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Can We Obtain Dependency Plots for Single CART Trees?

The short answer is YES such plots can be generated. Historically, we concluded that such graphs would normally not be that interesting as they would frequently be single step functions reflecting the fact that individual variables often appear only once or twice in a tree. Also, such graphs would not properly reflect the effect of a varible across most of its range of values. Thus, as of SPM 7.0 CART does not offer such plots. However, we can see what such plots would look like by using TreeNet to grow a one-tree model. To do this, just set up a normal model, choose the TreeNet analysis method, and set the number of trees to be grown to 1 (see green arrow below).

CART

Classification and Regression Trees

CART 6.0 ProEX Features

CART 6.0 ProEX Features

CART 6.0 ProEX Download

CART 6.0 ProEX, released in 2008, comes with a huge list of new features that will help analysts work more rapidly and guide their models to the best-performing trees. This is a dramatic upgrade of our flagship product and is drawing rave reviews from our customers. All of the new CART 6.0 ProEX features are explained in detail in our feature matrix (PDF) some highlights are listed below:

Tree Controls

  • Force splitters into nodes
  • Confine select splitters to specific regions of a tree (Structured Tree™)

HotSpot Detector™

  • Search data for ultra-high performance segments.
  • HotspotDetector trees are specifically designed to yield extraordinarily high-lift or high-risk nodes. The process focuses on individual nodes and generally discards the remainder of the tree.

Train/Test Consistency Assessment

  • Node-by-node summaries of agreement between train and test data on both class assignment and rank ordering of the nodes.
  • Quickly identifies ideally-performing robust trees.

Modeling Automation

  • Automatically generates entire collections of trees exploring different control parameters.
  • Nineteen automated batteries cover exploration of multiple splitting rules, five alternative missing value handling strategies, random selection of alternative predictor lists, progressively smaller (or larger) training sample sizes, and much more.

Predictor Refinement

  • Includes stepwise backwards predictor elimination using any of three predictor ranking criteria (lowest variable importance rank, lowest loss of area under the ROC curve, highest variable importance rank).

Model Assessment via Monte Carlo Testing

  • Measures possible overfitting with automated Monte Carlo randomization tests.

Constructed Features

  • New tools for automatic construction of new features (as linear combinations of predictors).
  • Identification of multiple lists of candidates allows precise control over which predictors may be combined into a single new feature.

Unsupervised Learning Mode

  • Uses Breiman's column scrambler to automatically detect potential clusters with no need to scale data, address missing values, or select variables for clustering.

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CART and Large Datasets

CART is capable of determining the number of records in your data sets, and uses this information to predict the memory and workspace requirements for trees that you build. Also, CART will read your entire data set each time a tree is built. At times these actions may be problematic, especially if you have enormous data sets.

CART Supported File Types

CART Supported File Types

The CART® data-translation engine supports data conversions for more than 80 file formats, including popular statistical-analysis packages such as SAS® and SPSS®, databases such as Oracle and Informix, and spreadsheets such as Microsoft Excel and Lotus 1-2-3.

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How to I define penalties to make it harder for a predictor to become the primary splitter in the node?

CART supports three "improvement penalties." The "natural" improvement for a splitter is always computed according to the CART methodology. A penalty may be imposed, however, that causes the improvement to be lessened depending, affecting the penalized splitter´s relative ranking among competitor splits. If the penalty is enough to cause the top competitor to be replaced by a competitor, the tree is changed.

Model Deployment

Any CART model can be easily deployed when translated into one of the supported languages (SAS®-compatible, C, Java, and PMML) or into the classic text output. This is critical for using your CART trees in large scale production work.

The decision logic of a CART tree, including the surrogate rules utilized if primary splitting values are missing, is automatically implemented. The resulting source code can be dropped into external applications, thus eliminating errors due to hand coding of decision rules and enabling fast and accurate model deployment.

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What if there are too many levels in a categorical predictor?

CART will only search over all possible subsets of a categorical predictor for a limited number of levels. Beyond a threshold set by computational feasibility, CART will simply reject the problem. You can control this limit with the BOPTION NCLASSES = m command, but be aware that for m larger than 15, computation times increase dramatically.

What is CART?

CART is an acronym for Classification and Regression Trees, a decision-tree procedure introduced in 1984 by world-renowned UC Berkeley and Stanford statisticians, Leo Breiman, Jerome Friedman, Richard Olshen, and Charles Stone. Their landmark work created the modern field of sophisticated, mathematically- and theoretically-founded decision trees. The CART methodology solves a number of performance, accuracy, and operational problems that still plague many other current decision-tree methods. CART's innovations include:

What is cross validation?

Cross-validation is a method for estimating what the error rate of a sub-tree (of the maximal tree) would be if you had test data. Regardless of what value you set for V-fold cross validation, CART grows the same maximal tree. The monograph provides evidence that using a V of 10-20 gives better results than using a smaller number, but each number could result in a slightly different error estimate. The optimal tree — which is derived from the maximal tree by pruning — could differ from one V to another because each cross-validation run will come up with slightly different estimates of the error rates of sub-trees and thus might differ in which tree was actually best.

What is the systat dataset format?

CART and MARS continue to read data stored in the legacy SYSTAT format, a binary (i.e., not human-readable) format widely used by statisticians and researchers using the SYSTAT statistical programs. Relative to comma-separated-text and some other binary formats, the legacy SYSTAT format is quite restrictive (limited variable name lengths, limited lengths of character data). We do not recommend that you use it. However, for our clients that do need to work with this format, we provide the following C and Fortran programs that illustrate how legacy SYSTAT datasets are structured. Originally, legacy SYSTAT format was written and read with Fortran code. Thus, because the format must accommodate the record segmentation and padding typical of Fortran I/O, the C version handles these issues explicitly.
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