arXiv subjects

Giles Hooker

Publications and source records attributed to Giles Hooker.

At least 19 recordsLinked to original sources

arXiv2026

Fairness Testing for Algorithmic Pricing

Algorithmic systems now set prices across auto insurance, credit, and lending markets, and regulators increasingly require firms to demonstrate that these systems do not discriminate against protected groups. The standard audit regresses pricing output on a protected attribute and legitimate rating factors, then tests the resulting coefficient using ordinary least squares standard errors. We show that this approach is structurally invalid. Pricing algorithms are usually deterministic, so residuals reflect approximation error rather than sampling variability, rendering classical standard errors invalid in both direction and magnitude. We derive correct asymptotic variance estimators for OLS and GLM audit regressions and the correct cross-covariance formula for proxy discrimination testing. Applied to quoted premiums from 34 Illinois auto insurers, every insurer fails the conditional demographic parity test, with minority zip codes paying $34-$158 more per year than comparable-risk white zip codes. The standard proxy discrimination formula flags zero insurers. However, our corrected formula identifies all 34 as statistically significant, of which 16 exceed the substantive threshold. Our framework provides statistically valid audit tools for any deterministic algorithmic system subject to regression-based fairness testing.

stat.AP↗

arXiv2026

Estimating Implicit Regularization in Deep Learning

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization -- connecting it to an equivalent penalty that augments the learning objective. However, modern deep learning systems are complex, carrying modifications to the training procedure and architecture (e.g. early stopping, minibatching, dropout) whose effects are not always directly interpretable. Although estimating the resulting implicit regularization could aid theorists in algorithm design and practitioners in interpreting their hyperparameter choices, this problem has received little direct attention. It is also tractable: regularization makes weight updates deviate from loss gradients, promising a signal for identifying implicit bias. Here we provide gradient matching methods that can be used to empirically estimate the implicit regularization. Our method works on networks with known regularization, recovering popular explicit penalties like $\ell_1$ and $\ell_2$. It also replicates known implicit effects, like the quadratic weight penalty induced by early stopping in gradient descent, demonstrating that it can be used to test theories of implicit regularization. Crucially, because our method is empirical, it can handle implicit regularization in arbitrary networks. We demonstrate this use by characterizing the effects of dropout in deep networks, showing implicit $\ell_2$ effects in this popular method. Our work shows that practitioners can use gradient matching to understand regularization in networks with implicit biases that are too complicated to derive analytically.

stat.ML↗

arXiv2026

Statistical Inference for Explainable Boosting Machines

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal MSE for fitting Lipschitz GAMs with $p$ features of $O(p n^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs. Code is available at https://github.com/hetankevin/ebm-inference.

stat.ML↗

arXiv2026

How Proxy Race Distorts Regression-Based Fairness Audits

Proxy-based race inference is increasingly used to conduct fairness assessments when protected-class data are unavailable or legally restricted -- most prominently in U.S. fair-lending enforcement, and now explicitly contemplated in emerging insurance regulation, including Colorado's draft SB21-169 testing framework and New York's Insurance Circular Letter No. 7. Despite this growing regulatory relevance, little is known about how standard regression-based discrimination analyses behave when race is measured with error through proxies such as Bayesian Improved Surname Geocoding (BISG) or Bayesian Improved First Name and Surname Geocoding (BIFSG). This paper studies the consequences of using proxy-imputed race as a categorical regressor in regression-based fairness assessments. Treating proxy race as a categorical covariate subject to misclassification, we show that proxy-based coefficients become weighted mixtures of true group effects, systematically shrinking estimated disparities toward the majority group -- even when overall classification accuracy is high. Empirically, using a linked North Carolina voter-insurance dataset with self-reported race and ZIP-level auto insurance premiums, we demonstrate two mechanisms through which it distorts inference: (i) the intrinsic mixing of group effects implied by misclassification, and (ii) structured errors that vary with ZIP-level racial composition and socioeconomic conditions and remain correlated with pricing residuals after controls. As a result, regression-based disparity estimates can be attenuated or amplified relative to analogous analyses based on self-reported race. Our findings caution against treating proxy race as a plug-in substitute in regulatory testing and highlight design implications for proxy-based audit frameworks in insurance and other high-stakes domains.

stat.AP↗

arXiv2025

Targeted Learning for Variable Importance

Variable importance is one of the most widely used measures for interpreting machine learning with significant interest from both statistics and machine learning communities. Recently, increasing attention has been directed toward uncertainty quantification in these metrics. Current approaches largely rely on one-step procedures, which, while asymptotically efficient, can present higher sensitivity and instability in finite sample settings. To address these limitations, we propose a novel method by employing the targeted learning (TL) framework, designed to enhance robustness in inference for variable importance metrics. Our approach is particularly suited for conditional permutation variable importance. We show that it (i) retains the asymptotic efficiency of traditional methods, (ii) maintains comparable computational complexity, and (iii) delivers improved accuracy, especially in finite sample contexts. We further support these findings with numerical experiments that illustrate the practical advantages of our method and validate the theoretical results.

stat.ML↗

arXiv2025

Differentiable Programming for Differential Equations: A Review

The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations, where differentiable programming plays a crucial role in calculating model sensitivities, inverting model parameters, and training hybrid models that combine differential equations with data-driven approaches. Furthermore, recognizing the strong synergies between inverse methods and machine learning offers the opportunity to establish a coherent framework applicable to both fields. Differentiating functions based on the numerical solution of differential equations is non-trivial. Numerous methods based on a wide variety of paradigms have been proposed in the literature, each with pros and cons specific to the type of problem investigated. Here, we provide a comprehensive review of existing techniques to compute derivatives of numerical solutions of differential equations. We first discuss the importance of gradients of solutions of differential equations in a variety of scientific domains. Second, we lay out the mathematical foundations of the various approaches and compare them with each other. Third, we cover the computational considerations and explore the solutions available in modern scientific software. Last but not least, we provide best-practices and recommendations for practitioners. We hope that this work accelerates the fusion of scientific models and data, and fosters a modern approach to scientific modelling.

math.NA↗

arXiv2025

Statistical Inference for Gradient Boosting Regression

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance. Numerical experiments demonstrate that our algorithms perform well, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

stat.ML↗

arXiv2025

Gaussian Rank Verification

Statistical experiments often seek to identify random variables with the largest population means. This inferential task, known as rank verification, has been well-studied on Gaussian data with equal variances. This work provides the first treatment of the unequal variances case, utilizing ideas from the selective inference literature. We design a hypothesis test that verifies the rank of the largest observed value without losing power due to multiple testing corrections. This test is subsequently extended for two procedures: Identifying some number of correctly-ordered Gaussian means, and validating the top-K set. The testing procedures are validated on NHANES survey data.

stat.ME↗

arXiv2025

Statistical Significance of Feature Importance Rankings

Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from hypothesis testing, we devise techniques that ensure the most important features are correct with high-probability guarantees. These assess the set of $K$ top-ranked features, as well as the order of its elements. Given a set of local or global importance scores, we demonstrate how to retrospectively verify the stability of the highest ranks. We then introduce two efficient sampling algorithms that identify the $K$ most important features, perhaps in order, with probability exceeding $1-α$. The theoretical justification for these procedures is validated empirically on SHAP and LIME.

stat.ML↗

arXiv2025

Unifying Image Counterfactuals and Feature Attributions with Latent-Space Adversarial Attacks

Counterfactuals are a popular framework for interpreting machine learning predictions. These what if explanations are notoriously challenging to create for computer vision models: standard gradient-based methods are prone to produce adversarial examples, in which imperceptible modifications to image pixels provoke large changes in predictions. We introduce a new, easy-to-implement framework for counterfactual images that can flexibly adapt to contemporary advances in generative modeling. Our method, Counterfactual Attacks, resembles an adversarial attack on the representation of the image along a low-dimensional manifold. In addition, given an auxiliary dataset of image descriptors, we show how to accompany counterfactuals with feature attribution that quantify the changes between the original and counterfactual images. These importance scores can be aggregated into global counterfactual explanations that highlight the overall features driving model predictions. While this unification is possible for any counterfactual method, it has particular computational efficiency for ours. We demonstrate the efficacy of our approach with the MNIST and CelebA datasets.

cs.LG↗

arXiv2025

CLaRe: Compact near-lossless Latent Representations of High-Dimensional Object Data

Latent feature representation methods play an important role in the dimension reduction and statistical modeling of high-dimensional complex data objects. However, existing approaches to assess the quality of these methods often rely on aggregated statistics that reflect the central tendency of the distribution of information losses, such as average or total loss, which can mask variation across individual observations. We argue that controlling average performance is insufficient to guarantee that statistical analysis in the latent space reflects the data-generating process and instead advocate for controlling the worst-case generalization error, or a tail quantile of the generalization error distribution. Our framework, CLaRe (Compact near-lossless Latent Representations), introduces a systematic way to balance compactness of the representation with preservation of information when assessing and selecting among latent feature representation methods. To facilitate the application of the CLaRe framework, we have developed GLaRe (Graphical Analysis of Latent Representations), an open-source R package that implements the framework and provides graphical summaries of the full generalization error distribution. We demonstrate the utility of CLaRe through three case studies on high-dimensional datasets from diverse fields of application. We apply the CLaRe framework to select among principal components, wavelets and autoencoder representations for each dataset. The case studies reveal that the optimal latent feature representation varies depending on dataset characteristics, emphasizing the importance of a flexible evaluation framework.

stat.ME↗

arXiv2025

Targeted Learning for Data Fairness

Data and algorithms have the potential to produce and perpetuate discrimination and disparate treatment. As such, significant effort has been invested in developing approaches to defining, detecting, and eliminating unfair outcomes in algorithms. In this paper, we focus on performing statistical inference for fairness. Prior work in fairness inference has largely focused on inferring the fairness properties of a given predictive algorithm. Here, we expand fairness inference by evaluating fairness in the data generating process itself, referred to here as data fairness. We perform inference on data fairness using targeted learning, a flexible framework for nonparametric inference. We derive estimators demographic parity, equal opportunity, and conditional mutual information. Additionally, we find that our estimators for probabilistic metrics exploit double robustness. To validate our approach, we perform several simulations and apply our estimators to real data.

cs.LG↗

arXiv2024

Targeted Maximum Likelihood Estimation for Integral Projection Models in Population Ecology

Integral projection models (IPMs) are widely used to study population growth and the dynamics of demographic structure (e.g. age and size distributions) within a population.These models use data on individuals' growth, survival, and reproduction to predict changes in the population from one time point to the next and use these in turn to ask about long-term growth rates, the sensitivity of that growth rate to environmental factors, and aspects of the long term population such as how much reproduction concentrates in a few individuals; these quantities are not directly measurable from data and must be inferred from the model. Building IPMs requires us to develop models for individual fates over the next time step -- Did they survive? How much did they grow or shrink? Did they Reproduce? -- conditional on their initial state as well as on environmental covariates in a manner that accounts for the unobservable quantities that are are ultimately interested in estimating.Targeted maximum likelihood estimation (TMLE) methods are particularly well-suited to a framework in which we are largely interested in the consequences of models. These build machine learning-based models that estimate the probability distribution of the data we observe and define a target of inference as a function of these. The initial estimate for the distribution is then modified by tilting in the direction of the efficient influence function to both de-bias the parameter estimate and provide more accurate inference. In this paper, we employ TMLE to develop robust and efficient estimators for properties derived from a fitted IPM. Mathematically, we derive the efficient influence function and formulate the paths for the least favorable sub-models. Empirically, we conduct extensive simulations using real data from both long term studies of Idaho steppe plant communities and experimental Rotifer populations.

stat.ME↗

arXiv2024

Accelerated Inference for Partially Observed Markov Processes using Automatic Differentiation

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant to AD techniques because widely used particle filter algorithms yield an estimated likelihood function that is discontinuous as a function of the model parameters. We show how to embed two existing AD particle filter methods in a theoretical framework that provides an extension to a new class of algorithms. This new class permits a bias/variance tradeoff and hence a mean squared error substantially lower than the existing algorithms. We develop likelihood maximization algorithms suited to the Monte Carlo properties of the AD gradient estimate. Our algorithms require only a differentiable simulator for the latent dynamic system; by contrast, most previous approaches to AD likelihood maximization for particle filters require access to the system's transition probabilities. Numerical results indicate that a hybrid algorithm that uses AD to refine a coarse solution from an iterated filtering algorithm show substantial improvement on current state-of-the-art methods for a challenging scientific benchmark problem.

stat.ME↗

arXiv2024

An Understanding of Principal Differential Analysis

In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to estimate a linear ordinary differential equation from functional data in a technique called Principal Differential Analysis, by formulating a functional regression in which the highest-order derivative of a function is modelled as a time-varying linear combination of its lower-order derivatives. Principal Differential Analysis was introduced as a technique for data reduction and representation, using solutions of the estimated differential equation as a basis to represent the functional data. In this work, we re-formulate PDA as a generative statistical model in which functional observations arise as solutions of a deterministic ODE that is forced by a smooth random error process. This viewpoint defines a flexible class of functional models based on differential equations and leads to an improved understanding and characterisation of the sources of variability in Principal Differential Analysis. It does, however, result in parameter estimates that can be heavily biased under the standard estimation approach of PDA. Therefore, we introduce an iterative bias-reduction algorithm that can be applied to improve parameter estimates. We also examine the utility of our approach when the form of the deterministic part of the differential equation is unknown and possibly non-linear, where Principal Differential Analysis is treated as an approximate model based on time-varying linearisation. We demonstrate our approach on simulated data from linear and non-linear differential equations and on real data from human movement biomechanics. Supplementary R code for this manuscript is available at \url{https://github.com/edwardgunning/UnderstandingOfPDAManuscript}.

stat.ME↗

arXiv2024

Why You Should Not Trust Interpretations in Machine Learning: Adversarial Attacks on Partial Dependence Plots

The adoption of artificial intelligence (AI) across industries has led to the widespread use of complex black-box models and interpretation tools for decision making. This paper proposes an adversarial framework to uncover the vulnerability of permutation-based interpretation methods for machine learning tasks, with a particular focus on partial dependence (PD) plots. This adversarial framework modifies the original black box model to manipulate its predictions for instances in the extrapolation domain. As a result, it produces deceptive PD plots that can conceal discriminatory behaviors while preserving most of the original model's predictions. This framework can produce multiple fooled PD plots via a single model. By using real-world datasets including an auto insurance claims dataset and COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) dataset, our results show that it is possible to intentionally hide the discriminatory behavior of a predictor and make the black-box model appear neutral through interpretation tools like PD plots while retaining almost all the predictions of the original black-box model. Managerial insights for regulators and practitioners are provided based on the findings.

cs.LG↗

arXiv2024

Stabilizing Estimates of Shapley Values with Control Variates

Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable degree of uncertainty. To stabilize these model explanations, we propose ControlSHAP, an approach based on the Monte Carlo technique of control variates. Our methodology is applicable to any machine learning model and requires virtually no extra computation or modeling effort. On several high-dimensional datasets, we find it can produce dramatic reductions in the Monte Carlo variability of Shapley estimates.

stat.ML↗

arXiv2024

Longitudinal Counterfactuals: Constraints and Opportunities

Counterfactual explanations are a common approach to providing recourse to data subjects. However, current methodology can produce counterfactuals that cannot be achieved by the subject, making the use of counterfactuals for recourse difficult to justify in practice. Though there is agreement that plausibility is an important quality when using counterfactuals for algorithmic recourse, ground truth plausibility continues to be difficult to quantify. In this paper, we propose using longitudinal data to assess and improve plausibility in counterfactuals. In particular, we develop a metric that compares longitudinal differences to counterfactual differences, allowing us to evaluate how similar a counterfactual is to prior observed changes. Furthermore, we use this metric to generate plausible counterfactuals. Finally, we discuss some of the inherent difficulties of using counterfactuals for recourse.

cs.LG↗