arXiv subjects

Chris U. Carmona

Publications and source records attributed to Chris U. Carmona.

6 recordsLinked to original sources

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

Simultaneous Reconstruction of Spatial Frequency Fields and Sample Locations via Bayesian Semi-Modular Inference

Traditional methods for spatial inference estimate smooth interpolating fields based on features measured at well-located points. When the spatial locations of some observations are missing, joint inference of the fields and locations is possible as the fields inform the locations and vice versa. If the number of missing locations is large, conventional Bayesian Inference fails if the generative model for the data is even slightly mis-specified, due to feedback between estimated fields and the imputed locations. Semi-Modular Inference (SMI) offers a solution by controlling the feedback between different modular components of the joint model using a hyper-parameter called the influence parameter. Our work is motivated by linguistic studies on a large corpus of late-medieval English textual dialects. We simultaneously learn dialect fields using dialect features observed in ``anchor texts'' with known location and estimate the location of origin for ``floating'' textual dialects of unknown origin. The optimal influence parameter minimises a loss measuring the accuracy of held-out anchor data. We compute a (flow-based) variational approximation to the SMI posterior for our model. This allows efficient computation of the optimal influence. MCMC-based approaches, feasible on small subsets of the data, are used to check the variational approximation.

stat.AP↗

arXiv2022

Scalable Semi-Modular Inference with Variational Meta-Posteriors

The Cut posterior and related Semi-Modular Inference are Generalised Bayes methods for Modular Bayesian evidence combination. Analysis is broken up over modular sub-models of the joint posterior distribution. Model-misspecification in multi-modular models can be hard to fix by model elaboration alone and the Cut posterior and SMI offer a way round this. Information entering the analysis from misspecified modules is controlled by an influence parameter $η$ related to the learning rate. This paper contains two substantial new methods. First, we give variational methods for approximating the Cut and SMI posteriors which are adapted to the inferential goals of evidence combination. We parameterise a family of variational posteriors using a Normalising Flow for accurate approximation and end-to-end training. Secondly, we show that analysis of models with multiple cuts is feasible using a new Variational Meta-Posterior. This approximates a family of SMI posteriors indexed by $η$ using a single set of variational parameters.

stat.ML↗

arXiv2022

Valid belief updates for prequentially additive loss functions arising in Semi-Modular Inference

Model-based Bayesian evidence combination leads to models with multiple parameteric modules. In this setting the effects of model misspecification in one of the modules may in some cases be ameliorated by cutting the flow of information from the misspecified module. Semi-Modular Inference (SMI) is a framework allowing partial cuts which modulate but do not completely cut the flow of information between modules. We show that SMI is part of a family of inference procedures which implement partial cuts. It has been shown that additive losses determine an optimal, valid and order-coherent belief update. The losses which arise in Cut models and SMI are not additive. However, like the prequential score function, they have a kind of prequential additivity which we define. We show that prequential additivity is sufficient to determine the optimal valid and order-coherent belief update and that this belief update coincides with the belief update in each of our SMI schemes.

stat.ME↗

arXiv2021

Neural Contextual Anomaly Detection for Time Series

We introduce Neural Contextual Anomaly Detection (NCAD), a framework for anomaly detection on time series that scales seamlessly from the unsupervised to supervised setting, and is applicable to both univariate and multivariate time series. This is achieved by effectively combining recent developments in representation learning for multivariate time series, with techniques for deep anomaly detection originally developed for computer vision that we tailor to the time series setting. Our window-based approach facilitates learning the boundary between normal and anomalous classes by injecting generic synthetic anomalies into the available data. Moreover, our method can effectively take advantage of all the available information, be it as domain knowledge, or as training labels in the semi-supervised setting. We demonstrate empirically on standard benchmark datasets that our approach obtains a state-of-the-art performance in these settings.

cs.LG↗

arXiv2020

Semi-Modular Inference: enhanced learning in multi-modular models by tempering the influence of components

Bayesian statistical inference loses predictive optimality when generative models are misspecified. Working within an existing coherent loss-based generalisation of Bayesian inference, we show existing Modular/Cut-model inference is coherent, and write down a new family of Semi-Modular Inference (SMI) schemes, indexed by an influence parameter, with Bayesian inference and Cut-models as special cases. We give a meta-learning criterion and estimation procedure to choose the inference scheme. This returns Bayesian inference when there is no misspecification. The framework applies naturally to Multi-modular models. Cut-model inference allows directed information flow from well-specified modules to misspecified modules, but not vice versa. An existing alternative power posterior method gives tunable but undirected control of information flow, improving prediction in some settings. In contrast, SMI allows tunable and directed information flow between modules. We illustrate our methods on two standard test cases from the literature and a motivating archaeological data set.

stat.ME↗