29.05.2018

Latent variable modelling

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In this project we develop methods suitable for ecological and signal processing applications. The main focus is in latent variable modelling. In ecology, latent variable models can be used to specify joint models for abundances across many taxa. In signal processing applications, for example in brain imaging, we use latent variable models to perform blind source separation.


Main Researchers:

Some Collaborators

Professor David Warton (University of New South Wales, Sydney), PhD Francis Hui (Australian National University, Canberra), Professor (Emeritus) Antti Penttinen, Professor (Emeritus) Hannu Oja, Joni Virta, Markus Matilainen (University of Turku), A.Prof. Klaus Nordhausen (Vienna University of Technology), Jari Miettinen (Aalto University).

Research

Generalized linear latent variable models for joint modelling in ecology

(Research Team: S. Taskinen, J. Niku)

In many ecological studies, counts or biomass of interacting species are collected from several sites. Such data are often very sparse, high-dimensional and include highly correlated responses, and the main aim of the statistical analysis is to understand relationships among such multiple, correlated responses. Recent studies have shown that generalized linear latent variable models can be easily used to analyse data common in ecological studies. By extending the standard generalized linear modelling framework to include latent variables, we can account for any covariation between species not accounted for by the predictors, species interactions and correlations driven by missing covariates. As usual, a model-based approach gives us tools for diagnostics, model selection and statistical inference. Computationally efficient algorithms for fitting generalized linear latent variable models are proposed.

Publications

  • Niku, J., Warton, D.I., Hui, F.K,C and Taskinen, S. (2017), "Generalized linear latent variable models for multivariate count and biomass data in ecology", Journal of Agricultural, Biological, and Environmental Statistics, 22, 498-522.
  • Hui, F.K.C., Warton, D.I., Ormerod, J., Haapaniemi, V. and Taskinen, S. (2017), "Variational approximations for generalized linear latent variable models", Journal of Computational and Graphical Statistics, 26 , 35-43.
  • Warton, D.I., Blanchet, F.G., O'Hara, R.B., Ovaskainen, O., Taskinen, S., Walker, S.C., and Hui, F.K.C. (2015). "So many variables: Joint modeling in community ecology", Trends in Ecology and Evolution, 30, 766 - 779, DOI: 10.1016/j.tree.2015.09.007
  • Hui, F.K.C.,Taskinen, S., Pledger, S., Foster, S.D. and Warton, D.I. (2015), "Model-based approaches to unconstrained ordination", Methods in Ecology and Evolution, 6, 399-411.

Blind source separation

(Research Team: S. Taskinen)

Blind source separation (BSS) is a signal processing tool, which is widely used in various fields. Examples include biomedical signal separation, brain imaging and economic time series applications. In BSS, one assumes that the observed data is a linear mixture of p latent variables. The aim is then to find an estimate for an unmixing matrix, which transforms the observed data back to unknown latent variables.Blind source separation has its roots in the mid-1980s and in the signal processing community. Since then, a large amount of new algorithms have been proposed to solve the BSS problem. However, the study on the statistical properties of the methods has been insufficient. In this project we propose new methods for BSS estimation as well as keep studying the statistical properties of well established methods. Rigorous analysis of the statistical properties allow us to make comparisons between different methods, and also choose the best method for the problem at hand. Results can also be applied to different inference procedures, including hypothesis testing and model selection.

Publications

  • Miettinen, J., Nordhausen, K. and Taskinen, S. (2017), "Blind source separation based on joint diagonalization in R: The packages JADE and BSSasymp", Journal of Statistical Software, 76(1), 1-31.
  • Miettinen, J., Nordhausen, K., Oja, H., Taskinen, S. and Virta, J. (2017), "The squared symmetric FastICA estimator", Signal Processing, 131, 402-411.
  • Virta, J., Taskinen, S. and Nordhausen, K. (2016). "Applying fully tensorial ICA to fMRI data". In the proceedings of 2016 IEEE Signal Processing in Medicine and Biology Symposium (SPMB). DOI: 10.1109/SPMB.2016.7846858
  • Matilainen, M., Miettinen, J., Nordhausen, K., Oja, H. and Taskinen, S. (2015). "On Independent component analysis with stochastic volatility models", Austrian Journal of Statistics, 46, 57-66.
  • Miettinen, J., Illner, K., Nordhausen, K., Oja, H., Taskinen, S. and Theis, F.J. (2015). "Separation of uncorrelated stationary time series using autocovariance matrices". Journal of Time Series Analysis, 37, 337-354.
  • Miettinen, J., Taskinen, S., Nordhausen, K. and Oja, H. (2015), "Fourth moments and independent component analysis", Statistical Science, 30, 372-390.
  • Miettinen, J., Nordhausen, K., Oja, H. and Taskinen, S. (2014), "Deflation-based separation of uncorrelated stationary time series.", Journal of Multivariate Analysis, 123, 214-227.
  • Miettinen, J., Nordhausen, K. Oja, H. and Taskinen, S. (2014), "Deflation-based FastICA with adaptive choices of contrast functions", IEEE Transactions on Signal Processing, 62, 5716-5724.