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Geoff K. Nicholls

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Computation Machine Learning Applications Biological Physics Methodology Neurons and Cognition

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preprint2026arXiv

A Differentiable Bayesian Relaxation for Latent Partial-Order Inference

Many ranking and agent trace datasets are recorded as linear orders even though their latent structure is only partially ordered. This is especially common in agent and workflow traces, where observed order may reflect arbitrary linearization rather than true prerequisites. We introduce a differentiable relaxation for latent partial-order inference from such traces. Starting from a hard frontier-constrained model of noisy linear extensions, we replace discontinuous product-order precedence and binary frontier feasibility with smooth surrogates, yielding a continuous posterior that preserves closure-level partial-order semantics and supports gradient-based MCMC and variational inference. We prove soft transitivity, sharp-limit frontier recovery, and convergence to the hard likelihood. Experiments on synthetic data, records of social dominance relations, and cloud-agent traces show close posterior fidelity to hard MCMC on small instances and improved runtime--accuracy trade-offs on larger problems.

preprint2022arXiv

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.

preprint2022arXiv

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.

preprint2020arXiv

Distortion estimates for approximate Bayesian inference

Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of question by looking at performance averaged over data space, or otherwise lack diagnostic detail. However, if the approximation is bad for most data, but good at the observed data, then we may discard a useful approximation. We give graphical diagnostics for posterior approximation at the observed data. We estimate a "distortion map" that acts on univariate marginals of the approximate posterior to move them closer to the exact posterior, without recourse to the exact posterior.

preprint2020arXiv

Large Scale Tensor Regression using Kernels and Variational Inference

We outline an inherent weakness of tensor factorization models when latent factors are expressed as a function of side information and propose a novel method to mitigate this weakness. We coin our method \textit{Kernel Fried Tensor}(KFT) and present it as a large scale forecasting tool for high dimensional data. Our results show superior performance against \textit{LightGBM} and \textit{Field Aware Factorization Machines}(FFM), two algorithms with proven track records widely used in industrial forecasting. We also develop a variational inference framework for KFT and associate our forecasts with calibrated uncertainty estimates on three large scale datasets. Furthermore, KFT is empirically shown to be robust against uninformative side information in terms of constants and Gaussian noise.

preprint2013arXiv

A Cell-Level Mechanism of Contrast Gain Control

The gain of neurons' responses in the auditory cortex is sensitive to contrast changes in the stimulus within a spectrotemporal range similar to their receptive fields, which can be interpreted to represent the tuning of the input to a neuron. This indicates a local mechanism of contrast gain control, which we explore with a minimal mechanistic model here. Gain control through noisy input has been observed in vitro and in a range of computational models. We investigate the behaviour of the simplest of such models to showcase gain control, a stochastic leaky integrate-and-fire (sLIF) neuron, which exhibits gain control through divisive normalisation of the input both with and without accompanying subtractive shift of the input-response curve, depending on whether input noise is proportional to or independent of its mean. To get a more direct understanding of how the input statistics change the response, we construct an analytic approximation to the firing rate of a sLIF neuron constituted of the expression for the deterministic case and a weighted average over the derived approximate steady-state distribution of conductance due to poissonian synaptic inputs. This analytic approximation qualitatively produces the same behaviour as simulations and could be extended by spectrotemporally tuned inputs to give a simple, physiological and local mechanism of contrast gain control in auditory sensing, building on recent experimental work that has hitherto only been described by phenomenological models. By comparing our weighted average firing rate curve with the commonly used sigmoidal input-response function, we demonstrate a nearly linear relationship between both the horizontal shift (or stimulus inflection point) and the inverse gain of the sigmoid and statistics derived from the sLIF model parameters, thus providing a structural constraint on the sigmoid parameter choice.

preprint2012arXiv

Coupled MCMC with a randomized acceptance probability

We consider Metropolis Hastings MCMC in cases where the log of the ratio of target distributions is replaced by an estimator. The estimator is based on m samples from an independent online Monte Carlo simulation. Under some conditions on the distribution of the estimator the process resembles Metropolis Hastings MCMC with a randomized transition kernel. When this is the case there is a correction to the estimated acceptance probability which ensures that the target distribution remains the equilibrium distribution. The simplest versions of the Penalty Method of Ceperley and Dewing (1999), the Universal Algorithm of Ball et al. (2003) and the Single Variable Exchange algorithm of Murray et al. (2006) are special cases. In many applications of interest the correction terms cannot be computed. We consider approximate versions of the algorithms. We show that on average O(m) of the samples realized by a simulation approximating a randomized chain of length n are exactly the same as those of a coupled (exact) randomized chain. Approximation biases Monte Carlo estimates with terms O(1/m) or smaller. This should be compared to the Monte Carlo error which is O(1/sqrt(n)).

preprint2010arXiv

On building and fitting a spatio-temporal change-point model for settlement and growth at Bourewa, Fiji Islands

The Bourewa beach site on the Rove Peninsula of Viti Levu is the earliest known human settlement in the Fiji Islands. How did the settlement at Bourewa develop in space and time? We have radiocarbon dates on sixty specimens, found in association with evidence for human presence, taken from pits across the site. Owing to the lack of diagnostic stratigraphy, there is no direct archaeological evidence for distinct phases of occupation through the period of interest. We give a spatio-temporal analysis of settlement at Bourewa in which the deposition rate for dated specimens plays an important role. Spatio-temporal mapping of radiocarbon date intensity is confounded by uneven post-depositional thinning. We assume that the confounding processes act in such a way that the absence of dates remains informative of zero rate for the original deposition process. We model and fit the onset-field, that is, we estimate for each location across the site the time at which deposition of datable specimens began. The temporal process generating our spatial onset-field is a model of the original settlement dynamics.