arXiv subjects

Aaron Fisher

Publications and source records attributed to Aaron Fisher.

13 recordsLinked to original sources

arXiv2023

The Connection Between R-Learning and Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effects

Many methods for estimating conditional average treatment effects (CATEs) can be expressed as weighted pseudo-outcome regressions (PORs). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. For example, we point out that R-Learning implicitly performs a POR with inverse-variance weights (IVWs). In the CATE setting, IVWs mitigate the instability associated with inverse-propensity weights, and lead to convenient simplifications of bias terms. We demonstrate the superior performance of IVWs in simulations, and derive convergence rates for IVWs that are, to our knowledge, the fastest yet shown without assuming knowledge of the covariate distribution.

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arXiv2023

Three-way Cross-Fitting and Pseudo-Outcome Regression for Estimation of Conditional Effects and other Linear Functionals

We propose an approach to better inform treatment decisions at an individual level by adapting recent advances in average treatment effect estimation to conditional average treatment effect estimation. Our work is based on doubly robust estimation methods, which combine flexible machine learning tools to produce efficient effect estimates while relaxing parametric assumptions about the data generating process. Refinements to doubly robust methods have achieved faster convergence by incorporating 3-way cross-fitting, which entails dividing the sample into three partitions, using the first to estimate the conditional probability of treatment, the second to estimate the conditional expectation of the outcome, and the third to perform a first order bias correction step. Here, we combine the approaches of 3-way cross-fitting and pseudo-outcome regression to produce personalized effect estimates. We show that this approach yields fast convergence rates under a smoothness condition on the conditional expectation of the outcome.

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arXiv2022

Treatment Effect Bias from Sample Snooping: Blinding Outcomes is Neither Necessary nor Sufficient

Popular guidance on observational data analysis states that outcomes should be blinded when determining matching criteria or propensity scores. Such a blinding is informally said to maintain the "objectivity" of the analysis, and to prevent analysts from fishing for positive results by exploiting chance imbalances. Contrary to this notion, we show that outcome blinding is not a sufficient safeguard against fishing. Blinded and unblinded analysts can produce bias of the same order of magnitude in cases where the outcomes can be approximately predicted from baseline covariates. We illustrate this vulnerability with a combination of analytical results and simulations. Finally, to show that outcome blinding is not necessary to prevent bias, we outline an alternative sample partitioning procedure for estimating the average treatment effect on the controls, or the average treatment effect on the treated. This procedure uses all of the the outcome data from all partitions in the final analysis step, but does not require the analysis to not be fully prespecified.

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arXiv2022

Gaussian Latent Dirichlet Allocation for Discrete Human State Discovery

In this article we propose and validate an unsupervised probabilistic model, Gaussian Latent Dirichlet Allocation (GLDA), for the problem of discrete state discovery from repeated, multivariate psychophysiological samples collected from multiple, inherently distinct, individuals. Psychology and medical research heavily involves measuring potentially related but individually inconclusive variables from a cohort of participants to derive diagnosis, necessitating clustering analysis. Traditional probabilistic clustering models such as Gaussian Mixture Model (GMM) assume a global mixture of component distributions, which may not be realistic for observations from different patients. The GLDA model borrows the individual-specific mixture structure from a popular topic model Latent Dirichlet Allocation (LDA) in Natural Language Processing and merges it with the Gaussian component distributions of GMM to suit continuous type data. We implemented GLDA using STAN (a probabilistic modeling language) and applied it on two datasets, one containing Ecological Momentary Assessments (EMA) and the other heart measures from electrocardiogram and impedance cardiograph. We found that in both datasets the GLDA-learned class weights achieved significantly higher correlations with clinically assessed depression, anxiety, and stress scores than those produced by the baseline GMM. Our findings demonstrate the advantage of GLDA over conventional finite mixture models for human state discovery from repeated multivariate data, likely due to better characterization of potential underlying between-participant differences. Future work is required to validate the utility of this model on a broader range of applications.

cs.LG↗

arXiv2022

Online False Discovery Rate Control for LORD & SAFFRON Under Positive, Local Dependence

Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha investing, LORD++ (hereafter, LORD), and SAFFRON. These three methods have been shown to provide online control of the "modified" false discovery rate (mFDR) under a condition known as conditional superuniformity. However, to our knowledge, LORD & SAFFRON have only been shown to control the traditional false discovery rate (FDR) under an independence condition on the test statistics. Our work bolsters these results by showing that SAFFRON and LORD additionally ensure online control of the FDR under a "local" form of nonnegative dependence. Further, FDR control is maintained under certain types of adaptive stopping rules, such as stopping after a certain number of rejections have been observed. Because alpha investing can be recovered as a special case of the SAFFRON framework, our results immediately apply to alpha investing as well. In the process of deriving these results, we also formally characterize how the conditional superuniformity assumption implicitly limits the allowed p-value dependencies. This implicit limitation is important not only to our proposed FDR result, but also to many existing mFDR results.

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arXiv2021

Online Control of the False Discovery Rate under "Decision Deadlines"

Online testing procedures aim to control the extent of false discoveries over a sequence of hypothesis tests, allowing for the possibility that early-stage test results influence the choice of hypotheses to be tested in later stages. Typically, online methods assume that a permanent decision regarding the current test (reject or not reject) must be made before advancing to the next test. We instead assume that each hypothesis requires an immediate preliminary decision, but also allows us to update that decision until a preset deadline. Roughly speaking, this lets us apply a Benjamini-Hochberg-type procedure over a moving window of hypotheses, where the threshold parameters for upcoming tests can be determined based on preliminary results. Our method controls the false discovery rate (FDR) at every stage of testing, as well as at adaptively chosen stopping times. These results apply even under arbitrary p-value dependency structures.

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arXiv2021

Optimizing Rescoring Rules with Interpretable Representations of Long-Term Information

Analyzing temporal data (e.g., wearable device data) requires a decision about how to combine information from the recent and distant past. In the context of classifying sleep status from actigraphy, Webster's rescoring rules offer one popular solution based on the long-term patterns in the output of a moving-window model. Unfortunately, the question of how to optimize rescoring rules for any given setting has remained unsolved. To address this problem and expand the possible use cases of rescoring rules, we propose rephrasing these rules in terms of epoch-specific features. Our features take two general forms: (1) the time lag between now and the most recent [or closest upcoming] bout of time spent in a given state, and (2) the length of the most recent [or closest upcoming] bout of time spent in a given state. Given any initial moving window model, these features can be defined recursively, allowing for straightforward optimization of rescoring rules. Joint optimization of the moving window model and the subsequent rescoring rules can also be implemented using gradient-based optimization software, such as Tensorflow. Beyond binary classification problems (e.g., sleep-wake), the same approach can be applied to summarize long-term patterns for multi-state classification problems (e.g., sitting, walking, or stair climbing). We find that optimized rescoring rules improve the performance of sleep-wake classifiers, achieving accuracy comparable to that of certain neural network architectures.

cs.LG↗

arXiv2020

MFEM: a modular finite element methods library

MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM's goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library.

cs.MS↗

arXiv2019

All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously

Variable importance (VI) tools describe how much covariates contribute to a prediction model's accuracy. However, important variables for one well-performing model (for example, a linear model $f(\mathbf{x})=\mathbf{x}^{T}β$ with a fixed coefficient vector $β$) may be unimportant for another model. In this paper, we propose model class reliance (MCR) as the range of VI values across all well-performing model in a prespecified class. Thus, MCR gives a more comprehensive description of importance by accounting for the fact that many prediction models, possibly of different parametric forms, may fit the data well. In the process of deriving MCR, we show several informative results for permutation-based VI estimates, based on the VI measures used in Random Forests. Specifically, we derive connections between permutation importance estimates for a single prediction model, U-statistics, conditional variable importance, conditional causal effects, and linear model coefficients. We then give probabilistic bounds for MCR, using a novel, generalizable technique. We apply MCR to a public data set of Broward County criminal records to study the reliance of recidivism prediction models on sex and race. In this application, MCR can be used to help inform VI for unknown, proprietary models.

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arXiv2019

Visually Communicating and Teaching Intuition for Influence Functions

Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of a treatment), rather than on estimating the full underlying data generating distribution, IF-based estimators are often able to achieve asymptotically optimal mean-squared error. Still, many researchers find IF-based estimators to be opaque or overly technical, which makes their use less prevalent and their benefits less available. To help foster understanding and trust in IF-based estimators, we present tangible, visual illustrations of when and how IF-based estimators can outperform standard ``plug-in'' estimators. The figures we show are based on connections between IFs, gradients, linear approximations, and Newton-Raphson.

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arXiv2014

interAdapt -- An Interactive Tool for Designing and Evaluating Randomized Trials with Adaptive Enrollment Criteria

The interAdapt R package is designed to be used by statisticians and clinical investigators to plan randomized trials. It can be used to determine if certain adaptive designs offer tangible benefits compared to standard designs, in the context of investigators' specific trial goals and constraints. Specifically, interAdapt compares the performance of trial designs with adaptive enrollment criteria versus standard (non-adaptive) group sequential trial designs. Performance is compared in terms of power, expected trial duration, and expected sample size. Users can either work directly in the R console, or with a user-friendly shiny application that requires no programming experience. Several added features are available when using the shiny application. For example, the application allows users to immediately download the results of the performance comparison as a csv-table, or as a printable, html-based report.

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arXiv2014

Fast, Exact Bootstrap Principal Component Analysis for p>1 million

Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject ($p$) is much larger than the number of subjects ($n$), the challenge of calculating and storing the leading principal components from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap principal components, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same $n$-dimensional subspace as the original sample. As a result, all bootstrap principal components are limited to the same $n$-dimensional subspace and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low dimensional coordinates, without calculating or storing the $p$-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram (EEG) recordings ($p=900$, $n=392$), and to a dataset of brain magnetic resonance images (MRIs) ($p\approx$ 3 million, $n=352$). For the brain MRI dataset, our method allows for standard errors for the first 3 principal components based on 1000 bootstrap samples to be calculated on a standard laptop in 47 minutes, as opposed to approximately 4 days with standard methods.

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arXiv2014

A randomized trial in a massive online open course shows people don't know what a statistically significant relationship looks like, but they can learn

Scatterplots are the most common way for statisticians, scientists, and the public to visually detect relationships between measured variables. At the same time, and despite widely publicized controversy, P-values remain the most commonly used measure to statistically justify relationships identified between variables. Here we measure the ability to detect statistically significant relationships from scatterplots in a randomized trial of 2,039 students in a statistics massive open online course (MOOC). Each subject was shown a random set of scatterplots and asked to visually determine if the underlying relationships were statistically significant at the P < 0.05 level. Subjects correctly classified only 47.4% (95% CI: 45.1%-49.7%) of statistically significant relationships, and 74.6% (95% CI: 72.5%-76.6%) of non-significant relationships. Adding visual aids such as a best fit line or scatterplot smooth increased the probability a relationship was called significant, regardless of whether the relationship was actually significant. Classification of statistically significant relationships improved on repeat attempts of the survey, although classification of non-significant relationships did not. Our results suggest: (1) that evidence-based data analysis can be used to identify weaknesses in theoretical procedures in the hands of average users, (2) data analysts can be trained to improve detection of statistically significant results with practice, but (3) data analysts have incorrect intuition about what statistically significant relationships look like, particularly for small effects. We have built a web tool for people to compare scatterplots with their corresponding p-values which is available here: http://glimmer.rstudio.com/afisher/EDA/.

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