Efficient algorithms for decision tree cross-validation

Cross-validation is a useful and generally applicable technique often employed in machine learning, including decision tree induction. An important disadvantage of straightforward implementation of the technique is its computational overhead. In this paper we show that, for decision trees, the computational overhead of cross-validation can be reduced significantly by integrating the cross-validation with the normal decision tree induction process. We discuss how existing decision tree algorithms can be adapted to this aim, and provide an analysis of the speedups these adaptations may yield. The analysis is supported by experimental results.Comment: 9 pages, 6 figures. http://www.cs.kuleuven.ac.be/cgi-bin-dtai/publ_info.pl?id=3478

Inducing safer oblique trees without costs

Decision tree induction has been widely studied and applied. In safety applications, such as determining whether a chemical process is safe or whether a person has a medical condition, the cost of misclassification in one of the classes is significantly higher than in the other class. Several authors have tackled this problem by developing cost-sensitive decision tree learning algorithms or have suggested ways of changing the distribution of training examples to bias the decision tree learning process so as to take account of costs. A prerequisite for applying such algorithms is the availability of costs of misclassification. Although this may be possible for some applications, obtaining reasonable estimates of costs of misclassification is not easy in the area of safety. This paper presents a new algorithm for applications where the cost of misclassifications cannot be quantified, although the cost of misclassification in one class is known to be significantly higher than in another class. The algorithm utilizes linear discriminant analysis to identify oblique relationships between continuous attributes and then carries out an appropriate modification to ensure that the resulting tree errs on the side of safety. The algorithm is evaluated with respect to one of the best known cost-sensitive algorithms (ICET), a well-known oblique decision tree algorithm (OC1) and an algorithm that utilizes robust linear programming

Random Prism: An Alternative to Random Forests.

Ensemble learning techniques generate multiple classifiers, so called base classifiers, whose combined classification results are used in order to increase the overall classification accuracy. In most ensemble classifiers the base classifiers are based on the Top Down Induction of Decision Trees (TDIDT) approach. However, an alternative approach for the induction of rule based classifiers is the Prism family of algorithms. Prism algorithms produce modular classification rules that do not necessarily fit into a decision tree structure. Prism classification rulesets achieve a comparable and sometimes higher classification accuracy compared with decision tree classifiers, if the data is noisy and large. Yet Prism still suffers from overfitting on noisy and large datasets. In practice ensemble techniques tend to reduce the overfitting, however there exists no ensemble learner for modular classification rule inducers such as the Prism family of algorithms. This article describes the first development of an ensemble learner based on the Prism family of algorithms in order to enhance Prism’s classification accuracy by reducing overfitting

Porting Decision Tree Algorithms to Multicore using FastFlow

The whole computer hardware industry embraced multicores. For these machines, the extreme optimisation of sequential algorithms is no longer sufficient to squeeze the real machine power, which can be only exploited via thread-level parallelism. Decision tree algorithms exhibit natural concurrency that makes them suitable to be parallelised. This paper presents an approach for easy-yet-efficient porting of an implementation of the C4.5 algorithm on multicores. The parallel porting requires minimal changes to the original sequential code, and it is able to exploit up to 7X speedup on an Intel dual-quad core machine.Comment: 18 pages + cove

Machine Learning Decision Tree Models for Differentiation of Posterior Fossa Tumors Using Diffusion Histogram Analysis and Structural MRI Findings.

We applied machine learning algorithms for differentiation of posterior fossa tumors using apparent diffusion coefficient (ADC) histogram analysis and structural MRI findings. A total of 256 patients with intra-axial posterior fossa tumors were identified, of whom 248 were included in machine learning analysis, with at least 6 representative subjects per each tumor pathology. The ADC histograms of solid components of tumors, structural MRI findings, and patients' age were applied to construct decision models using Classification and Regression Tree analysis. We also compared different machine learning classification algorithms (i.e., naïve Bayes, random forest, neural networks, support vector machine with linear and polynomial kernel) for dichotomized differentiation of the 5 most common tumors in our cohort: metastasis (n = 65), hemangioblastoma (n = 44), pilocytic astrocytoma (n = 43), ependymoma (n = 27), and medulloblastoma (n = 26). The decision tree model could differentiate seven tumor histopathologies with terminal nodes yielding up to 90% accurate classification rates. In receiver operating characteristics (ROC) analysis, the decision tree model achieved greater area under the curve (AUC) for differentiation of pilocytic astrocytoma (p = 0.020); and atypical teratoid/rhabdoid tumor ATRT (p = 0.001) from other types of neoplasms compared to the official clinical report. However, neuroradiologists' interpretations had greater accuracy in differentiating metastases (p = 0.001). Among different machine learning algorithms, random forest models yielded the highest accuracy in dichotomized classification of the 5 most common tumor types; and in multiclass differentiation of all tumor types random forest yielded an averaged AUC of 0.961 in training datasets, and 0.873 in validation samples. Our study demonstrates the potential application of machine learning algorithms and decision trees for accurate differentiation of brain tumors based on pretreatment MRI. Using easy to apply and understandable imaging metrics, the proposed decision tree model can help radiologists with differentiation of posterior fossa tumors, especially in tumors with similar qualitative imaging characteristics. In particular, our decision tree model provided more accurate differentiation of pilocytic astrocytomas from ATRT than by neuroradiologists in clinical reads

Top-Down Induction of Decision Trees: Rigorous Guarantees and Inherent Limitations

Consider the following heuristic for building a decision tree for a function $f : \{0,1\}^n \to \{\pm 1\}$. Place the most influential variable $x_i$ of $f$ at the root, and recurse on the subfunctions $f_{x_i=0}$ and $f_{x_i=1}$ on the left and right subtrees respectively; terminate once the tree is an $\varepsilon$-approximation of $f$. We analyze the quality of this heuristic, obtaining near-matching upper and lower bounds: $\circ$ Upper bound: For every $f$ with decision tree size $s$ and every $\varepsilon \in (0,\frac1{2})$, this heuristic builds a decision tree of size at most $s^{O(\log(s/\varepsilon)\log(1/\varepsilon))}$. $\circ$ Lower bound: For every $\varepsilon \in (0,\frac1{2})$ and $s \le 2^{\tilde{O}(\sqrt{n})}$, there is an $f$ with decision tree size $s$ such that this heuristic builds a decision tree of size $s^{\tilde{\Omega}(\log s)}$. We also obtain upper and lower bounds for monotone functions: $s^{O(\sqrt{\log s}/\varepsilon)}$ and $s^{\tilde{\Omega}(\sqrt[4]{\log s } )}$ respectively. The lower bound disproves conjectures of Fiat and Pechyony (2004) and Lee (2009). Our upper bounds yield new algorithms for properly learning decision trees under the uniform distribution. We show that these algorithms---which are motivated by widely employed and empirically successful top-down decision tree learning heuristics such as ID3, C4.5, and CART---achieve provable guarantees that compare favorably with those of the current fastest algorithm (Ehrenfeucht and Haussler, 1989). Our lower bounds shed new light on the limitations of these heuristics. Finally, we revisit the classic work of Ehrenfeucht and Haussler. We extend it to give the first uniform-distribution proper learning algorithm that achieves polynomial sample and memory complexity, while matching its state-of-the-art quasipolynomial runtime