Author name cluster

Seth R. Flaxman

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5 papers

2 author rows

UAI Conference 2021 Conference Paper

Gaussian process nowcasting: application to COVID-19 mortality reporting

Iwona Hawryluk
Henrique Hoeltgebaum
Swapnil Mishra
Xenia Miscouridou
Ricardo P. Schnekenberg
Charles Whittaker
Michaela A. C. Vollmer
Seth R. Flaxman

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the changing auto-correlation structure present in the reporting time-delay surface. This approach also yields robust estimates of uncertainty for the estimated nowcasted numbers of deaths. We test assumptions in model specification such as the choice of kernel or hyper priors, and evaluate model performance on a challenging real dataset from Brazil. Our experiments show that Gaussian process nowcasting performs favourably against both comparable methods, and against a small sample of expert human predictions. Our approach has substantial practical utility in disease modelling — by applying our approach to COVID-19 mortality data from Brazil, where reporting delays are large, we can make informative predictions on important epidemiological quantities such as the current effective reproduction number.

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UAI Conference 2017 Conference Paper

Feature-to-Feature Regression for a Two-Step Conditional Independence Test

Qinyi Zhang 0002
Sarah Filippi
Seth R. Flaxman
Dino Sejdinovic

The algorithms for causal discovery and more broadly for learning the structure of graphical models require well calibrated and consistent conditional independence (CI) tests. We revisit the CI tests which are based on two-step procedures and involve regression with subsequent (unconditional) independence test (RESIT) on regression residuals and investigate the assumptions under which these tests operate. In particular, we demonstrate that when going beyond simple functional relationships with additive noise, such tests can lead to an inflated number of false discoveries. We study the relationship of these tests with those based on dependence measures using reproducing kernel Hilbert spaces (RKHS) and propose an extension of RESIT which uses RKHS-valued regression. The resulting test inherits the simple two-step testing procedure of RESIT, while giving correct Type I control and competitive power. When used as a component of the PC algorithm, the proposed test is more robust to the case where hidden variables induce a switching behaviour in the associations present in the data.

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UAI Conference 2016 Conference Paper

Bayesian Learning of Kernel Embeddings

Seth R. Flaxman
Dino Sejdinovic
John P. Cunningham
Sarah Filippi

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of kernel mean embeddings of probability measures. For characteristic kernels, which include most commonly used ones, the kernel mean embedding uniquely determines its probability measure, so it can be used to design a powerful statistical testing framework, which includes nonparametric two-sample and independence tests. In practice, however, the performance of these tests can be very sensitive to the choice of kernel and its lengthscale parameters. To address this central issue, we propose a new probabilistic model for kernel mean embeddings, the Bayesian Kernel Embedding model, combining a Gaussian process prior over the Reproducing Kernel Hilbert Space containing the mean embedding with a conjugate likelihood function, thus yielding a closed form posterior over the mean embedding. The posterior mean of our model is closely related to recently proposed shrinkage estimators for kernel mean embeddings, while the posterior uncertainty is a new, interesting feature with various possible applications. Critically for the purposes of kernel learning, our model gives a simple, closed form marginal pseudolikelihood of the observed data given the kernel hyperparameters. This marginal pseudolikelihood can either be optimized to inform the hyperparameter choice or fully Bayesian inference can be used.

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ICML Conference 2015 Conference Paper

Fast Kronecker Inference in Gaussian Processes with non-Gaussian Likelihoods

Seth R. Flaxman
Andrew Gordon Wilson
Daniel B. Neill
Hannes Nickisch
Alexander J. Smola

Gaussian processes (GPs) are a flexible class of methods with state of the art performance on spatial statistics applications. However, GPs require O(n^3) computations and O(n^2) storage, and popular GP kernels are typically limited to smoothing and interpolation. To address these difficulties, Kronecker methods have been used to exploit structure in the GP covariance matrix for scalability, while allowing for expressive kernel learning (Wilson et al. , 2014). However, fast Kronecker methods have been confined to Gaussian likelihoods. We propose new scalable Kronecker methods for Gaussian processes with non-Gaussian likelihoods, using a Laplace approximation which involves linear conjugate gradients for inference, and a lower bound on the GP marginal likelihood for kernel learning. Our approach has near linear scaling, requiring O(D n^(D+1)/D) operations and O(D n^2/D) storage, for n training data-points on a dense D > 1 dimensional grid. Moreover, we introduce a log Gaussian Cox process, with highly expressive kernels, for modelling spatiotemporal count processes, and apply it to a point pattern (n = 233, 088) of a decade of crime events in Chicago. Using our model, we discover spatially varying multiscale seasonal trends and produce highly accurate long-range local area forecasts.

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TIST Journal 2015 Journal Article

Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference

Seth R. Flaxman
Daniel B. Neill
Alexander J. Smola

In applied fields, practitioners hoping to apply causal structure learning or causal orientation algorithms face an important question: which independence test is appropriate for my data? In the case of real-valued iid data, linear dependencies, and Gaussian error terms, partial correlation is sufficient. But once any of these assumptions is modified, the situation becomes more complex. Kernel-based tests of independence have gained popularity to deal with nonlinear dependencies in recent years, but testing for conditional independence remains a challenging problem. We highlight the important issue of non-iid observations: when data are observed in space, time, or on a network, “nearby” observations are likely to be similar. This fact biases estimates of dependence between variables. Inspired by the success of Gaussian process regression for handling non-iid observations in a wide variety of areas and by the usefulness of the Hilbert-Schmidt Independence Criterion (HSIC), a kernel-based independence test, we propose a simple framework to address all of these issues: first, use Gaussian process regression to control for certain variables and to obtain residuals. Second, use HSIC to test for independence. We illustrate this on two classic datasets, one spatial, the other temporal, that are usually treated as iid. We show how properly accounting for spatial and temporal variation can lead to more reasonable causal graphs. We also show how highly structured data, like images and text, can be used in a causal inference framework using a novel structured input/output Gaussian process formulation. We demonstrate this idea on a dataset of translated sentences, trying to predict the source language.

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