In this paper we challenge three of the underlying principles of CART, a well know approach to the construction of classification and regression trees. Our primary concern is with the penalization strategy employed to prune back an initial, overgrown tree. We reason, based on both intuitive and theoretical arguments, that the pruning rule for classification should be different from that used fo...

We propose a tree-based algorithm (μCART) for classification and regression problems in the context of functional data analysis, which allows to leverage measure learning multiple splitting rules at node level, with objective reducing error while retaining interpretability tree. For each internal node, our main contribution is idea weighted space by means constrained convex optimization, then u...

Fifty years have passed since the publication of the first regression tree algorithm. New techniques have added capabilities that far surpass those of the early methods. Modern classification trees can partition the data with linear splits on subsets of variables and fit nearest neighbor, kernel density, and other models in the partitions. Regression trees can fit almost every kind of tradition...

The terminal nodes of a binary tree classifier represent discrete classes to be recognized. In this paper the classes are considered to be fuzzy sets in which a specific sample can belong to more than one class with different degrees of membership. The terminal nodes is this case will contain information about the degrees to which test samples belong to particular classes. This will allow the d...

This thesis investigates whether stock picking based on classification and regression trees can be implemented as a successful algorithmic trading system, if only based on technical analysis. To evaluate the performance of this method a fictional portfolio was constructed from the Stockholm Stock Exchange OMX30, traded on a five-year period. By means of implementation, classification of the ass...

In designing a decision tree for classification or regression, one selects at each node a feature to be tested, and partitions the range of that feature into a small number of bins, each bin corresponding to a child of the node. When the feature’s range is discrete with N unordered outcomes, the optimal partition, that is, the partition minimizing an expected loss, is usually found by an exhaus...

Nonsmooth local optimization problems occur in many fields, including engineering, mathematics, and economics. In economics, nonsmooth problems can be found in finance, mathematical economics and production theory. Examples include, nonsmooth utility maximization and exact penalty functions. However there are few convergent optimization algorithms to solve general nonsmooth or discontinuous pro...