applications, ranging from monitoring content changes on the web, social networks, and user activities to detecting failure on large systems with many individual machines. We consider a large system consists of many nodes, where each node has its own rate of generating new events, or items. A monitoring application can probe a small number of nodes at each step, and our goal is to compute a probing schedule that minimizes the expected number of undiscovered items at the system, or equivalently, minimizes the expected time to discover a new item in the system. We study the Schedule Optimization problem both for deterministic and randomized memoryless algorithms. We provide lower bounds on the cost of an optimal schedule and construct close to optimal schedules with rigorous mathematical guarantees. Finally, we present an adaptive algorithm that starts with no prior information on the system and converges to the optimal memoryless algorithms by adapting to observed data.

Olga Ohrimenko, Michael T. Goodrich, Roberto Tamassia et al.

We present a simple, efficient, and secure data-oblivious randomized shuffle algorithm. This is the first secure data-oblivious shuffle that is not based on sorting. Our method can be used to improve previous oblivious storage solutions for network-based outsourcing of data.

Robert Kleinberg, Aleksandrs Slivkins, Eli Upfal

In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials so as to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is quite well understood, bandit problems with large strategy sets are still a topic of very active investigation, motivated by practical applications such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions which enable the design of efficient solutions. In this work we study a very general setting for the multi-armed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the "Lipschitz MAB problem". We present a solution for the multi-armed bandit problem in this setting. That is, for every metric space we define an isometry invariant which bounds from below the performance of Lipschitz MAB algorithms for this metric space, and we present an algorithm which comes arbitrarily close to meeting this bound. Furthermore, our technique gives even better results for benign payoff functions. We also address the full-feedback ("best expert") version of the problem, where after every round the payoffs from all arms are revealed.

Milos Hauskrecht, Eli Upfal

In this work we focus on efficient heuristics for solving a class of stochastic planning problems that arise in a variety of business, investment, and industrial applications. The problem is best described in terms of future buy and sell contracts. By buying less reliable, but less expensive, buy (supply) contracts, a company or a trader can cover a position of more reliable and more expensive sell contracts. The goal is to maximize the expected net gain (profit) by constructing a dose to optimum portfolio out of the available buy and sell contracts. This stochastic planning problem can be formulated as a two-stage stochastic linear programming problem with recourse. However, this formalization leads to solutions that are exponential in the number of possible failure combinations. Thus, this approach is not feasible for large scale problems. In this work we investigate heuristic approximation techniques alleviating the efficiency problem. We primarily focus on the clustering approach and devise heuristics for finding clusterings leading to good approximations. We illustrate the quality and feasibility of the approach through experimental data.