arXiv subjects

Stephen Bates

Publications and source records attributed to Stephen Bates.

59 records · Page 4Linked to original sources

arXiv2021

Test-time Collective Prediction

An increasingly common setting in machine learning involves multiple parties, each with their own data, who want to jointly make predictions on future test points. Agents wish to benefit from the collective expertise of the full set of agents to make better predictions than they would individually, but may not be willing to release their data or model parameters. In this work, we explore a decentralized mechanism to make collective predictions at test time, leveraging each agent's pre-trained model without relying on external validation, model retraining, or data pooling. Our approach takes inspiration from the literature in social science on human consensus-making. We analyze our mechanism theoretically, showing that it converges to inverse meansquared-error (MSE) weighting in the large-sample limit. To compute error bars on the collective predictions we propose a decentralized Jackknife procedure that evaluates the sensitivity of our mechanism to a single agent's prediction. Empirically, we demonstrate that our scheme effectively combines models with differing quality across the input space. The proposed consensus prediction achieves significant gains over classical model averaging, and even outperforms weighted averaging schemes that have access to additional validation data.

cs.LG↗

arXiv2020

Achieving Equalized Odds by Resampling Sensitive Attributes

We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this criterion. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. To rigorously evaluate fitted models, we develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature. Both the model fitting and hypothesis testing leverage a resampled version of the sensitive attribute obeying equalized odds, by construction. We demonstrate the applicability and validity of the proposed framework both in regression and multi-class classification problems, reporting improved performance over state-of-the-art methods. Lastly, we show how to incorporate techniques for equitable uncertainty quantification---unbiased for each group under study---to communicate the results of the data analysis in exact terms.

stat.ML↗

arXiv2020

Causal Inference in Genetic Trio Studies

We introduce a method to rigorously draw causal inferences---inferences immune to all possible confounding---from genetic data that include parents and offspring. Causal conclusions are possible with these data because the natural randomness in meiosis can be viewed as a high-dimensional randomized experiment. We make this observation actionable by developing a novel conditional independence test that identifies regions of the genome containing distinct causal variants. The proposed Digital Twin Test compares an observed offspring to carefully constructed synthetic offspring from the same parents in order to determine statistical significance, and it can leverage any black-box multivariate model and additional non-trio genetic data in order to increase power. Crucially, our inferences are based only on a well-established mathematical description of the rearrangement of genetic material during meiosis and make no assumptions about the relationship between the genotypes and phenotypes.

stat.ME↗

arXiv2019

Metropolized Knockoff Sampling

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This paper introduces techniques for knockoff generation in great generality: we provide a sequential characterization of all possible knockoff distributions, which leads to a Metropolis-Hastingsformulation of an exact knockoff sampler. We further show how to use conditional independence structure to speed up computations. Combining these two threads, we introduce an explicit set of sequential algorithms and empirically demonstrate their effectiveness. Our theoretical analysis proves that our algorithms achieve near-optimal computational complexity in certain cases. The techniques we develop are sufficiently rich to enable knockoff sampling in challenging models including cases where the covariates are continuous and heavy-tailed, and follow a graphical model such as the Ising model.

stat.ME↗

arXiv2017

Log-ratio Lasso: Scalable, Sparse Estimation for Log-ratio Models

Positive-valued signal data is common in many biological and medical applications, where the data are often generated from imaging techniques such as mass spectrometry. In such a setting, the relative intensities of the raw features are often the scientifically meaningful quantities, so it is of interest to identify relevant features that take the form of log-ratios of the raw inputs. When including the log-ratios of all pairs of predictors, the dimensionality of this predictor space becomes large, so computationally efficient statistical procedures are required. We introduce an embedding of the log-ratio parameter space into a space of much lower dimension and develop efficient penalized fitting procedure using this more tractable representation. This procedure serves as the foundation for a two-step fitting procedure that combines a convex filtering step with a second non-convex pruning step to yield highly sparse solutions. On a cancer proteomics data set we find that these methods fit highly sparse models with log-ratio features of known biological relevance while greatly improving upon the predictive accuracy of less interpretable methods.

stat.ME↗