Related papers: Entropy, Derivation Operators and Huffman Trees
The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Fr\"uhwirth, we consider an extension of this theory with an additional…
There is an unproven duality theory hypothesizing that random discrete trees and their poissonized embeddings in continuous time share fundamental properties. We give additional evidence in favor of this theory by showing that several…
We describe the proalgebraic groups represented by three Hopf algebras on planar binary trees previously introduced by the author and Christian Brouder in relation with the renormalization of quantum electrodynamics. Using two monoidal…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…
A classical longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
I give a simple proof for the fact that positive entropy subshifts contain infinite binary trees where branching happens synchronously in each branch, and that the branching times form a set with positive lower asymptotic density.
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described…
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In…
The definition of $k^{th}$-order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to…
Modeling worlds and actions under uncertainty is one of the central problems in the framework of decision-theoretic planning. The representation must be general enough to capture real-world problems but at the same time it must provide a…
The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these…
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more…
A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space $(X,\mu)$. These have…