1. Discovery of Hidden Structure in High-Dimensional Data
Aapo Hyvärinen
Senior Research Scientist
University of Helsinki
Helsinki University of Technology

2. Discovery of Hidden Structure in High-Dimensional Data
Science produces enormous data sets, often with hidden structure
This theme: Typically continuous data and/or probabilistic models
Tasks
Parsimonious models
Decomposition into dependent components
Non-Gaussian Bayesian networks
Spatiotemporal models
Applications
Neuroinformatics: imaging data analysis, functional modelling
Bioinformatics: Genome structure, metabolic models, gene regulation
Telecom, linguistics, forestry, ecology, atmospheric data, etc.
Main teams Hyvärinen & Mannila

3. Highlight/Background: Independent Component Analysis
Linear decomposition of multivariate data
Finds hidden directions (green), in contrast to classic PCA (red)
Application in blind source separation, e.g. in brain imaging data
FastICA: the most popular ICA algorithm (Hyvärinen. IEEE Trans. NN, 1999)
Standard reference book on the theory: Independent Component Analysis. Hyvärinen, Karhunen, Oja. Wiley, 2001.
Mixing process

4. Task: Decomposition into Dependent Components
Components are not independent in general
Extend to dependent components (Hyvärinen team)
Grouping and visual ordering (Hyvärinen et al. Neural Comput & 2001)
Separation with some dependency (Hyvärinen and Hurri. Signal Proc., 2004)
Future: More general dependency structures
Related to nonlinear decompositions
Extend to binary data (teams Mannila, Toivonen)
Analyze stability of components (Himberg et al, NeuroImage, 2004)

5. Highlight and Task: Non-Gaussian Bayesian Networks
Non-gaussianity enables learning network structure and weights in basic linear DAG case (Shimizu, Hoyer, Hyvärinen, Kerminen. J. Mach. Learn. Res., 2006)
Another example of the power of non-gaussianity
Enables inference on the direction of causality
Currently extending to, e.g.:
hidden confounding variables (Hyvärinen team)
nonlinearities (Hyvärinen team)
(partly) binary data (Mannila & Hyvärinen teams)
Applications to gene networks, brain imaging data to be explored

6. Future Vision
Probabilistic methods with emphasis on algorithmic aspects
Interface between computer science and statistics
Combine expertise on algorithms and multivariate statistics
Discovery of hidden components, clusters, or connections
Continuous data: nongaussianity a nonclassic yet central tool
Discrete data: e.g., covering approaches
Applications in many different fields of science
Our special competence in neuro- and bioinformatics