3-Year PhD position in Saint-Etienne: Probabilistic study of instantiated gaussian processes and application to spatio-temporal data.
Context: The thesis will take place in the Saint-Etienne part of Camille Jordan Institute. The research will be undertaken in the context of an interdisciplinary project involving also Hubert Curien Laboratory from the University Jean Monnet of St Etienne. The consortium has scientific expertise on probability and statistics, information and image processing, and machine learning, providing a stimulating scientific environment for this thesis.
Gaussian processes are non-linear models of continuous random processes which are widely used to describe numerical data as sounds, images, videos, etc. (see for e.g. [W08,Z16]).
A Gaussian process is defined mainly by its expectation function and its covariance function (the kernel).
The description of the kernel using parametric functions and the estimation of these parameters form the focus of many recent works [L05,D16].
In the context of image sequences (knowing that our study is intended to address other types of data), the main objective is no longer to describe a Gaussian process but a set of Gaussian processes that can possess instances (Different temporal or spatial supports), with the aim to analyse videos with dynamic textures (lights, waves, clouds, fields of wheat ...) taken from different angles for example.
The main objective of the thesis is to provide a precise mathematical framework for these instanciated Gaussian processes in order to be able to estimate the different parameters (instances, mathematical expectations and kernels' parameters).
First, the PhD student will be intended to make a state-of-the-art about the different kernels and their properties, mainly their stationarity in time and space in order to propose new kernels. The next step is to develop robust parameter estimation methods and to work on the automatic selection of the kernels. Then, the formalism of non-stationary and instanciated Gaussian processes will be developed, together with their numerical simulations. The last step concerns the mixture of instanciated Gaussian processes and their application to real data like videos.
We are looking for a motivated student holding a Master degree (on the 1st of September 2015) in the field of applied mathematics (probability, data analysis, estimation and optimization, ...) or "computer science" (or "computer vision") with strong skills in applied mathematics. A good background in software development (algorithmic, Matlab/Octave/Scilab or Python, ...) is expected. Knowledges in image processing and machine learning would also be appreciated.
Net salary: around 1400 euros without teaching activities and around 1650 euros with teaching activities (64 hours per year).
Your application should include the following documents:
[D16] N. Durrande1, J. Hensman, M. Rattray, N. D. Lawrence, “Detecting periodicities with Gaussian processes.” PeerJ Computer Science 2:e50 https://doi.org/10.7717/peerj-cs.50.
[L05] Neil Lawrence, “Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models.” Journal of Machine Learning Research 6 (2005) 1783–1816.
[W08] Jack M. Wang, David J. Fleet and Aaron Hertzmann, “Gaussian Process Dynamical Models for Human Motion.” IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 30, no. 2, Feb. 2008.
[Z16] Ziqi Zhu, Xinge You, Shujian Yu, Jixin Zou and Haiquan Zhao, “Dynamic texture modeling and synthesis using multi-kernel Gaussian process dynamic model.” Signal Processing, Vol. 124, July 2016, Pages 63–71. Big Data Meets Multimedia Analytics — Containing a selection of papers from the 21st International Conference on Multimedia Modelling (MMM2015).
(c) GdR 720 ISIS - CNRS - 2011-2015.