Abstract
The minimum description length principle (MDL principle) is a data-compression-based methodology for optimal estimation and prediction from data. It gives a unifying strategy for designing machine learning algorithms and plays an important role in knowledge discovery from big data. Conventionally, the MDL principle has been extensively studied under the assumption that the information sources are stationary and are represented as regular probabilistic models. This paper first gives a survey of the fundamental concept of the MDL principle. Then, it introduces recent advances in MDL research for the situation where the information sources are nonstationary, irregular, and nonprobabilistic. It also shows trends in the nonasymptotic analysis of the MDL and refers to applications to data mining.
