At the core of any theory of inference or prediction is the assumption that the world is “simple” or “uniform” in a certain way that makes induction possible. Statistical learning theory is a mathematical theory that makes these concepts precise and thus investigates what we can hope to learn about the future from the past.
The centerpiece of this theory is the uniform law of large numbers, a theorem that provides the necessary and sufficient conditions under which a theory's ability to fit past data is a reliable indicator of its ability to accurately predict future data. Amazingly, this theorem can be proven without making any assumptions about the underlying mechanism that generates the data.
This course will introduce some of the core concepts and methods of statistical learning theory and provide a deep understanding of the proof of the uniform law of large numbers.
The centerpiece of this theory is the uniform law of large numbers, a theorem that provides the necessary and sufficient conditions under which a theory's ability to fit past data is a reliable indicator of its ability to accurately predict future data. Amazingly, this theorem can be proven without making any assumptions about the underlying mechanism that generates the data.
This course will introduce some of the core concepts and methods of statistical learning theory and provide a deep understanding of the proof of the uniform law of large numbers.
The course was held in January 2015 by Mathias Winther Madsen at the ILLC and is now over. For more information, contact [email protected].