From Gauss to Kolmogorov: Localized measures of complexity for ellipses
نویسندگان
چکیده
منابع مشابه
From Gauss to Kolmogorov: Localized Measures of Complexity for Ellipses
The Gaussian width is a fundamental quantity in probability, statistics and geometry, known to underlie the intrinsic difficulty of estimation and hypothesis testing. In this work, we show how the Gaussian width, when localized to any given point of an ellipse, can be controlled by the Kolmogorov width of a set similarly localized. This connection leads to an explicit characterization of the es...
متن کاملEntropy Measures vs. Kolmogorov Complexity
Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...
متن کاملCalculating Kolmogorov Complexity from the Transcriptome Data
Information entropy is used to summarize transcriptome data, but ignoring zero count data contained them. Ignoring zero count data causes loss of information and sometimes it was difficult to distinguish between multiple transcriptomes. Here, we estimate Kolmogorov complexity of transcriptome treating zero count data and distinguish similar transcriptome data.
متن کاملKolmogorov Complexity of Categories
Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to describe categories, functors, and natural transformations. With this in hand, we define the informational content of these categorical structures as the shorte...
متن کاملKolmogorov Complexity Based Information Measures Applied to the Analysis of Different River Flow Regimes
We have used the Kolmogorov complexities and the Kolmogorov complexity spectrum to quantify the randomness degree in river flow time series of seven rivers with different regimes in Bosnia and Herzegovina, representing their different type of courses, for the period 1965–1986. In particular, we have examined: (i) the Neretva, Bosnia and the Drina (mountain and lowland parts), (ii) the Miljacka ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2020
ISSN: 1935-7524
DOI: 10.1214/20-ejs1739