David M. Pennock

Abdulaziz A. Almuzaini, Chidansh A. Bhatt, David M. Pennock et al.

The idealization of a static machine-learned model, trained once and deployed forever, is not practical. As input distributions change over time, the model will not only lose accuracy, any constraints to reduce bias against a protected class may fail to work as intended. Thus, researchers have begun to explore ways to maintain algorithmic fairness over time. One line of work focuses on dynamic learning: retraining after each batch, and the other on robust learning which tries to make algorithms robust against all possible future changes. Dynamic learning seeks to reduce biases soon after they have occurred and robust learning often yields (overly) conservative models. We propose an anticipatory dynamic learning approach for correcting the algorithm to mitigate bias before it occurs. Specifically, we make use of anticipations regarding the relative distributions of population subgroups (e.g., relative ratios of male and female applicants) in the next cycle to identify the right parameters for an importance weighing fairness approach. Results from experiments over multiple real-world datasets suggest that this approach has promise for anticipatory bias correction.

Tatiana Chakravorti, Robert Fraleigh, Timothy Fritton et al.

We present a prototype hybrid prediction market and demonstrate the avenue it represents for meaningful human-AI collaboration. We build on prior work proposing artificial prediction markets as a novel machine-learning algorithm. In an artificial prediction market, trained AI agents buy and sell outcomes of future events. Classification decisions can be framed as outcomes of future events, and accordingly, the price of an asset corresponding to a given classification outcome can be taken as a proxy for the confidence of the system in that decision. By embedding human participants in these markets alongside bot traders, we can bring together insights from both. In this paper, we detail pilot studies with prototype hybrid markets for the prediction of replication study outcomes. We highlight challenges and opportunities, share insights from semi-structured interviews with hybrid market participants, and outline a vision for ongoing and future work.

Yichi Zhang, Shengwei Xu, David Pennock et al.

Eliciting reliable human feedback is essential for many machine learning tasks, such as learning from noisy labels and aligning AI systems with human preferences. Peer prediction mechanisms incentivize truthful reporting without ground truth verification by scoring agents based on correlations with peers. Traditional mechanisms, which ensure that truth-telling maximizes the expected scores in equilibrium, can elicit honest information while assuming agents' utilities are linear functions of their scores. However, in practice, non-linear payment rules are usually preferred, or agents' utilities are inherently non-linear. We propose stochastically dominant truthfulness (SD-truthfulness) as a stronger guarantee: the score distribution of truth-telling stochastically dominates all other strategies, incentivizing truthful reporting for a wide range of monotone utility functions. Our first observation is that no existing peer prediction mechanism naturally satisfies this criterion without strong assumptions. A simple solution -- rounding scores into binary lotteries -- can enforce SD-truthfulness, but often degrades sensitivity, a key property related to fairness and statistical efficiency. We demonstrate how a more careful application of rounding can better preserve sensitivity. Furthermore, we introduce a new enforced agreement (EA) mechanism that is theoretically guaranteed to be SD-truthful in binary-signal settings under mild assumptions, and empirically achieves the highest sensitivity among all known SD-truthful mechanisms.

Sarah Rajtmajer, Christopher Griffin, Jian Wu et al.

Explainably estimating confidence in published scholarly work offers opportunity for faster and more robust scientific progress. We develop a synthetic prediction market to assess the credibility of published claims in the social and behavioral sciences literature. We demonstrate our system and detail our findings using a collection of known replication projects. We suggest that this work lays the foundation for a research agenda that creatively uses AI for peer review.

Rupert Freeman, David M. Pennock, Chara Podimata et al.

We study online learning settings in which experts act strategically to maximize their influence on the learning algorithm's predictions by potentially misreporting their beliefs about a sequence of binary events. Our goal is twofold. First, we want the learning algorithm to be no-regret with respect to the best fixed expert in hindsight. Second, we want incentive compatibility, a guarantee that each expert's best strategy is to report his true beliefs about the realization of each event. To achieve this goal, we build on the literature on wagering mechanisms, a type of multi-agent scoring rule. We provide algorithms that achieve no regret and incentive compatibility for myopic experts for both the full and partial information settings. In experiments on datasets from FiveThirtyEight, our algorithms have regret comparable to classic no-regret algorithms, which are not incentive-compatible. Finally, we identify an incentive-compatible algorithm for forward-looking strategic agents that exhibits diminishing regret in practice.

Rupert Freeman, Sebastien Lahaie, David M. Pennock

A prediction market is a useful means of aggregating information about a future event. To function, the market needs a trusted entity who will verify the true outcome in the end. Motivated by the recent introduction of decentralized prediction markets, we introduce a mechanism that allows for the outcome to be determined by the votes of a group of arbiters who may themselves hold stakes in the market. Despite the potential conflict of interest, we derive conditions under which we can incentivize arbiters to vote truthfully by using funds raised from market fees to implement a peer prediction mechanism. Finally, we investigate what parameter values could be used in a real-world implementation of our mechanism.

Rachel Cummings, David M. Pennock, Jennifer Wortman Vaughan

We consider the design of private prediction markets, financial markets designed to elicit predictions about uncertain events without revealing too much information about market participants' actions or beliefs. Our goal is to design market mechanisms in which participants' trades or wagers influence the market's behavior in a way that leads to accurate predictions, yet no single participant has too much influence over what others are able to observe. We study the possibilities and limitations of such mechanisms using tools from differential privacy. We begin by designing a private one-shot wagering mechanism in which bettors specify a belief about the likelihood of a future event and a corresponding monetary wager. Wagers are redistributed among bettors in a way that more highly rewards those with accurate predictions. We provide a class of wagering mechanisms that are guaranteed to satisfy truthfulness, budget balance in expectation, and other desirable properties while additionally guaranteeing epsilon-joint differential privacy in the bettors' reported beliefs, and analyze the trade-off between the achievable level of privacy and the sensitivity of a bettor's payment to her own report. We then ask whether it is possible to obtain privacy in dynamic prediction markets, focusing our attention on the popular cost-function framework in which securities with payments linked to future events are bought and sold by an automated market maker. We show that under general conditions, it is impossible for such a market maker to simultaneously achieve bounded worst-case loss and epsilon-differential privacy without allowing the privacy guarantee to degrade extremely quickly as the number of trades grows, making such markets impractical in settings in which privacy is valued. We conclude by suggesting several avenues for potentially circumventing this lower bound.

Nikhil Devanur, Miroslav Dudík, Zhiyi Huang et al.

We give a detailed characterization of optimal trades under budget constraints in a prediction market with a cost-function-based automated market maker. We study how the budget constraints of individual traders affect their ability to impact the market price. As a concrete application of our characterization, we give sufficient conditions for a property we call budget additivity: two traders with budgets B and B' and the same beliefs would have a combined impact equal to a single trader with budget B+B'. That way, even if a single trader cannot move the market much, a crowd of like-minded traders can have the same desired effect. When the set of payoff vectors associated with outcomes, with coordinates corresponding to securities, is affinely independent, we obtain that a generalization of the heavily-used logarithmic market scoring rule is budget additive, but the quadratic market scoring rule is not. Our results may be used both descriptively, to understand if a particular market maker is affected by budget constraints or not, and prescriptively, as a recipe to construct markets.

David M. Pennock, Michael P. Wellman

We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and producers trade in uncertain propositions. We demonstrate the correspondence between the equilibrium prices of goods in this economy and the probabilities represented by the Bayesian network. A computational market model such as this may provide a useful framework for investigations of belief aggregation, distributed probabilistic inference, resource allocation under uncertainty, and other problems of decentralized uncertainty.

David M. Pennock, Michael P. Wellman

We consider the problem of belief aggregation: given a group of individual agents with probabilistic beliefs over a set of uncertain events, formulate a sensible consensus or aggregate probability distribution over these events. Researchers have proposed many aggregation methods, although on the question of which is best the general consensus is that there is no consensus. We develop a market-based approach to this problem, where agents bet on uncertain events by buying or selling securities contingent on their outcomes. Each agent acts in the market so as to maximize expected utility at given securities prices, limited in its activity only by its own risk aversion. The equilibrium prices of goods in this market represent aggregate beliefs. For agents with constant risk aversion, we demonstrate that the aggregate probability exhibits several desirable properties, and is related to independently motivated techniques. We argue that the market-based approach provides a plausible mechanism for belief aggregation in multiagent systems, as it directly addresses self-motivated agent incentives for participation and for truthfulness, and can provide a decision-theoretic foundation for the "expert weights" often employed in centralized pooling techniques.

David M. Pennock

I present a parallel algorithm for exact probabilistic inference in Bayesian networks. For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel random-access machine) with n processors, for any constant number of evidence variables. For arbitrary networks, the time complexity is O(r^{3w}*log n) for n processors, or O(w*log n) for r^{3w}*n processors, where r is the maximum range of any variable, and w is the induced width (the maximum clique size), after moralizing and triangulating the network.

David M. Pennock, Michael P. Wellman

Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We prove, under relatively mild assumptions, that even if everyone agrees on a common graph topology, no method of combining beliefs can maintain that structure. Even weaker conditions rule out local aggregation within conditional probability tables. On a more positive note, we show that if probabilities are combined with the logarithmic opinion pool (LogOP), then commonly held Markov independencies are maintained. This suggests a straightforward procedure for constructing a consensus Markov network. We describe an algorithm for computing the LogOP with time complexity comparable to that of exact Bayesian inference.

David M. Pennock, Eric J. Horvitz, Steve Lawrence et al.

The growth of Internet commerce has stimulated the use of collaborative filtering (CF) algorithms as recommender systems. Such systems leverage knowledge about the known preferences of multiple users to recommend items of interest to other users. CF methods have been harnessed to make recommendations about such items as web pages, movies, books, and toys. Researchers have proposed and evaluated many approaches for generating recommendations. We describe and evaluate a new method called emph{personality diagnosis (PD)}. Given a user's preferences for some items, we compute the probability that he or she is of the same "personality type" as other users, and, in turn, the probability that he or she will like new items. PD retains some of the advantages of traditional similarity-weighting techniques in that all data is brought to bear on each prediction and new data can be added easily and incrementally. Additionally, PD has a meaningful probabilistic interpretation, which may be leveraged to justify, explain, and augment results. We report empirical results on the EachMovie database of movie ratings, and on user profile data collected from the CiteSeer digital library of Computer Science research papers. The probabilistic framework naturally supports a variety of descriptive measurements - in particular, we consider the applicability of a value of information (VOI) computation.

Alexandrin Popescul, Lyle H. Ungar, David M Pennock et al.

Recommender systems leverage product and community information to target products to consumers. Researchers have developed collaborative recommenders, content-based recommenders, and (largely ad-hoc) hybrid systems. We propose a unified probabilistic framework for merging collaborative and content-based recommendations. We extend Hofmann's [1999] aspect model to incorporate three-way co-occurrence data among users, items, and item content. The relative influence of collaboration data versus content data is not imposed as an exogenous parameter, but rather emerges naturally from the given data sources. Global probabilistic models coupled with standard Expectation Maximization (EM) learning algorithms tend to drastically overfit in sparse-data situations, as is typical in recommendation applications. We show that secondary content information can often be used to overcome sparsity. Experiments on data from the ResearchIndex library of Computer Science publications show that appropriate mixture models incorporating secondary data produce significantly better quality recommenders than k-nearest neighbors (k-NN). Global probabilistic models also allow more general inferences than local methods like k-NN.

Shyong, K. Lam, David M Pennock et al.

We exploit the redundancy and volume of information on the web to build a computerized player for the ABC TV game show 'Who Wants To Be A Millionaire?' The player consists of a question-answering module and a decision-making module. The question-answering module utilizes question transformation techniques, natural language parsing, multiple information retrieval algorithms, and multiple search engines; results are combined in the spirit of ensemble learning using an adaptive weighting scheme. Empirically, the system correctly answers about 75% of questions from the Millionaire CD-ROM, 3rd edition - general-interest trivia questions often about popular culture and common knowledge. The decision-making module chooses from allowable actions in the game in order to maximize expected risk-adjusted winnings, where the estimated probability of answering correctly is a function of past performance and confidence in in correctly answering the current question. When given a six question head start (i.e., when starting from the $2,000 level), we find that the system performs about as well on average as humans starting at the beginning. Our system demonstrates the potential of simple but well-chosen techniques for mining answers from unstructured information such as the web.

Varsha Dani, Omid Madani, David M Pennock et al.

Predicting the outcomes of future events is a challenging problem for which a variety of solution methods have been explored and attempted. We present an empirical comparison of a variety of online and offline adaptive algorithms for aggregating experts' predictions of the outcomes of five years of US National Football League games (1319 games) using expert probability elicitations obtained from an Internet contest called ProbabilitySports. We find that it is difficult to improve over simple averaging of the predictions in terms of prediction accuracy, but that there is room for improvement in quadratic loss. Somewhat surprisingly, a Bayesian estimation algorithm which estimates the variance of each expert's prediction exhibits the most consistent superior performance over simple averaging among our collection of algorithms.

David M. Pennock, Lirong Xia

To overcome the #P-hardness of computing/updating prices in logarithm market scoring rule-based (LMSR-based) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial predictionmarkets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly extend this idea by employing Bayesian networks in general combinatorial prediction markets. We reveal a very natural connection between LMSR-based combinatorial prediction markets and probabilistic belief aggregation,which leads to a complete characterization of all structure preserving securities for decomposable network structures. Notably, the main results by Chen et al. [5] are corollaries of our characterization. We then prove that in order for a very basic set of securities to be structure preserving, the graph of the Bayesian network must be decomposable. We also discuss some approximation techniques for securities that are not structure preserving.

Alina Beygelzimer, John Langford, David Pennock

In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called "wisdom of crowds" effect, which roughly says that the average of participants performs much better than the average participant. The market price---an average or at least aggregate of traders' beliefs---offers a better estimate than most any individual trader's opinion. In this paper, we ask a stronger question: how does the market price compare to the best trader's belief, not just the average trader. We measure the market's worst-case log regret, a notion common in machine learning theory. To arrive at a meaningful answer, we need to assume something about how traders behave. We suppose that every trader optimizes according to the Kelly criteria, a strategy that provably maximizes the compound growth of wealth over an (infinite) sequence of market interactions. We show several consequences. First, the market prediction is a wealth-weighted average of the individual participants' beliefs. Second, the market learns at the optimal rate, the market price reacts exactly as if updating according to Bayes' Law, and the market prediction has low worst-case log regret to the best individual participant. We simulate a sequence of markets where an underlying true probability exists, showing that the market converges to the true objective frequency as if updating a Beta distribution, as the theory predicts. If agents adopt a fractional Kelly criteria, a common practical variant, we show that agents behave like full-Kelly agents with beliefs weighted between their own and the market's, and that the market price converges to a time-discounted frequency. Our analysis provides a new justification for fractional Kelly betting, a strategy widely used in practice for ad-hoc reasons. Finally, we propose a method for an agent to learn her own optimal Kelly fraction.