arXiv subjects

Brieuc Lehmann

Publications and source records attributed to Brieuc Lehmann.

10 recordsLinked to original sources

arXiv2026

Targeted Highly Adaptive Lasso Minimum Loss Estimation of Target Functions

We propose a Targeted Highly Adaptive Lasso for estimation of non-pathwise differentiable functional parameters such as the dose-response curve (DRC) for continuous exposure. We assume the target function lies in the $k$-th order smoothness class used to define the $k$-th order Highly Adaptive Lasso (HAL), which can be well approximated by linear spans of $k$-th order spline basis functions. We construct a projection of the true target function onto a large finite dimensional working model spanned by an initial set of $k$-th order spline basis functions, which defines a pathwise differentiable approximation of the target functional parameter. A standard TMLE is then applied with a data-adaptive initial fit, replacing the MLE targeting step with a LASSO step over HAL spline basis functions that span the target function. We prove that the resulting Targeted HAL-MLE is pointwise asymptotically normally distributed and achieves a convergence rate determined solely by the dimension and smoothness of the target function, giving dimension free rates up till $\log n$-factors. Through a simulation study for the DRC, we show that the Targeted HAL outperforms a HAL plug-in estimator in terms of bias and mean squared error. Targeted HAL offers a fully data-adaptive approach to inference on functional parameters without requiring sieve specification or parametric assumptions.

stat.ME↗

arXiv2026

FairBED: A Bayesian Experimental Design Approach to Gathering Fairer Data

Frameworks for ensuring fairness in machine learning typically focus on learning fair models from existing data. But this endeavor is often undermined by biases already present in that data. We therefore look to modify the data acquisition process itself to help gather fairer data that is inherently more suitable for training fair predictors. To this end, we introduce FairBED, which provides novel formulations for quantifying the fairness of datasets themselves based on the idea that fair datasets should be uninformative about sensitive attributes. We then use this to construct practical fairness-aware Bayesian experimental design (BED) objectives that maximize expected information gain about the target quantity of interest while minimizing expected information gain about sensitive attributes. We further derive a theoretical link between FairBED and demographic parity, and show empirically that models trained on data gathered using FairBED provide improved fairness-accuracy trade-offs compared to randomly acquired data and conventional BED.

stat.ML↗

arXiv2026

Population-scale Ancestral Recombination Graphs with tskit 1.0

Ancestral recombination graphs (ARGs) are an increasingly important component of population and statistical genetics. The tskit library has become key infrastructure for the field, providing an expressive and general representation of ARGs together with a suite of efficient fundamental operations. In this note, we announce tskit version 1.0, describe its underlying rationale, and document its stability guarantees. These guarantees provide a foundation for durable computational artefacts and support long-term reproducibility of code and analyses.

q-bio.PE↗

arXiv2024

Causal-ICM: A Data Fusion Framework For Heterogeneous Treatment Effect Estimation With Multi-Task Gaussian Processes

Bridging the gap between internal and external validity is crucial for heterogeneous treatment effect estimation. Randomised controlled trials (RCTs), favoured for their internal validity due to randomisation, often encounter challenges in generalising findings due to strict eligibility criteria. Observational studies, on the other hand, may provide stronger external validity through larger and more representative samples but can suffer from compromised internal validity due to unmeasured confounding. Motivated by these complementary characteristics, we propose a novel Bayesian nonparametric approach, Causal-ICM, leveraging multi-task Gaussian processes to integrate data from both RCTs and observational studies. In particular, we introduce a parameter that controls the degree of borrowing between the datasets and prevents the observational dataset from dominating the estimation. We propose a data-adaptive procedure for choosing the optimal value of the parameter. Causal-ICM outperforms other data fusion methods in point estimation across the covariate support of the observational study and provides principled uncertainty quantification for the estimated treatment effects. We demonstrate the robust performance of Causal-ICM in diverse scenarios through multiple simulation studies and a real-world study.

stat.ME↗

arXiv2023

Learning from data with structured missingness

Missing data are an unavoidable complication in many machine learning tasks. When data are `missing at random' there exist a range of tools and techniques to deal with the issue. However, as machine learning studies become more ambitious, and seek to learn from ever-larger volumes of heterogeneous data, an increasingly encountered problem arises in which missing values exhibit an association or structure, either explicitly or implicitly. Such `structured missingness' raises a range of challenges that have not yet been systematically addressed, and presents a fundamental hindrance to machine learning at scale. Here, we outline the current literature and propose a set of grand challenges in learning from data with structured missingness.

stat.ML↗

arXiv2023

Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the posterior predictive of the Dirichlet process mixture model. In general, direct estimation of the posterior predictive is intractable and so methods typically resort to approximating the posterior distribution as an intermediate step. The recent development of quasi-Bayesian predictive copula updates, however, has made it possible to perform tractable predictive density estimation without the need for posterior approximation. Although these estimators are computationally appealing, they tend to struggle on non-smooth data distributions. This is due to the comparatively restrictive form of the likelihood models from which the proposed copula updates were derived. To address this shortcoming, we consider a Bayesian nonparametric model with an autoregressive likelihood decomposition and a Gaussian process prior. While the predictive update of such a model is typically intractable, we derive a quasi-Bayesian predictive update that achieves state-of-the-art results in small-data regimes.

stat.ML↗

arXiv2022

Neural Score Matching for High-Dimensional Causal Inference

Traditional methods for matching in causal inference are impractical for high-dimensional datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact matching find exponentially fewer matches as the input dimension grows, and propensity score matching may match highly unrelated units together. To overcome this problem, we develop theoretical results which motivate the use of neural networks to obtain non-trivial, multivariate balancing scores of a chosen level of coarseness, in contrast to the classical, scalar propensity score. We leverage these balancing scores to perform matching for high-dimensional causal inference and call this procedure neural score matching. We show that our method is competitive against other matching approaches on semi-synthetic high-dimensional datasets, both in terms of treatment effect estimation and reducing imbalance.

stat.ML↗

arXiv2022

A Predictive Approach to Bayesian Nonparametric Survival Analysis

Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is conjugate with respect to right-censored data. Eliciting these priors, particularly in the presence of covariates, can be challenging and inference typically relies on computationally intensive Markov chain Monte Carlo schemes. In this paper, we build on recent work that recasts Bayesian inference as assigning a predictive distribution on the unseen values of a population conditional on the observed samples, thus avoiding the need to specify a complex prior. We describe a copula-based predictive update which admits a scalable sequential importance sampling algorithm to perform inference that properly accounts for right-censoring. We provide theoretical justification through an extension of Doob's consistency theorem and illustrate the method on a number of simulated and real data sets, including an example with covariates. Our approach enables analysts to perform Bayesian nonparametric inference through only the specification of a predictive distribution.

stat.ME↗

arXiv2021

Bayesian exponential random graph models for populations of networks

The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging study collects one or more brain scans across multiple individuals, each of which can be modelled as a network with nodes corresponding to distinct brain regions and edges corresponding to structural or functional connections between these regions. Most statistical network models, however, were originally proposed to describe a single underlying relational structure, although recent years have seen a drive to extend these models to populations of networks. Here, we propose one such extension: a multilevel framework for populations of networks based on exponential random graph models. By pooling information across the individual networks, this framework provides a principled approach to characterise the relational structure for an entire population. To perform inference, we devise a novel exchange-within-Gibbs MCMC algorithm that generates samples from the doubly-intractable posterior. To illustrate our framework, we use it to assess group-level variations in networks derived from fMRI scans, enabling the inference of age-related differences in the topological structure of the brain's functional connectivity.

stat.ME↗

arXiv2021

Bayesian imputation of COVID-19 positive test counts for nowcasting under reporting lag

Obtaining up to date information on the number of UK COVID-19 regional infections is hampered by the reporting lag in positive test results for people with COVID-19 symptoms. In the UK, for "Pillar 2" swab tests for those showing symptoms, it can take up to five days for results to be collated. We make use of the stability of the under reporting process over time to motivate a statistical temporal model that infers the final total count given the partial count information as it arrives. We adopt a Bayesian approach that provides for subjective priors on parameters and a hierarchical structure for an underlying latent intensity process for the infection counts. This results in a smoothed time-series representation now-casting the expected number of daily counts of positive tests with uncertainty bands that can be used to aid decision making. Inference is performed using sequential Monte Carlo.

stat.AP↗