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Register a new userTowards Personalized Modeling of the Female Hormonal Cycle: Experiments with Mechanistic Models and Gaussian Processes
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In this paper, we introduce a novel task for machine learning in healthcare, namely personalized modeling of the female hormonal cycle. The motivation for this work is to model the hormonal cycle and predict its phases in time, both for healthy individuals and for those with disorders of the reproductive system. Because there are individual differences in the menstrual cycle, we are particularly interested in personalized models that can account for individual idiosyncracies, towards identifying phenotypes of menstrual cycles. As a first step, we consider the hormonal cycle as a set of observations through time. We use a previously validated mechanistic model to generate realistic hormonal patterns, and experiment with Gaussian process regression to estimate their values over time. Specifically, we are interested in the feasibility of predicting menstrual cycle phases under varying learning conditions: number of cycles used for training, hormonal measurement noise and sampling rates, and informed vs. agnostic sampling of hormonal measurements. Our results indicate that Gaussian processes can help model the female menstrual cycle. We discuss the implications of our experiments in the context of modeling the female menstrual cycle.
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We present a personalized and reliable prediction model for healthcare, which can provide individually tailored medical services such as diagnosis, disease treatment, and prevention. Our proposed framework targets at making personalized and reliable predictions from time-series data, such as Electronic Health Records (EHR), by modeling two complementary components: i) a shared component that captures global trend across diverse patients and ii) a patient-specific component that models idiosyncratic variability for each patient. To this end, we propose a composite model of a deep neural network to learn complex global trends from the large number of patients, and Gaussian Processes (GP) to probabilistically model individual time-series given relatively small number of visits per patient. We evaluate our model on diverse and heterogeneous tasks from EHR datasets and show practical advantages over standard time-series deep models such as pure Recurrent Neural Network (RNN).
The data association problem is concerned with separating data coming from different generating processes, for example when data come from different data sources, contain significant noise, or exhibit multimodality. We present a fully Bayesian approach to this problem. Our model is capable of simultaneously solving the data association problem and the induced supervised learning problems. Underpinning our approach is the use of Gaussian process priors to encode the structure of both the data and the data associations. We present an efficient learning scheme based on doubly stochastic variational inference and discuss how it can be applied to deep Gaussian process priors.
Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective. This classical approach known as Type-II maximum likelihood (ML-II) yields point estimates of the hyperparameters, and continues to be the default method for training GPs. However, this approach risks underestimating predictive uncertainty and is prone to overfitting especially when there are many hyperparameters. Furthermore, gradient based optimisation makes ML-II point estimates highly susceptible to the presence of local minima. This work presents an alternative learning procedure where the hyperparameters of the kernel function are marginalised using Nested Sampling (NS), a technique that is well suited to sample from complex, multi-modal distributions. We focus on regression tasks with the spectral mixture (SM) class of kernels and find that a principled approach to quantifying model uncertainty leads to substantial gains in predictive performance across a range of synthetic and benchmark data sets. In this context, nested sampling is also found to offer a speed advantage over Hamiltonian Monte Carlo (HMC), widely considered to be the gold-standard in MCMC based inference.
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to a linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e. a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together with fast but accurate posterior inference. We investigate several variations of the convolutional kernel, and apply it to MNIST and CIFAR-10, which have both been known to be challenging for Gaussian processes. We also show how the marginal likelihood can be used to find an optimal weighting between convolutional and RBF kernels to further improve performance. We hope that this illustration of the usefulness of a marginal likelihood will help automate discovering architectures in larger models.
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