Jake A. Soloff

Jake A. Soloff, Rina Foygel Barber, Rebecca Willett

Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on the properties of the base algorithm, or on the dimensionality of the covariates. Our guarantee applies to many variants of bagging and is optimal up to a constant. Empirical results validate our findings, showing that bagging successfully stabilizes even highly unstable base algorithms.

Stephen Bates, Michael I. Jordan, Michael Sklar et al.

Consider the relationship between a regulator (the principal) and an experimenter (the agent) such as a pharmaceutical company. The pharmaceutical company wishes to sell a drug for profit, whereas the regulator wishes to allow only efficacious drugs to be marketed. The efficacy of the drug is not known to the regulator, so the pharmaceutical company must run a costly trial to prove efficacy to the regulator. Critically, the statistical protocol used to establish efficacy affects the behavior of a strategic, self-interested agent; a lower standard of statistical evidence incentivizes the agent to run more trials that are less likely to be effective. The interaction between the statistical protocol and the incentives of the pharmaceutical company is crucial for understanding this system and designing protocols with high social utility. In this work, we discuss how the regulator can set up a protocol with payoffs based on statistical evidence. We show how to design protocols that are robust to an agent's strategic actions, and derive the optimal protocol in the presence of strategic entrants.

Stephen Bates, Michael I. Jordan, Michael Sklar et al.

Contemporary scientific research is a distributed, collaborative endeavor, carried out by teams of researchers, regulatory institutions, funding agencies, commercial partners, and scientific bodies, all interacting with each other and facing different incentives. To maintain scientific rigor, statistical methods should acknowledge this state of affairs. To this end, we study hypothesis testing when there is an agent (e.g., a researcher or a pharmaceutical company) with a private prior about an unknown parameter and a principal (e.g., a policymaker or regulator) who wishes to make decisions based on the parameter value. The agent chooses whether to run a statistical trial based on their private prior and then the result of the trial is used by the principal to reach a decision. We show how the principal can conduct statistical inference that leverages the information that is revealed by an agent's strategic behavior -- their choice to run a trial or not. In particular, we show how the principal can design a policy to elucidate partial information about the agent's private prior beliefs and use this to control the posterior probability of the null. One implication is a simple guideline for the choice of significance threshold in clinical trials: the type-I error level should be set to be strictly less than the cost of the trial divided by the firm's profit if the trial is successful.

Jake A. Soloff, Rina Foygel Barber, Rebecca Willett

We propose a new framework for algorithmic stability in the context of multiclass classification. In practice, classification algorithms often operate by first assigning a continuous score (for instance, an estimated probability) to each possible label, then taking the maximizer -- i.e., selecting the class that has the highest score. A drawback of this type of approach is that it is inherently unstable, meaning that it is very sensitive to slight perturbations of the training data, since taking the maximizer is discontinuous. Motivated by this challenge, we propose a pipeline for constructing stable classifiers from data, using bagging (i.e., resampling and averaging) to produce stable continuous scores, and then using a stable relaxation of argmax, which we call the "inflated argmax," to convert these scores to a set of candidate labels. The resulting stability guarantee places no distributional assumptions on the data, does not depend on the number of classes or dimensionality of the covariates, and holds for any base classifier. Using a common benchmark data set, we demonstrate that the inflated argmax provides necessary protection against unstable classifiers, without loss of accuracy.

Ruiting Liang, Jake A. Soloff, Rina Foygel Barber et al.

In this work, we consider ranking problems among a finite set of candidates: for instance, selecting the top-$k$ items among a larger list of candidates or obtaining the full ranking of all items in the set. These problems are often unstable, in the sense that estimating a ranking from noisy data can exhibit high sensitivity to small perturbations. Concretely, if we use data to provide a score for each item (say, by aggregating preference data over a sample of users), then for two items with similar scores, small fluctuations in the data can alter the relative ranking of those items. Many existing theoretical results for ranking problems assume a separation condition to avoid this challenge, but real-world data often contains items whose scores are approximately tied, limiting the applicability of existing theory. To address this gap, we develop a new algorithmic stability framework for ranking problems, and propose two novel ranking operators for achieving stable ranking: the \emph{inflated top-$k$} for the top-$k$ selection problem and the \emph{inflated full ranking} for ranking the full list. To enable stability, each method allows for expressing some uncertainty in the output. For both of these two problems, our proposed methods provide guaranteed stability, with no assumptions on data distributions and no dependence on the total number of candidates to be ranked. Experiments on real-world data confirm that the proposed methods offer stability without compromising the informativeness of the output.

Melissa Adrian, Jake A. Soloff, Rebecca Willett

Model selection is the process of choosing from a class of candidate models given data. For instance, methods such as the LASSO and sparse identification of nonlinear dynamics (SINDy) formulate model selection as finding a sparse solution to a linear system of equations determined by training data. However, absent strong assumptions, such methods are highly unstable: if a single data point is removed from the training set, a different model may be selected. In this paper, we present a new approach to stabilizing model selection with theoretical stability guarantees that leverages a combination of bagging and an ''inflated'' argmax operation. Our method selects a small collection of models that all fit the data, and it is stable in that, with high probability, the removal of any training point will result in a collection of selected models that overlaps with the original collection. We illustrate this method in (a) a simulation in which strongly correlated covariates make standard LASSO model selection highly unstable, (b) a Lotka-Volterra model selection problem focused on identifying how competition in an ecosystem influences species' abundances, and (c) a graph subset selection problem using cell-signaling data from proteomics. In these settings, the proposed method yields stable, compact, and accurate collections of selected models, outperforming a variety of benchmarks.