Related papers: Essential Inputs and Minimal Tree Automata
We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…
Random forests are a widely used machine learning algorithm, but their computational efficiency is undermined when applied to large-scale datasets with numerous instances and useless features. Herein, we propose a nonparametric feature…
We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of $p$-variation of the path, and integration with respect to the path. In particular, the…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing…
We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Tree ensemble methods such as random forests [Breiman, 2001] are very popular to handle high-dimensional tabular data sets, notably because of their good predictive accuracy. However, when machine learning is used for decision-making…
We introduce tree representations for $ \alpha$-determinantal point processes. The $ \alpha$-determinantal point processes is introduced as a one parameter extension of the determinantal point process. In the previous paper with H.Osada,…
In biomedical applications of machine learning, relevant information often has a rich structure that is not easily encoded as real-valued predictors. Examples of such data include DNA or RNA sequences, gene sets or pathways, gene…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Domestic and service robots have the potential to transform industries such as health care and small-scale manufacturing, as well as the homes in which we live. However, due to the overwhelming variety of tasks these robots will be expected…
We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language…
Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data-structures. Categorically, they arise as final coalgebras for polynomial…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…