Decision trees have proved to be valuable tools for the description, classification and generalization of data. Work on constructing decision trees from data exists in multiple disciplines such as statistics, pattern recognition, decision theory, signal processing, machine learning and artificial neural networks. Researchers in these disciplines, sometimes working on quite different problems, identified similar issues and heuristics for decision tree construction. This paper surveys existing work on decision tree construction, attempting to identify the important issues involved, directions the work has taken and the current state of the art.

Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey

Preliminaries. Categories. Functors. Diagrams. Naturality and Sketches. Products and Sums. Catesian Closed Categories. Finite Discrete Sketches. Limits and Colimits. More About Sketches. Fibrations. Adjoints. Algebras for Endofunctors. Toposes.

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Category Theory For Computing Science

This article presents an incremental algorithm for inducing decision trees equivalent to those formed by Quinlan's nonincremental ID3 algorithm, given the same training instances. The new algorithm, named ID5R, lets one apply the ID3 induction process to learning tasks in which training instances are presented serially. Although the basic tree-building algorithms differ only in how the decision trees are constructed, experiments show that incremental training makes it possible to select training instances more carefully, which can result in smaller decision trees. The ID3 algorithm and its variants are compared in terms of theoretical complexity and empirical behavior.

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Incremental Induction of Decision Trees

This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and others who use diagrammatic reasoning We have opted for a somewhat informal treatment of topological notions, and have omitted most proofs Nevertheless, the exposition is sufficiently detailed to make it clear what is presently known, and to serve as a starting place for more in-depth study Where possible, we provide pointers to more rigorous treatments in the literature Where we include results that have only been proved in special cases, we indicate this in the form of caveats

/pdf/a-survey-of-graphical-languages-for-monoidal-categories-5b7ir66g53.pdf

A Survey of Graphical Languages for Monoidal Categories

Handbook of logic in computer science.

Weakly distributive categories

http://pages.cpsc.ucalgary.ca/~robin/FMCS/FMCS_06/RestrictionsI.pdf

Restriction categories I: categories of partial maps

Natural deduction and coherence for weakly distributive categories

Following work of Ehrhard and Regnier, we introduce the notion of a differential category: an additive symmetric monoidal category with a comonad (a ‘coalgebra modality’) and a differential combinator satisfying a number of coherence conditions. In such a category one should imagine the morphisms in the base category as being linear maps and the morphisms in the coKleisli category as being smooth (infinitely differentiable). Although such categories do not necessarily arise from models of linear logic, one should think of this as replacing the usual dichotomy of linear vs. stable maps established for coherence spaces.After establishing the basic axioms, we give a number of examples. The most important example arises from a general construction, a comonad $S_\infty$ on the category of vector spaces. This comonad and associated differential operators fully capture the usual notion of derivatives of smooth maps. Finally, we derive additional properties of differential categories in certain special cases, especially when the comonad is a storage modality, as in linear logic. In particular, we introduce the notion of a categorical model of the differential calculus, and show that it captures the not-necessarily-closed fragment of Ehrhard–Regnier differential $\lambda$-calculus.

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Differential categories

This note applies techniques we h a ve developed to study coherence in monoidal categories with two tensors, corresponding to the tensor{par fragment o f linear logic, to several new situations, including Hyland and de Paiva's Full Intuitionistic Linear Logic (FILL), and Lambek's Bilinear Logic (BILL). Note that the latter is a non-commutative logicc we also consider the noncommutative v ersion of FILL. The essential diierence between FILL and BILL lies in requiring that a certain tensorial strength be an isomorphism. I n a n y FILL category, it is possible to isolate a full subcategory of objects (the \nucleus") for which this transformation is an isomorphism. In addition, we deene and study the appropriate categorical structure underlying the MIX rule. For all these structures, we do not restrict consideration to the \pure" logic as we a l l o w non-logical axioms. We deene the appropriate notion of proof nets for these logics, and use them to describe coherence results for the corresponding categorical structures. 0. Introduction In CS91] we i n troduced the notion of \weakly distributive category", now renamed \lin-early distributive category", in order to study the pure proof theory of the cut rule for the sequent calculus with nite sequences of formulas on both sides of the turnstile. This is generally thought of as the \classical" sequent calculus, but in fact this proof theory is not truly \classical" in any real sense, and may be thought o f a s t h e tensor{par fragment of linear logic with no negation. We w i s h e d t o s h o w h o w features could be added in a modular fashion to this basic categorical setting, in order to model the more expressive fragments of linear logic: this program is now largely complete, see CS91, BCST, BCS92], and includes the subject matter of this paper. Crucial to this program was the provision of an intrinsic characterization of the par. In classical linear logic the negation was an obstruction, for it allowed the par to be viewed as merely the de Morgan dual of the usual tensor product, and so for its special

J. R. B. Cockett

Papers

Weakly distributive categories

Restriction categories I: categories of partial maps

Natural deduction and coherence for weakly distributive categories

Differential categories

Proof theory for full intuitionistic linear logic, bilinear logic, and MIX categories.