37 citations · 180 across the 24 of their papers we have counts for
4 papers · 1 filter
Vocabulary Growth Fundamentals: Bernstein Functions and Hausdorff Sequences
Łukasz Dębowski
We survey the theory of vocabulary growth founded in the setting of stochastic processes. In particular, we model the expected number of types through Bernstein functions and Hausd…
From Letters to Words and Back: Invertible Coding of Stationary Measures
Łukasz Dębowski
Motivated by problems of statistical language modeling, we consider probability measures on infinite sequences over two countable alphabets of a different cardinality, such as lett…
Universal Coding and Prediction on Ergodic Martin-Löf Random Points
Łukasz Dębowski, Tomasz Steifer
Suppose that we have a method which estimates the conditional probabilities of some unknown stochastic source and we use it to guess which of the outcomes will happen. We want to m…
Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures
Łukasz Dębowski
We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asympto…