Monitoring Short Term Changes of Infectious Diseases in Uganda with Gaussian Processes

A method to monitor infectious diseases based on health records is proposed. Infectious diseases, specially Malaria, are a constant threat for Ugandan public health. The method is applied to health facility records of Malaria in Uganda. The first challenge to overcome is the noise introduced by missing reports of the health facilities. We use Gaussian processes with vector-valued kernels to estimate the missing values in the time series. Later on, for aggregate data at a District level, we use a combination of kernels to decompose the case-counts time series into short and long term components. This method allows not only to remove the effect of specific components, but to study the components of interest with more detail. The short term variations of an infection are divided into four cyclical stages. The progress of an infection across the population can be easily analysed and compared between different Districts. The graphical tool provided can help quick response planning and resources allocation.

[1]  D. Myers.  Matrix formulation of co-kriging , 1982 .

[2]  Ole Winther,et al.  Bayesian Leave-One-Out Cross-Validation Approximations for Gaussian Latent Variable Models , 2014, J. Mach. Learn. Res..

[3]  Marianne Baxter,et al.  Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series , 1999 .

[4]  Paul W. Goldberg,et al.  Regression with Input-dependent Noise: A Gaussian Process Treatment , 1997, NIPS.

[5]  Simo Särkkä,et al.  Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression , 2011, ICANN.

[6]  Aki Vehtari,et al.  A survey of Bayesian predictive methods for model assessment, selection and comparison , 2012 .

[7]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[8]  Charles A. Micchelli,et al.  On Learning Vector-Valued Functions , 2005, Neural Computation.

[9]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[10]  Aki Vehtari,et al.  Expectation propagation for nonstationary heteroscedastic Gaussian process regression , 2014, 2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP).

[11]  G. C. Tiao,et al.  Decomposition of Seasonal Time Series: A Model for the Census X-11 Program , 1976 .

[12]  Zoubin Ghahramani,et al.  Sparse Gaussian Processes using Pseudo-inputs , 2005, NIPS.

[13]  U. Dalrymple,et al.  The effect of malaria control on Plasmodium falciparum in Africa between 2000 and 2015 , 2015, Nature.

[14]  N. Cressie,et al.  Universal cokriging under intrinsic coregionalization , 1994 .

[15]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[16]  Neil D. Lawrence,et al.  Kernels for Vector-Valued Functions: a Review , 2011, Found. Trends Mach. Learn..

[17]  Miguel Lázaro-Gredilla,et al.  Variational Heteroscedastic Gaussian Process Regression , 2011, ICML.

[18]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[19]  Charles A. Micchelli,et al.  Kernels for Multi--task Learning , 2004, NIPS.

[20]  P. Diggle,et al.  Model‐based geostatistics , 2007 .

[21]  Neil D. Lawrence,et al.  Gaussian process models for periodicity detection , 2013, 1303.7090.

[22]  E. Parzen.  An Approach to Time Series Analysis , 1961 .

[23]  S. Hay,et al.  From predicting mosquito habitat to malaria seasons using remotely sensed data: practice, problems and perspectives. , 1998, Parasitology today.

[24]  Peter J. Diggle,et al.  Spatial and spatio-temporal Log-Gaussian Cox processes:extending the geostatistical paradigm , 2013, 1312.6536.

[25]  Michalis K. Titsias,et al.  Variational Learning of Inducing Variables in Sparse Gaussian Processes , 2009, AISTATS.

[26]  E. Parzen.  STATISTICAL INFERENCE ON TIME SERIES BY RKHS METHODS. , 1970 .

[27]  Lorenzo Rosasco,et al.  Multi-output learning via spectral filtering , 2012, Machine Learning.

[28]  Zoubin Ghahramani,et al.  Gaussian Process Volatility Model , 2014, NIPS.