16 research outputs found
Locally Simultaneous Inference
Selective inference is the problem of giving valid answers to statistical
questions chosen in a data-driven manner. A standard solution to selective
inference is simultaneous inference, which delivers valid answers to the set of
all questions that could possibly have been asked. However, simultaneous
inference can be unnecessarily conservative if this set includes many questions
that were unlikely to be asked in the first place. We introduce a less
conservative solution to selective inference that we call locally simultaneous
inference, which only answers those questions that could plausibly have been
asked in light of the observed data, all the while preserving rigorous type I
error guarantees. For example, if the objective is to construct a confidence
interval for the "winning" treatment effect in a clinical trial with multiple
treatments, and it is obvious in hindsight that only one treatment had a chance
to win, then our approach will return an interval that is nearly the same as
the uncorrected, standard interval. Under mild conditions satisfied by common
confidence intervals, locally simultaneous inference strictly dominates
simultaneous inference, meaning it can never yield less statistical power but
only more. Compared to conditional selective inference, which demands stronger
guarantees, locally simultaneous inference is more easily applicable in
nonparametric settings and is more numerically stable
A Note on Zeroth-Order Optimization on the Simplex
We construct a zeroth-order gradient estimator for a smooth function defined
on the probability simplex. The proposed estimator queries the simplex only. We
prove that projected gradient descent and the exponential weights algorithm,
when run with this estimator instead of exact gradients, converge at a
rate
Plug-in Performative Optimization
When predictions are performative, the choice of which predictor to deploy
influences the distribution of future observations. The overarching goal in
learning under performativity is to find a predictor that has low
\emph{performative risk}, that is, good performance on its induced
distribution. One family of solutions for optimizing the performative risk,
including bandits and other derivative-free methods, is agnostic to any
structure in the performative feedback, leading to exceedingly slow convergence
rates. A complementary family of solutions makes use of explicit \emph{models}
for the feedback, such as best-response models in strategic classification,
enabling significantly faster rates. However, these rates critically rely on
the feedback model being well-specified. In this work we initiate a study of
the use of possibly \emph{misspecified} models in performative prediction. We
study a general protocol for making use of models, called \emph{plug-in
performative optimization}, and prove bounds on its excess risk. We show that
plug-in performative optimization can be far more efficient than model-agnostic
strategies, as long as the misspecification is not too extreme. Altogether, our
results support the hypothesis that models--even if misspecified--can indeed
help with learning in performative settings
PPI++: Efficient Prediction-Powered Inference
We present PPI++: a computationally lightweight methodology for estimation
and inference based on a small labeled dataset and a typically much larger
dataset of machine-learning predictions. The methods automatically adapt to the
quality of available predictions, yielding easy-to-compute confidence sets --
for parameters of any dimensionality -- that always improve on classical
intervals using only the labeled data. PPI++ builds on prediction-powered
inference (PPI), which targets the same problem setting, improving its
computational and statistical efficiency. Real and synthetic experiments
demonstrate the benefits of the proposed adaptations.Comment: Code available at https://github.com/aangelopoulos/ppi_p