# Microsoft Decision Trees Algorithm Technical Reference

SQL Server 2016 and later

Applies To: SQL Server 2016

The Microsoft Decision Trees algorithm is a hybrid algorithm that incorporates different methods for creating a tree, and supports multiple analytic tasks, including regression, classification, and association. The Microsoft Decision Trees algorithm supports modeling of both discrete and continuous attributes.

This topic explains the implementation of the algorithm, describes how to customize the behavior of the algorithm for different tasks, and provides links to additional information about querying decision tree models.

## Implementation of the Decision Trees Algorithm

The Microsoft Decision Trees algorithm applies the Bayesian approach to learning causal interaction models by obtaining approximate posterior distributions for the models. For a detailed explanation of this approach, see the paper on the Microsoft Research site, by Structure and Parameter Learning.

The methodology for assessing the information value of the priors needed for learning is based on the assumption of likelihood equivalence. This assumption says that data should not help to discriminate network structures that otherwise represent the same assertions of conditional independence. Each case is assumed to have a single Bayesian prior network and a single measure of confidence for that network.

Using these prior networks, the algorithm then computes the relative posterior probabilities of network structures given the current training data, and identifies the network structures that have the highest posterior probabilities.

The Microsoft Decision Trees algorithm uses different methods to compute the best tree. The method used depends on the task, which can be linear regression, classification, or association analysis. A single model can contain multiple trees for different predictable attributes. Moreover, each tree can contain multiple branches, depending on how many attributes and values there are in the data. The shape and depth of the tree built in a particular model depends on the scoring method and other parameters that were used. Changes in the parameters can also affect where the nodes split.

### Building the Tree

When the Microsoft Decision Trees algorithm creates the set of possible input values, it performs feature selection to identify the attributes and values that provide the most information, and removes from consideration the values that are very rare. The algorithm also groups values into bins, to create groupings of values that can be processed as a unit to optimize performance.

A tree is built by determining the correlations between an input and the targeted outcome. After all the attributes have been correlated, the algorithm identifies the single attribute that most cleanly separates the outcomes. This point of the best separation is measured by using an equation that calculates information gain. The attribute that has the best score for information gain is used to divide the cases into subsets, which are then recursively analyzed by the same process, until the tree cannot be split any more.

The exact equation used to evaluate information gain depends on the parameters set when you created the algorithm, the data type of the predictable column, and the data type of the input.

### Discrete and Continuous Inputs

When the predictable attribute is discrete and the inputs are discrete, counting the outcomes per input is a matter of creating a matrix and generating scores for each cell in the matrix.

However, when the predictable attribute is discrete and the inputs are continuous, the input of the continuous columns are automatically discretized. You can accept the default and have Analysis Services find the optimum number of bins, or you can control the manner in which continuous inputs are discretized by setting the DiscretizationMethod and DiscretizationBucketCount properties. For more information, see Change the Discretization of a Column in a Mining Model.

For continuous attributes, the algorithm uses linear regression to determine where a decision tree splits.

When the predictable attribute is a continuous numeric data type, feature selection is applied to the outputs as well, to reduce the possible number of outcomes and build the model faster. You can change the threshold for feature selection and thereby increase or decrease the number of possible values by setting the MAXIMUM_OUTPUT_ATTRIBUTES parameter.

For a more detained explanation about how the Microsoft Decision Trees algorithm works with discrete predictable columns, see Learning Bayesian Networks: The Combination of Knowledge and Statistical Data. For more information about how the Microsoft Decision Trees algorithm works with a continuous predictable column, see the appendix of Autoregressive Tree Models for Time-Series Analysis.

### Scoring Methods and Feature Selection

The Microsoft Decision Trees algorithm offers three formulas for scoring information gain: Shannon's entropy, Bayesian network with K2 prior, and Bayesian network with a uniform Dirichlet distribution of priors. All three methods are well established in the data mining field. We recommend that you experiment with different parameters and scoring methods to determine which provides the best results. For more information about these scoring methods, see Feature Selection.

All Analysis Services data mining algorithms automatically use feature selection to improve analysis and reduce processing load. The method used for feature selection depends on the algorithm that is used to build the model. The algorithm parameters that control feature selection for a decision trees model are MAXIMUM_INPUT_ATTRIBUTES and MAXIMUM_OUTPUT.

Decision TreesInterestingness score

Shannon's Entropy

Bayesian with K2 Prior

Bayesian Dirichlet with uniform prior (default)
If any columns contain non-binary continuous values, the interestingness score is used for all columns, to ensure consistency. Otherwise, the default or specified method is used.
Linear RegressionInterestingness scoreLinear Regression only uses interestingness, because it only supports continuous columns.

### Scalability and Performance

Classification is an important data mining strategy. Generally, the amount of information that is needed to classify the cases grows in direct proportion to the number of input records. This limits the size of the data that can be classified. The Microsoft Decision Trees algorithm using uses the following methods to resolve these problems, improve performance, and eliminate memory restrictions:

• Feature selection to optimize the selection of attributes.

• Bayesian scoring to control tree growth.

• Optimization of binning for continuous attributes.

• Dynamic grouping of input values to determine the most important values.

The Microsoft Decision Trees algorithm is fast and scalable, and has been designed to be easily parallelized, meaning that all processors work together to build a single, consistent model. The combination of these characteristics makes the decision-tree classifier an ideal tool for data mining.

If performance constraints are severe, you might be able to improve processing time during the training of a decision tree model by using the following methods. However, if you do so, be aware that eliminating attributes to improve processing performance will change the results of the model, and possibly make it less representative of the total population.

• Increase the value of the COMPLEXITY_PENALTY parameter to limit tree growth.

• Limit the number of items in association models to limit the number of trees that are built.

• Increase the value of the MINIMUM_SUPPORT parameter to avoid overfitting.

• Restrict the number of discrete values for any attribute to 10 or less. You might try grouping values in different ways in different models.

Note

You can use the data exploration tools available in SQL Server 2016 Integration Services (SSIS) to visualize the distribution of values in your data and group your values appropriately before beginning data mining. For more information, see Data Profiling Task and Viewer. You can also use the Data Mining Add-ins for Excel 2007, to explore, group and relabel data in Microsoft Excel.

## Customizing the Decision Trees Algorithm

The Microsoft Decision Trees algorithm supports parameters that affect the performance and accuracy of the resulting mining model. You can also set modeling flags on the mining model columns or mining structure columns to control the way that data is processed.

Note

The Microsoft Decision Trees algorithm is available in all editions of SQL Server; however, some advanced parameters for customizing the behavior of the Microsoft Decision Trees algorithm are available for use only in specific editions of SQL Server. For a list of features that are supported by the editions of SQL Server, see Features Supported by the Editions of SQL Server 2012 (http://go.microsoft.com/fwlink/?linkid=232473).

### Setting Algorithm Parameters

The following table describes the parameters that you can use with the Microsoft Decision Trees algorithm.

COMPLEXITY_PENALTY
Controls the growth of the decision tree. A low value increases the number of splits, and a high value decreases the number of splits. The default value is based on the number of attributes for a particular model, as described in the following list:

• For 1 through 9 attributes, the default is 0.5.

• For 10 through 99 attributes, the default is 0.9.

• For 100 or more attributes, the default is 0.99.

FORCE_REGRESSOR
Forces the algorithm to use the specified columns as regressors, regardless of the importance of the columns as calculated by the algorithm. This parameter is only used for decision trees that are predicting a continuous attribute.

Note

By setting this parameter, you force the algorithm to try to use the attribute as a regressor. However, whether the attribute is actually used as a regressor in the final model depends on the results of analysis. You can find out which columns were used as regressors by querying the model content.

[Available only in some editions of SQL Server ]

MAXIMUM_INPUT_ATTRIBUTES
Defines the number of input attributes that the algorithm can handle before it invokes feature selection.

The default is 255.

Set this value to 0 to turn off feature selection.

[Available only in some editions of SQL Server]

MAXIMUM_OUTPUT_ATTRIBUTES
Defines the number of output attributes that the algorithm can handle before it invokes feature selection.

The default is 255.

Set this value to 0 to turn off feature selection.

[Available only in some editions of SQL Server]

MINIMUM_SUPPORT
Determines the minimum number of leaf cases that is required to generate a split in the decision tree.

The default is 10.

You may need to increase this value if the dataset is very large, to avoid overtraining.

SCORE_METHOD
Determines the method that is used to calculate the split score. The following options are available:

IDName
1Entropy
3Bayesian with K2 Prior
4Bayesian Dirichlet Equivalent (BDE) with uniform prior

(default)

The default is 4, or BDE.

For an explanation of these scoring methods, see Feature Selection.

SPLIT_METHOD
Determines the method that is used to split the node. The following options are available:

IDName
1Binary: Indicates that regardless of the actual number of values for the attribute, the tree should be split into two branches.
2Complete: Indicates that the tree can create as many splits as there are attribute values.
3Both: Specifies that Analysis Services can determine whether a binary or complete split should be used to produce the best results.

The default is 3.

### Modeling Flags

The Microsoft Decision Trees algorithm supports the following modeling flags. When you create the mining structure or mining model, you define modeling flags to specify how values in each column are handled during analysis. For more information, see Modeling Flags (Data Mining).

Modeling FlagDescription
MODEL_EXISTENCE_ONLYMeans that the column will be treated as having two possible states: Missing and Existing. A null is a missing value.

Applies to mining model columns.
NOT NULLIndicates that the column cannot contain a null. An error will result if Analysis Services encounters a null during model training.

Applies to mining structure columns.

### Regressors in Decision Tree Models

Even if you do not use the Microsoft Linear Regression algorithm, any decision tree model that has continuous numeric inputs and outputs can potentially include nodes that represent a regression on a continuous attribute.

You do not need to specify that a column of continuous numeric data represents a regressor. The Microsoft Decision Trees algorithm will automatically use the column as a potential regressor and partition the dataset into regions with meaningful patterns even if you do not set the REGRESSOR flag on the column.

However, you can use the FORCE_REGRESSOR parameter to guarantee that the algorithm will use a particular regressor. This parameter can be used only with the Microsoft Decision Trees and Microsoft Linear Regression algorithms. When you set the modeling flag, the algorithm will try to find regression equations of the form `a*C1 + b*C2 + ...` to fit the patterns in the nodes of the tree. The sum of the residuals is calculated, and if the deviation is too great, a split is forced in the tree.

For example, if you are predicting customer purchasing behavior using Income as an attribute, and set the REGRESSOR modeling flag on the column, the algorithm will first try to fit the Income values by using a standard regression formula. If the deviation is too great, the regression formula is abandoned and the tree will be split on another attribute. The decision tree algorithm will then try to fit a regressor for income in each of the branches after the split.

## Requirements

A decision tree model must contain a key column, input columns, and at least one predictable column.

### Input and Predictable Columns

The Microsoft Decision Trees algorithm supports the specific input columns and predictable columns that are listed in the following table. For more information about what the content types mean when used in a mining model, see Content Types (Data Mining).

ColumnContent types
Input attributeContinuous, Cyclical, Discrete, Discretized, Key, Ordered, Table
Predictable attributeContinuous, Cyclical, Discrete, Discretized, Ordered, Table
Note

Cyclical and Ordered content types are supported, but the algorithm treats them as discrete values and does not perform special processing.