Kernel Complexity for Nonparametric Distributions and Detection of Its Changes

So Hirai; Kenji Yamanishi

doi:10.20944/preprints201911.0381.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 28 November 2019 / Approved: 3 December 2019 / Online: 3 December 2019 (03:34:19 CET)

This paper addresses the issues of how we can quantify structural information for nonparametric distributions and how we can detect its changes. Structural information refers to an index for a global understanding of a data distribution. When we consider the problem of clustering using a parametric model such as a Gaussian mixture model, the number of mixture components (clusters) can be thought of as structural information in the model. However, there does not exist any notion of structural information for nonparametric modeling of data. In this paper we introduce a novel notion of {\em kernel complexity} (KC) as structural information in the nonparametric setting. The key idea of KC is to combine the information bias inspired by the Gini index with the information quantity measured in terms of the normalized maximum likelihood (NML) code length. We empirically show that KC has a property similar to the number of clusters in a parametric model. We further propose a framework for structural change detection with KC in nonparametric distributions. With synthetic and real data sets we empirically demonstrate that our framework enables us to detect structural changes underlying the data and their early warning signals.

change-point detection; kernel density estimation; normalized maximum likelihood (NML); minimum description length (MDL) principle; kernel complexity (KC)

MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics

Your full name

Your affiliation information (e.g., name of your university/institution/organization)

Not displayed online.

Your Email address (not made public)

Please leave your comment to this article below.

Mathematical equations can be typed in either LaTeX formats \\[ ... \\] or $$ ... $$, or MathML format <math> ... </math>. Try the LaTeX or MathML example.

Type equation:

Preview:

Copy equation into message below

Close menu

Please click a symbol to insert it into the message box below:

Please enter the link here:

Optionally, you can enter text that should appear as linked text:

Copy link into message below

Close menu

Please enter or paste the URL to the image here (please only use links to jpg/jpeg, png and gif images):

Copy image into message below

Close menu

Type author name or keywords to filter the list of references in this group (you can add a new citation under Bibliography):

No existing citations in Discussion Group

Wikify editor is a simple editor for wiki-style mark-up. It was written by MDPI for Sciforum in 2014. The rendering of the mark-up is based on Wiky.php with some tweaks. Rendering of mathematical equations is done with MathJax. Please send us a message for support or for reporting bugs.

Close menu

Please declare any conflicts of interest you may have with this paper, financial or otherwise.

I do not have a conflict of interest

I would like to declare a conflict of interest

Display my name on the website I want to get recognition for my comment on Publons

[what’s this?]. Link your accounts here

Captcha

Renew

I accept the following conditions:

Comments must follow the standards of professional discourse and should focus on the scientific content of the article. Insulting or offensive language, personal attacks and off-topic remarks will not be permitted. Comments must be written in English. Preprints reserves the right to remove comments without notice. Readers who post comments are obliged to declare any competing interests, financial or otherwise.

Notify me about updates to this article or when a peer-reviewed version is published.

Upload a Image(max file size 2MB)

Kernel Complexity for Nonparametric Distributions and Detection of Its Changes

Abstract

Keywords

Subject

Comments (0)