DeepAI

# The cut metric for probability distributions

Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called pinning on the space of limit objects and show how this operation yields a canonical cut metric approximation to a given probability distribution akin to the weak regularity lemma for graphons. We also establish the cut metric continuity of basic operations such as taking product measures.

• 18 publications
• 16 publications
10/31/2017

### Algorithmic learning of probability distributions from random data in the limit

We study the problem of identifying a probability distribution for some ...
10/22/2020

### Exponential Negation of a Probability Distribution

Negation operation is important in intelligent information processing. D...
01/05/2018

### An equivalence between learning of data and probability distributions, and some applications

Algorithmic learning theory traditionally studies the learnability of ef...
01/03/2022

### A New Modeling of Classical Folds in Computational Origami

This paper shows a cut along a crease on an origami sheet makes simple m...
01/05/2018

### Equivalences between learning of data and probability distributions, and their applications

Algorithmic learning theory traditionally studies the learnability of ef...
01/22/2022

### Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning

The framework of quantitative equational logic has been successfully app...
06/28/2017

### Approximation of probability density functions on the Euclidean group parametrized by dual quaternions

Perception is fundamental to many robot application areas especially in ...