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Individual probabilities refer to the probabilities of outcomes that are realized only once: the probability that it will rain tomorrow, the probability that Alice will die within the next 12 months, the probability that Bob will be arrested for a violent crime in the next 18 months, etc. Individual probabilities are fundamentally unknowable. Nevertheless, we show that two parties who agree on the data—or on how to sample from a data distribution—cannot agree to disagree on how to model individual probabilities. This is because any two models of individual probabilities that substantially disagree can together be used to empirically falsify and improve at least one of the two models. This can be efficiently iterated in a process of “reconciliation” that results in models that both parties agree are superior to the models they started with, and which themselves (almost) agree on the forecasts of individual probabilities (almost) everywhere. We conclude that although individual probabilities are unknowable, they are contestable via a computationally and data efficient process that must lead to agreement. Thus we cannot find ourselves in a situation in which we have two equally accurate and unimprovable models that disagree substantially in their predictions—providing an answer to what is sometimes called the predictive or model multiplicity problem. 

We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar property if and only if is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable , we give simple canonical algorithms for the batch and the online adversarial setting, that learn a -multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property is not elicitable by itself, but is elicitable conditionally on another elicitable property , then there is a canonical algorithm that jointly multicalibrates and ; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment. 

We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random variable that is dependent on the population one is born into. Individuals then apply to a downstream agent, which we treat as a university throughout the paper (but could also represent an employer) who makes a decision about whether to admit them or not. The university does not directly observe talent or wealth, but rather a signal (representing e.g. a standardized test) that is a convex combination of both. The university knows the distributions from which an individual's type and wealth are drawn, and makes its decisions based on the posterior distribution of the applicant's characteristics conditional on their population and signal. Each population's wealth distribution at the next round then depends on the fraction of that population that was admitted by the university at the previous round. We study wealth dynamics in this model, and give conditions under which the dynamics have a single attracting fixed point (which implies population wealth inequality is transitory), and conditions under which it can have multiple attracting fixed points (which implies that population wealth inequality can be persistent). In the case in which there are multiple attracting fixed points, we study interventions aimed at eliminating or mitigating inequality, including increasing the capacity of the university to admit more people, aligning the signal generated by individuals with the preferences of the university, and making direct monetary transfers to the less wealthy population. 

We develop fast distribution-free conformal prediction algorithms for obtaining multivalid coverage on exchangeable data in the batch setting. Multivalid coverage guarantees are stronger than marginal coverage guarantees in two ways: (1) They hold even conditional on group membership---that is, the target coverage level holds conditionally on membership in each of an arbitrary (potentially intersecting) group in a finite collection of regions in the feature space. (2) They hold even conditional on the value of the threshold used to produce the prediction set on a given example. In fact multivalid coverage guarantees hold even when conditioning on group membership and threshold value simultaneously. We give two algorithms: both take as input an arbitrary non-conformity score and an arbitrary collection of possibly intersecting groups , and then can equip arbitrary black-box predictors with prediction sets. Our first algorithm is a direct extension of quantile regression, needs to solve only a single convex minimization problem, and produces an estimator which has group-conditional guarantees for each group in . Our second algorithm is iterative, and gives the full guarantees of multivalid conformal prediction: prediction sets that are valid conditionally both on group membership and non-conformity threshold. We evaluate the performance of both of our algorithms in an extensive set of experiments. 

A reconstruction attack on a private dataset D takes as input some publicly accessible information about the dataset and produces a list of candidate elements of D . We introduce a class of data reconstruction attacks based on randomized methods for nonconvex optimization. We empirically demonstrate that our attacks can not only reconstruct full rows of D from aggregate query statistics Q ( D )∈ℝ m but can do so in a way that reliably ranks reconstructed rows by their odds of appearing in the private data, providing a signature that could be used for prioritizing reconstructed rows for further actions such as identity theft or hate crime. We also design a sequence of baselines for evaluating reconstruction attacks. Our attacks significantly outperform those that are based only on access to a public distribution or population from which the private dataset D was sampled, demonstrating that they are exploiting information in the aggregate statistics Q ( D ) and not simply the overall structure of the distribution. In other words, the queries Q ( D ) are permitting reconstruction of elements of this dataset, not the distribution from which D was drawn. These findings are established both on 2010 US decennial Census data and queries and Census-derived American Community Survey datasets. Taken together, our methods and experiments illustrate the risks in releasing numerically precise aggregate statistics of a large dataset and provide further motivation for the careful application of provably private techniques such as differential privacy. 

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available.