As machine learning models grow increasingly competent, their predictions can supplement scarce or expensive data in various important domains. In support of this paradigm, algorithms have emerged to combine a small amount of high-fidelity observed data with a much larger set of imputed model outputs to estimate some quantity of interest. Yet current hybrid-inference tools target only means or single quantiles, limiting their applicability for many critical domains and use cases. We present QuEst, a principled framework to merge observed and imputed data to deliver point estimates and rigorous confidence intervals for a wide family of quantile-based distributional measures. QuEst covers a range of measures, from tail risk (CVaR) to population segments such as quartiles, that are central to fields such as economics, sociology, education, medicine, and more. We extend QuEst to multidimensional metrics, and introduce an additional optimization technique to further reduce variance in this and other hybrid estimators. We demonstrate the utility of our framework through experiments in economic modeling, opinion polling, and language model auto-evaluation.

The availability of machine learning systems that can effectively perform arbitrary tasks has led to synthetic labels from these systems being used in applications of statistical inference, such as data analysis or model evaluation. The Prediction Powered Inference (PPI) framework provides a way of leveraging both a large pool of pseudo-labelled data and a small sample with real, high-quality labels to produce a low-variance, unbiased estimate of the quantity being evaluated for. Most work on PPI considers a relatively sizable set of labelled samples, which can be resource intensive to obtain. However, we find that when labelled data is scarce, the PPI++ method can perform even worse than classical inference. We analyze this phenomenon by relating PPI++ to ordinary least squares regression, which also experiences high variance with small sample sizes, and use this regression framework to better understand the efficacy of PPI. Motivated by this, we present two new PPI-based techniques that leverage robust regressors to produce even lower variance estimators in the few-label regime

Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression---the analogous problem for modeling continuous targets---remains relatively unexplored. To tackle this problem, we return to first principles and analyze how the closed-form solution for Ordinary Least Squares (OLS) regression is sensitive to covariate shift. We characterize the out-of-distribution risk of the OLS model in terms of the eigenspectrum decomposition of the source and target data. We then use this insight to propose a method called Spectral Adapted Regressor (SpAR) for adapting the weights of the last layer of a pre-trained neural regression model to perform better on input data originating from a different distribution. We demonstrate how this lightweight spectral adaptation procedure can improve out-of-distribution performance for synthetic and real-world datasets.

Research related to automatically detecting Alzheimer's disease (AD) is important, given the high prevalence of AD and the high cost of traditional methods. Since AD significantly affects the content and acoustics of spontaneous speech, natural language processing and machine learning provide promising techniques for reliably detecting AD. We compare and contrast the performance of two such approaches for AD detection on the recent ADReSS challenge dataset: 1) using domain knowledge-based hand-crafted features that capture linguistic and acoustic phenomena, and 2) fine-tuning Bidirectional Encoder Representations from Transformer (BERT)-based sequence classification models. We also compare multiple feature-based regression models for a neuropsychological score task in the challenge. We observe that fine-tuned BERT models, given the relative importance of linguistics in cognitive impairment detection, outperform feature-based approaches on the AD detection task.