Applied Mathematics and Statistics
- Statistics: Technological advances have enabled collection and processing of mountainous data troves. A great amount of effort, creativity and experimentation has gone into the development of algorithms to extract knowledge from large data sets. Some of these algorithms, such as deep learning, yield impressive results in practice. One of the main goals of statistics is to understand the performance limits of these algorithms, and enhance our understanding of why these algorithms perform so well in practice. Statistics for large data sets (also known as high dimensional statistics) utilizes deep mathematical ideas such as concentration of measure theory.
- Information Theory: Broadly speaking, information theory is the science of transmission, processing, extraction, and utilization of information. There are deep connections between information theory and statistics, and progress in one area influences progress in the other.
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