arXiv subjects

Laura Battaglia

Publications and source records attributed to Laura Battaglia.

6 recordsLinked to original sources

arXiv2026

Variational predictive resampling

Bayesian inference provides principled uncertainty quantification, but accurate posterior sampling with MCMC can be computationally prohibitive for modern applications. Variational inference (VI) offers a scalable alternative and often yields accurate predictive distributions, but cheap variational families such as mean-field (MF) can produce over-concentrated approximations that miss posterior dependence. We propose variational predictive resampling (VPR), a scalable posterior sampling method that exploits VI's predictive strength within a predictive-resampling framework to better approximate the Bayesian posterior. Given a prior-likelihood pair, VPR repeatedly imputes future observations from the current variational predictive, updates the variational approximation after each imputation, and records the parameter value implied by the completed sample. We establish conditions under which the law of the parameter returned by VPR is well defined and show that its finite-horizon approximation converges to this limit. In a tractable Gaussian location model, we show that VPR with MF variational predictives converges to the exact Bayesian posterior, whereas the optimal MF-VI approximation retains a non-vanishing asymptotic gap. Experiments on linear regression, logistic regression, and hierarchical linear mixed-effects models demonstrate that VPR substantially improves posterior uncertainty quantification and recovers posterior dependence missed by MF-VI, while remaining computationally competitive with, and often more efficient than, MCMC.

stat.ME↗

arXiv2025

Amortising over hyperparameters in Generalised Bayesian Inference

In Bayesian inference prior hyperparameters are chosen subjectively or estimated using empirical Bayes methods. Generalised Bayesian Inference (GBI) also has a learning rate hyperparameter. This is compounded in Semi-Modular Inference (SMI), a GBI framework for multiple datasets (multi-modular problems). As part of any GBI workflow it is necessary to check sensitivity to the choice of hyperparameters, but running MCMC or fitting a variational approximation at each of the hyperparameter values of interest is impractical. Simulation-based Inference has been used by previous authors to amortise over data and hyperparameters, fitting a posterior approximation targeting the forward-KL divergence. However, for GBI and SMI posteriors, it is not possible to amortise over data, as there is no generative model. Working with a variational family parameterised by a conditional normalising flow, we give a direct variational approximation for GBI and SMI posteriors, targeting the reverse-KL divergence, and amortised over prior and loss hyperparameters at fixed data. This can be sampled efficiently at different hyperparameter values without refitting, and supports efficient robustness checks and hyperparameter selection. We show that there exist amortised conditional normalising-flow architectures which are universal approximators. We illustrate our methods with an epidemiological example well known in SMI work and then give the motivating application, a spatial location-prediction task for linguistic-profile data. SMI gives improved prediction with hyperparameters chosen using our amortised framework. The code is available online.

stat.CO↗

arXiv2025

Inference for Regression with Variables Generated by AI or Machine Learning

Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating AI/ML-generated variables as "data" leads to biased estimates and invalid inference. To restore valid inference, we propose two methods: (1) an explicit bias correction with bias-corrected confidence intervals, and (2) joint estimation of the regression parameters and latent variables. We illustrate these ideas through applications involving label imputation, dimensionality reduction, and index construction via classification and aggregation.

econ.EM↗

arXiv2024

Marginal Causal Flows for Validation and Inference

Investigating the marginal causal effect of an intervention on an outcome from complex data remains challenging due to the inflexibility of employed models and the lack of complexity in causal benchmark datasets, which often fail to reproduce intricate real-world data patterns. In this paper we introduce Frugal Flows, a novel likelihood-based machine learning model that uses normalising flows to flexibly learn the data-generating process, while also directly inferring the marginal causal quantities from observational data. We propose that these models are exceptionally well suited for generating synthetic data to validate causal methods. They can create synthetic datasets that closely resemble the empirical dataset, while automatically and exactly satisfying a user-defined average treatment effect. To our knowledge, Frugal Flows are the first generative model to both learn flexible data representations and also exactly parameterise quantities such as the average treatment effect and the degree of unobserved confounding. We demonstrate the above with experiments on both simulated and real-world datasets.

cs.LG↗

arXiv2024

Hamiltonian Monte Carlo for Regression with High-Dimensional Categorical Data

Latent variable models are increasingly used in economics for high-dimensional categorical data like text and surveys. We demonstrate the effectiveness of Hamiltonian Monte Carlo (HMC) with parallelized automatic differentiation for analyzing such data in a computationally efficient and methodologically sound manner. Our new model, Supervised Topic Model with Covariates, shows that carefully modeling this type of data can have significant implications on conclusions compared to a simpler, frequently used, yet methodologically problematic, two-step approach. A simulation study and revisiting Bandiera et al. (2020)'s study of executive time use demonstrate these results. The approach accommodates thousands of parameters and doesn't require custom algorithms specific to each model, making it accessible for applied researchers

econ.EM↗

arXiv2023

Graphical model inference with external network data

We consider two applications where we study how dependence structure between many variables is linked to external network data. We first study the interplay between social media connectedness and the co-evolution of the COVID-19 pandemic across USA counties. We next study study how the dependence between stock market returns across firms relates to similarities in economic and policy indicators from text regulatory filings. Both applications are modelled via Gaussian graphical models where one has external network data. We develop spike-and-slab and graphical LASSO frameworks to integrate the network data, both facilitating the interpretation of the graphical model and improving inference. The goal is to detect when the network data relates to the graphical model and, if so, explain how. We found that counties strongly connected on Facebook are more likely to have similar COVID-19 evolution (positive partial correlations), accounting for various factors driving the mean. We also found that the association in stock market returns depends in a stronger fashion on economic than on policy indicators. The examples show that data integration can improve interpretation, statistical accuracy, and out-of-sample prediction, in some instances using significantly sparser graphical models.

stat.AP↗