Nonparametric Learning in High Dimensions.pdf (4.61 MB)
Nonparametric Learning in High Dimensions
thesis
posted on 2010-12-01, 00:00 authored by Han LiuThis thesis develops flexible and principled nonparametric learning algorithms
to explore, understand, and predict high dimensional and complex
datasets. Such data appear frequently in modern scientific domains and lead
to numerous important applications. For example, exploring high dimensional
functional magnetic resonance imaging data helps us to better understand
brain functionalities; inferring large-scale gene regulatory network is crucial
for new drug design and development; detecting anomalies in high dimensional
transaction databases is vital for corporate and government security.
Our main results include a rigorous theoretical framework and efficient nonparametric
learning algorithms that exploit hidden structures to overcome the
curse of dimensionality when analyzing massive high dimensional datasets.
These algorithms have strong theoretical guarantees and provide high dimensional
nonparametric recipes for many important learning tasks, ranging from
unsupervised exploratory data analysis to supervised predictive modeling. In
this thesis, we address three aspects:
1 Understanding the statistical theories of high dimensional nonparametric
inference, including risk, estimation, and model selection consistency;
2 Designing new methods for different data-analysis tasks, including
regression, classification, density estimation, graphical model learning,
multi-task learning, spatial-temporal adaptive learning;
3 Demonstrating the usefulness of these methods in scientific applications,
including functional genomics, cognitive neuroscience, and meteorology.
In the last part of this thesis, we also present the future vision of high
dimensional and large-scale nonparametric inference.
History
Date
2010-12-01Degree Type
- Dissertation
Department
- Machine Learning
Degree Name
- Doctor of Philosophy (PhD)