Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data

Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly and instead use a set of informative "representatives" are desirable. The paper investigates this problem for the grouped mixed-effect GP model where each individual response is given by a fixed-effect, taken from one of a set of unknown groups, plus a random individual effect function that captures variations among individuals. Such models have been widely used in previous work but no sparse solutions have been developed. The paper presents the first sparse solution for such problems, showing how the sparse approximation can be obtained by maximizing a variational lower bound on the marginal likelihood, generalizing ideas from single-task Gaussian processes to handle the mixed-effect model as well as grouping. Experiments using artificial and real data validate the approach showing that it can recover the performance of inference with the full sample, that it outperforms baseline methods, and that it outperforms state of the art sparse solutions for other multi-task GP formulations.Comment: Preliminary version appeared in ECML201

A multivariate timeseries modeling approach to severity of illness assessment and forecasting in ICU with sparse, heterogeneous clinical data

The ability to determine patient acuity (or severity of illness) has immediate practical use for clinicians. We evaluate the use of multivariate timeseries modeling with the multi-task Gaussian process (GP) models using noisy, incomplete, sparse, heterogeneous and unevenly-sampled clinical data, including both physiological signals and clinical notes. The learned multi-task GP (MTGP) hyperparameters are then used to assess and forecast patient acuity. Experiments were conducted with two real clinical data sets acquired from ICU patients: firstly, estimating cerebrovascular pressure reactivity, an important indicator of secondary damage for traumatic brain injury patients, by learning the interactions between intracranial pressure and mean arterial blood pressure signals, and secondly, mortality prediction using clinical progress notes. In both cases, MTGPs provided improved results: an MTGP model provided better results than single-task GP models for signal interpolation and forecasting (0.91 vs 0.69 RMSE), and the use of MTGP hyperparameters obtained improved results when used as additional classification features (0.812 vs 0.788 AUC).Intel Science and Technology Center for Big DataNational Institutes of Health. (U.S.). National Library of Medicine (Biomedical Informatics Research Training Grant NIH/NLM 2T15 LM007092-22)National Institute of Biomedical Imaging and Bioengineering (U.S.) (R01 Grant EB001659)Singapore. Agency for Science, Technology and Research (Graduate Scholarship

Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes

We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of longitudinal signals and a Cox model to map time-to-event data with longitudinal data modeled through the MGCP. Taking advantage of the unique structure imposed by convolved processes, we provide a variational inference framework to simultaneously estimate parameters in the joint MGCP-Cox model. This significantly reduces computational complexity and safeguards against model overfitting. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the art approaches built on two-stage inference and strong parametric assumptions