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<title>MADlib: Decision Tree</title>
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<div class="title">Decision Tree<div class="ingroups"><a class="el" href="group__grp__super.html">Supervised Learning</a> &raquo; <a class="el" href="group__grp__tree.html">Tree Methods</a></div></div> </div>
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<div class="contents">
<div class="toc"><b>Contents</b></p><ul>
<li class="level1">
<a href="#train">Training Function</a> </li>
<li class="level1">
<a href="#predict">Prediction Function</a> </li>
<li class="level1">
<a href="#display">Display Function</a> </li>
<li class="level1">
<a href="#examples">Examples</a> </li>
<li class="level1">
<a href="#related">Related Topics</a> </li>
</ul>
</div><p>Decision trees are a supervised learning method that uses a predictive model to predict the value of a target variable, based on several input variables. They use a tree-based representation of the model such that, the interior nodes of the tree correspond to the input variables, the edges of the nodes correspond to values that the input variables can take, and leaf nodes represent values of the target variable, given the values of the input variables, represented by the path from the root to the leaf nodes.</p>
<p><a class="anchor" id="train"></a></p><dl class="section user"><dt>Training Function</dt><dd>We implement the decision tree using the CART algorithm, introduced by Breiman et al. [1]. The training function has the following syntax: <pre class="syntax">
tree_train(
training_table_name,
output_table_name,
id_col_name,
dependent_variable,
list_of_features,
list_of_features_to_exclude,
split_criterion,
grouping_cols,
weights,
max_depth,
min_split,
min_bucket,
num_splits,
pruning_params,
surrogate_params,
verbosity
)
</pre> <b>Arguments</b> <dl class="arglist">
<dt>training_table_name </dt>
<dd><p class="startdd">TEXT. The name of the table containing the training data</p>
<p class="enddd"></p>
</dd>
<dt>output_table_name </dt>
<dd><p class="startdd">TEXT. The name of the generated table containing the model. If a table with the same name already exists, then the function will return an error.</p>
<p>The model table produced by the train function contains the following columns:</p>
<table class="output">
<tr>
<th>&lt;...&gt; </th><td>Grouping columns, if provided in input, same types as in the training table. This could be multiple columns depending on the <code>grouping_cols</code> input. </td></tr>
<tr>
<th>tree </th><td>BYTEA8. Trained decision tree model stored in a binary format. </td></tr>
<tr>
<th>cat_levels_in_text </th><td>TEXT[]. Ordered levels of categorical variables </td></tr>
<tr>
<th>cat_n_levels </th><td><p class="starttd">INTEGER[]. Number of levels for each categorical variable </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>tree_depth </th><td><p class="starttd">INTEGER. The maximum depth the tree obtained after training (root has depth 0) </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>pruning_cp </th><td><p class="starttd">DOUBLE PRECISION. The cost-complexity parameter used for pruning the trained tree(s). This would be different from the input cp value if cross-validation is used. </p>
<p class="endtd"></p>
</td></tr>
</table>
<p>A summary table named <em>&lt;model_table&gt;_summary</em> is also created at the same time, which has the following columns: </p><table class="output">
<tr>
<th>method </th><td><p class="starttd">TEXT. 'tree_train' </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>is_classification </th><td><p class="starttd">BOOLEAN. TRUE if the decision trees are for classification, FALSE if regression </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>source_table </th><td><p class="starttd">TEXT. The data source table name </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>model_table </th><td><p class="starttd">TEXT. The model table name </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>id_col_name </th><td><p class="starttd">TEXT. The ID column name </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>dependent_varname </th><td><p class="starttd">TEXT. The dependent variable </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>independent_varname </th><td><p class="starttd">TEXT. The independent variables </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>cat_features </th><td>TEXT. The list of categorical feature names as a comma-separated string </td></tr>
<tr>
<th>con_features </th><td><p class="starttd">TEXT. The list of continuous feature names as a comma-separated string </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>grouping_col </th><td><p class="starttd">TEXT. Names of grouping columns </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>num_all_groups </th><td><p class="starttd">INTEGER. Number of groups in decision tree training </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>num_failed_groups </th><td><p class="starttd">INTEGER. Number of failed groups in decision tree training </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>total_rows_processed </th><td><p class="starttd">BIGINT. Total numbers of rows processed in all groups </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>total_rows_skipped </th><td><p class="starttd">BIGINT. Total numbers of rows skipped in all groups due to missing values or failures </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>dependent_var_levels </th><td><p class="starttd">TEXT. For classification, the distinct levels of the dependent variable </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>dependent_var_type </th><td><p class="starttd">TEXT. The type of dependent variable </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>input_cp </th><td><p class="starttd">DOUBLE PRECISION. The complexity parameter (cp) used for pruning the trained tree(s) (before cross-validation is run). This is same as the cp value inputed through the <em>pruning_params</em> </p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>independent_var_types </th><td><p class="starttd">TEXT. A comma separated string, the types of independent variables </p>
<p class="endtd"></p>
</td></tr>
</table>
<p class="enddd"></p>
</dd>
<dt>id_col_name </dt>
<dd><p class="startdd">TEXT. Name of the column containing id information in the training data. This is a mandatory argument and is used for prediction and cross-validation. The values are expected to be unique for each row </p>
<p class="enddd"></p>
</dd>
<dt>dependent_variable </dt>
<dd><p class="startdd">TEXT. Name of the column that contains the output (response) for training. Boolean, integer and text types are considered classification outputs, while double precision values are considered regression outputs. The response variable for a classification tree can be multinomial, but the time and space complexity of train function increases linearly as the number of response classes increases.</p>
<p class="enddd"></p>
</dd>
<dt>list_of_features </dt>
<dd><p class="startdd">TEXT. Comma-separated string of column names to use as predictors. Can also be a '*' implying all columns are to be used as predictors (except the ones included in the next argument). The types of the features can be mixed where boolean, integer, and text columns are considered categorical and double precision columns are considered continuous. The categorical variables are not encoded and used as is for the training.</p>
<p>There are no limitations to the number of levels in a categorical variable. It is, however, important to note that we don't test for every combination of levels of a categorical variable for evaluating a split. We order the levels of the variable by the entropy of the varible in predicting the response. The splits at each node is evaluated between these ordered levels </p>
<p class="enddd"></p>
</dd>
<dt>list_of_features_to_exclude </dt>
<dd><p class="startdd">TEXT. Comma-separated string of column names to exclude from the predictors list. If the <em>dependent_variable</em> is an expression (including cast of a column name), then this list should include all columns present in the <em>dependent_variable</em> expression, otherwise those columns will be included in the features. The names in this parameter should be identical to the names used in the table and quoted appropriately</p>
<p class="enddd"></p>
</dd>
<dt>split_criterion </dt>
<dd><p class="startdd">TEXT, default = 'gini' for classification, 'mse' for regression. Impurity function to compute the feature to use for the split. Supported criteria are 'gini', 'entropy', 'misclassification' for classification trees. For regression trees, split_criterion of 'mse' is always used (irrespective of the input for this argument) </p>
<p class="enddd"></p>
</dd>
<dt>grouping_cols (optional) </dt>
<dd><p class="startdd">TEXT, default: NULL. Comma-separated list of column names to group the data by. This will lead to creating multiple decision trees, one for each group</p>
<p class="enddd"></p>
</dd>
<dt>weights (optional) </dt>
<dd><p class="startdd">TEXT. Column name containing weights for each observation</p>
<p class="enddd"></p>
</dd>
<dt>max_depth (optional) </dt>
<dd><p class="startdd">INTEGER, default: 10. Maximum depth of any node of the final tree, with the root node counted as depth 0</p>
<p class="enddd"></p>
</dd>
<dt>min_split (optional) </dt>
<dd><p class="startdd">INTEGER, default: 20. Minimum number of observations that must exist in a node for a split to be attempted. The best value for this parameter depends on the number of tuples in the dataset</p>
<p class="enddd"></p>
</dd>
<dt>min_bucket (optional) </dt>
<dd><p class="startdd">INTEGER, default: min_split/3. Minimum number of observations in any terminal node. If only one of min_bucket or min_split is specified, min_split is set to min_bucket*3 or min_bucket to min_split/3, as appropriate</p>
<p class="enddd"></p>
</dd>
<dt>num_splits (optional) </dt>
<dd><p class="startdd">INTEGER, default: 100. Continuous-valued features are binned into discrete quantiles to compute split boundaries. This global parameter is used to compute the resolution of splits for continuous features. Higher number of bins will lead to better prediction, but will also result in higher processing time</p>
<p class="enddd"></p>
</dd>
<dt>pruning_params (optional) </dt>
<dd><p class="startdd">TEXT. Comma-separated string of key-value pairs giving the parameters for pruning the tree. The parameters currently accepted are: </p><table class="output">
<tr>
<th>cp </th><td><p class="starttd">Default: 0. A split on a node is attempted only if it decreases the overall lack of fit by a factor of 'cp', else the split is pruned away. This value is used to create an initial tree before running cross-validation (see below).</p>
<p class="endtd"></p>
</td></tr>
<tr>
<th>n_folds </th><td><p class="starttd">Default: 0 (i.e. No cross-validation). Number of cross-validation folds to use to compute the best value of <em>cp</em>. To perform cross-validation, a positive value of <em>n_folds</em> (greater than 2) should be given. An additional output table <em>&lt;model_table&gt;_cv</em> is created containing the values of evaluated <em>cp</em> and the cross-validation error. The tree returned in the output table corresponds to the <em>cp</em> with the lowest cross-validation error (we pick the maximum <em>cp</em> if multiple values have same error).</p>
<p>The list of <em>cp</em> values are automatically computed by parsing through the tree initially trained on the complete dataset. The tree outputted is a subset of this initial tree corresponding to the best computed <em>cp</em>.</p>
<p class="endtd"></p>
</td></tr>
</table>
<p class="enddd"></p>
</dd>
<dt>surrogate_params </dt>
<dd><p class="startdd">TEXT. Comma-separated string of key-value pairs controlling the behavior of surrogate splits for each node. A surrogate variable is another predictor variable that is associated (correlated) with the primary predictor variable for a split. The surrogate variable comes into use when the primary predictior value is NULL. This parameter currently accepts the below argument: </p><table class="output">
<tr>
<th>max_surrogates </th><td>Default: 0. Number of surrogates to store for each node </td></tr>
</table>
<p class="enddd"></p>
</dd>
<dt>verbosity (optional) </dt>
<dd>BOOLEAN, default: FALSE. Provides verbose output of the results of training </dd>
</dl>
</dd></dl>
<dl class="section note"><dt>Note</dt><dd><ul>
<li>Many of the parameters are designed to be similar to the popular R package 'rpart'. An important distinction between rpart and the above MADlib function is that for both response and feature variables, MADlib considers integer values as categorical values, while rpart considers them as continuous.</li>
<li>When using no surrogates (<em>max_surrogates</em>=0), all rows containing NULL value for any of the features used for training will be ignored from training and prediction.</li>
<li>When cross-validation is not used (<em>n_folds</em>=0), each tree outputed is pruned by inputed cost-complextity (<em>cp</em>). With cross-validation, inputed <em>cp</em> is the minimum value of all the explored values of 'cp'. During cross-validation, we train an initial tree using the provided <em>cp</em> and explore all possible sub-trees (upto a single-node tree) to compute the optimal sub-tree. The optimal sub-tree and the 'cp' corresponding to this optimal sub-tree is placed in the <em>output_table</em>, with their columns named as <em>tree</em> and <em>pruning_cp</em> respectively.</li>
<li>The main parameters that affect memory usage are: depth of tree, number of features, and number of values per feature. If you are hitting VMEM limits, consider reducing one or more of these parameters.</li>
</ul>
</dd></dl>
<p><a class="anchor" id="predict"></a></p><dl class="section user"><dt>Prediction Function</dt><dd>The prediction function is provided to estimate the conditional mean given a new predictor. It has the following syntax: <pre class="syntax">
tree_predict(tree_model,
new_data_table,
output_table,
type)
</pre></dd></dl>
<p><b>Arguments</b> </p><dl class="arglist">
<dt>tree_model </dt>
<dd><p class="startdd">TEXT. Name of the table containing the decision tree model. This should be the output table returned from <em>tree_train</em></p>
<p class="enddd"></p>
</dd>
<dt>new_data_table </dt>
<dd><p class="startdd">TEXT. Name of the table containing prediction data. This table is expected to contain the same features that were used during training. The table should also contain <em>id_col_name</em> used for identifying each row</p>
<p class="enddd"></p>
</dd>
<dt>output_table </dt>
<dd><p class="startdd">TEXT. Name of the table to output prediction results to. If this table already exists then an error is returned. The table contains the <em>id_col_name</em> column giving the 'id' for each prediction and the prediction columns for the dependent variable.</p>
<p>If <em>type</em> = 'response', then the table has a single additional column with the prediction value of the response. The type of this column depends on the type of the response variable used during training.</p>
<p>If <em>type</em> = 'prob', then the table has multiple additional columns, one for each possible value of the response variable. The columns are labeled as 'estimated_prob_<em>dep_value</em>', where <em>dep_value</em> represents each value of the response</p>
<p class="enddd"></p>
</dd>
<dt>type </dt>
<dd>TEXT, optional, default: 'response'. For regression trees, the output is always the predicted value of the dependent variable. For classification trees, the <em>type</em> variable can be 'response', giving the classification prediction as output, or 'prob', giving the class probabilities as output. For each value of the dependent variable, a column with the probabilities is added to the output table </dd>
</dl>
<dl class="section note"><dt>Note</dt><dd>If the <em>new_data_table</em> contains categories of categorical variables not seen in the training data then the prediction for that row will be NULL.</dd></dl>
<p><a class="anchor" id="display"></a></p><dl class="section user"><dt>Display Function</dt><dd>The display function is provided to output a graph representation of the decision tree. The output can either be in the popular 'dot' format that can be visualized using various programs including those in the GraphViz package, or in a simple text format. The details of the text format is outputted with the tree. <pre class="syntax">
tree_display(tree_model, dot_format)
</pre></dd></dl>
<p>An additional display function is provided to output the surrogate splits chosen for each internal node. </p><pre class="syntax">
tree_surr_display(tree_model)
</pre><p>The output contains the list of surrogate splits for each internal node. The nodes are sorted in ascending order by id. This is equivalent to viewing the tree in a breadth-first manner. For each surrogate, we output the surrogate split (variable and threshold) and also give the number of rows that were common between the primary split and the surrogate split. Finally, the number of rows present in the majority branch of the primary split is also presented. Only surrogates that perform better than this majority branch are included in the surrogate list. When the primary variable has a NULL value the surrogate variables are used in order to compute the split for that node. If all surrogates variables are NULL, then the majority branch is used to compute the split for a tuple.</p>
<p><b>Arguments</b> </p><dl class="arglist">
<dt>tree_model_name </dt>
<dd>TEXT. Name of the table containing the decision tree model </dd>
<dt>dot_format </dt>
<dd>BOOLEAN, default = TRUE. Output can either be in a dot format or a text format. If TRUE, the result is in the dot format, else output is in text format </dd>
</dl>
<p>The output is always returned as a 'TEXT'. For the dot format, the output can be redirected to a file on the client side and then rendered using visualization programs.</p>
<p>If the user wants to export the dot format result to an external file, he can use the following method (Note: the user needs to use unaligned table output mode for psql with '-A' flag. And inside psql client, both '\t' and '\o' should be used):</p>
<pre class="example">
&gt; # under bash
&gt; psql -A my_database
# -- in psql now
# \t
# \o test.dot -- export to a file
# select madlib.tree_display('tree_out');
# \o
# \t
</pre><p>After the desired dot file has been generated, one can then use third-party plotting software to plot the trees in a nice figure: </p><pre class="example">
&gt; # under bash, convert the dot file into a PDF file
&gt; dot -Tpdf test.dot &gt; test.pdf
&gt; xpdf test.pdf&amp;
</pre><p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd>Decision tree classification example*</dd></dl>
<ol type="1">
<li>Prepare input data. <pre class="example">
DROP TABLE IF EXISTS dt_golf;
CREATE TABLE dt_golf (
id integer NOT NULL,
"OUTLOOK" text,
temperature double precision,
humidity double precision,
windy text,
class text
) ;
</pre> <pre class="example">
COPY dt_golf (id,"OUTLOOK",temperature,humidity,windy,class) FROM stdin WITH DELIMITER '|';
1|sunny|85|85|'false'|'Don''t Play'
2|sunny|80|90|'true'|'Don''t Play'
3|overcast|83|78|'false'|'Play'
4|rain|70|96|'false'|'Play'
5|rain|68|80|'false'|'Play'
6|rain|65|70|'true'|'Don''t Play'
7|overcast|64|65|'true'|'Play'
8|sunny|72|95|'false'|'Don''t Play'
9|sunny|69|70|'false'|'Play'
10|rain|75|80|'false'|'Play'
11|sunny|75|70|'true'|'Play'
12|overcast|72|90|'true'|'Play'
13|overcast|81|75|'false'|'Play'
14|rain|71|80|'true'|'Don''t Play'
\.
</pre></li>
<li>Run Decision tree train function. <pre class="example">
SELECT madlib.tree_train('dt_golf', -- source table
'train_output', -- output model table
'id', -- id column
'class', -- response
'"OUTLOOK", temperature, humidity, windy', -- features
NULL::text, -- exclude columns
'gini', -- split criterion
NULL::text, -- no grouping
NULL::text, -- no weights
5, -- max depth
3, -- min split
1, -- min bucket
10 -- number of bins per continuous variable
);
</pre></li>
<li>Predict output categories for the same data as was used for input. <pre class="example">
SELECT madlib.tree_predict('train_output',
'dt_golf',
'prediction_results',
'response');
SELECT * FROM prediction_results;
</pre> Result: <pre class="result">
id | estimated_class
&#160;----+-----------------
1 | Don't Play
2 | Don't Play
3 | Play
4 | Play
5 | Play
6 | Don't Play
7 | Play
8 | Don't Play
9 | Play
10 | Play
11 | Play
12 | Play
13 | Play
14 | Don't Play
(14 rows)
</pre></li>
<li>Obtain a dot format display of the tree <pre class="example">
SELECT madlib.tree_display('train_output');
</pre> Result: <pre class="result">
digraph "Classification tree for dt_golf" {
subgraph "cluster0"{
label=""
"g0_0" [label="\"OUTLOOK"&lt;={overcast}", shape=ellipse];
"g0_0" -&gt; "g0_1"[label="yes"];
"g0_1" [label=""Play"",shape=box];
"g0_0" -&gt; "g0_2"[label="no"];
"g0_2" [label="temperature&lt;=75", shape=ellipse];
"g0_2" -&gt; "g0_5"[label="yes"];
"g0_2" -&gt; "g0_6"[label="no"];
"g0_6" [label=""Don't Play"",shape=box];
"g0_5" [label="temperature&lt;=65", shape=ellipse];
"g0_5" -&gt; "g0_11"[label="yes"];
"g0_11" [label=""Don't Play"",shape=box];
"g0_5" -&gt; "g0_12"[label="no"];
"g0_12" [label="temperature&lt;=70", shape=ellipse];
"g0_12" -&gt; "g0_25"[label="yes"];
"g0_25" [label=""Play"",shape=box];
"g0_12" -&gt; "g0_26"[label="no"];
"g0_26" [label="temperature&lt;=72", shape=ellipse];
"g0_26" -&gt; "g0_53"[label="yes"];
"g0_53" [label=""Don't Play"",shape=box];
"g0_26" -&gt; "g0_54"[label="no"];
"g0_54" [label=""Play"",shape=box];
&#160;&#160;&#160;} //--- end of subgraph------------
&#160;} //---end of digraph---------
</pre></li>
<li><p class="startli">Obtain a text display of the tree </p><pre class="example">
SELECT madlib.tree_display('train_output', FALSE);
</pre><p> Result: </p><pre class="result">
&#160;-------------------------------------
&#160;- Each node represented by 'id' inside ().
&#160;- Leaf nodes have a * while internal nodes have the split condition at the end.
&#160;- For each internal node (i), it's children will be at (2i+1) and (2i+2).
&#160;- For each split the first indented child (2i+1) is the 'True' node and
second indented child (2i+2) is the 'False' node.
&#160;- Number of (weighted) rows for each response variable inside [].
&#160;- Order of values = ['"Don\'t Play"', '"Play"']
&#160;-------------------------------------
(0)[ 5 9] "OUTLOOK"&lt;={overcast}
(1)[ 0 4] *
(2)[ 5 5] temperature&lt;=75
(5)[ 3 5] temperature&lt;=65
(11)[ 1 0] *
(12)[ 2 5] temperature&lt;=70
(25)[ 0 3] *
(26)[ 2 2] temperature&lt;=72
(53)[ 2 0] *
(54)[ 0 2] *
(6)[ 2 0] *
&#160;-------------------------------------
</pre><p class="startli">Decision tree regression example*</p>
</li>
<li>Prepare input data. <pre class="example">
CREATE TABLE mt_cars (
id integer NOT NULL,
mpg double precision,
cyl integer,
disp double precision,
hp integer,
drat double precision,
wt double precision,
qsec double precision,
vs integer,
am integer,
gear integer,
carb integer
) ;
</pre> <pre class="example">
COPY mt_cars (id,mpg,cyl,disp,hp,drat,wt,qsec,vs,am,gear,carb) FROM stdin WITH DELIMITER '|' NULL '\null';
1|18.7|8|360|175|3.15|3.44|17.02|0|0|3|2
2|21|6|160|110|3.9|2.62|16.46|0|1|4|4
3|24.4|4|146.7|62|3.69|3.19|20|1|0|4|2
4|21|6|160|110|3.9|2.875|17.02|0|1|4|4
5|17.8|6|167.6|123|3.92|3.44|18.9|1|0|4|4
6|16.4|8|275.8|180|3.078|4.07|17.4|0|0|3|3
7|22.8|4|108|93|3.85|2.32|18.61|1|1|4|1
8|17.3|8|275.8|180|3.078|3.73|17.6|0|0|3|3
9|21.4|\null|258|110|3.08|3.215|19.44|1|0|3|1
10|15.2|8|275.8|180|3.078|3.78|18|0|0|3|3
11|18.1|6|225|105|2.768|3.46|20.22|1|0|3|1
12|32.4|4|78.7|66|4.08|2.20|19.47|1|1|4|1
13|14.3|8|360|245|3.21|3.578|15.84|0|0|3|4
14|22.8|4|140.8|95|3.92|3.15|22.9|1|0|4|2
15|30.4|4|75.7|52|4.93|1.615|18.52|1|1|4|2
16|19.2|6|167.6|123|3.92|3.44|18.3|1|0|4|4
17|33.9|4|71.14|65|4.22|1.835|19.9|1|1|4|1
18|15.2|\null|304|150|3.15|3.435|17.3|0|0|3|2
19|10.4|8|472|205|2.93|5.25|17.98|0|0|3|4
20|27.3|4|79|66|4.08|1.935|18.9|1|1|4|1
21|10.4|8|460|215|3|5.424|17.82|0|0|3|4
22|26|4|120.3|91|4.43|2.14|16.7|0|1|5|2
23|14.7|8|440|230|3.23|5.345|17.42|0|0|3|4
24|30.4|4|95.14|113|3.77|1.513|16.9|1|1|5|2
25|21.5|4|120.1|97|3.70|2.465|20.01|1|0|3|1
26|15.8|8|351|264|4.22|3.17|14.5|0|1|5|4
27|15.5|8|318|150|2.768|3.52|16.87|0|0|3|2
28|15|8|301|335|3.54|3.578|14.6|0|1|5|8
29|13.3|8|350|245|3.73|3.84|15.41|0|0|3|4
30|19.2|8|400|175|3.08|3.845|17.05|0|0|3|2
31|19.7|6|145|175|3.62|2.77|15.5|0|1|5|6
32|21.4|4|121|109|4.11|2.78|18.6|1|1|4|2
\.
</pre></li>
<li>Run Decision Tree train function. <pre class="example">
DROP TABLE IF EXISTS train_output, train_output_summary;
SELECT madlib.tree_train('mt_cars',
'train_output',
'id',
'mpg',
'*',
'id, hp, drat, am, gear, carb', -- exclude columns
'mse',
NULL::text,
NULL::text,
10,
8,
3,
10,
NULL,
'max_surrogates=2'
);
</pre></li>
<li>Display the decision tree in basic text format. <pre class="example">
SELECT madlib.tree_display('train_output', FALSE);
</pre> Result: <pre class="result">
&#160; -------------------------------------
&#160;- Each node represented by 'id' inside ().
&#160;- Each internal nodes has the split condition at the end, while each
&#160; leaf node has a * at the end.
&#160;- For each internal node (i), its child nodes are indented by 1 level
&#160; with ids (2i+1) for True node and (2i+2) for False node.
&#160;- Number of rows and average response value inside []. For a leaf node, this is the prediction.
&#160;-------------------------------------
(0)[32, 20.0906] cyl in {8,6}
(1)[21, 16.6476] disp &lt;= 258
(3)[7, 19.7429] *
(4)[14, 15.1] qsec &lt;= 17.42
(9)[10, 15.81] qsec &lt;= 16.9
(19)[5, 14.78] *
(20)[5, 16.84] *
(10)[4, 13.325] *
(2)[11, 26.6636] wt &lt;= 2.2
(5)[6, 30.0667] *
(6)[5, 22.58] *
&#160;-------------------------------------
(1 row)
</pre></li>
<li>Display the surrogates in the decision tree. <pre class="example">
SELECT madlib.tree_surr_display('train_output');
</pre> Result: <pre class="result">
&#160;-------------------------------------
Surrogates for internal nodes
&#160;-------------------------------------
(0) cyl in {8,6}
1: disp &gt; 146.7 [common rows = 29]
2: vs in {0} [common rows = 26]
[Majority branch = 19 ]
(1) disp &lt;= 258
1: cyl in {6,4} [common rows = 19]
2: vs in {1} [common rows = 18]
[Majority branch = 14 ]
(2) wt &lt;= 2.2
1: disp &lt;= 108 [common rows = 9]
2: qsec &lt;= 18.52 [common rows = 8]
[Majority branch = 6 ]
(4) qsec &lt;= 17.42
1: disp &gt; 275.8 [common rows = 11]
2: vs in {0} [common rows = 10]
[Majority branch = 10 ]
(9) qsec &lt;= 16.9
1: wt &lt;= 3.84 [common rows = 8]
2: disp &lt;= 360 [common rows = 7]
[Majority branch = 5 ]
&#160;-------------------------------------
(1 row)
</pre></li>
</ol>
<dl class="section note"><dt>Note</dt><dd>The 'cyl' parameter above has two tuples with null values. In the prediction example below, the surrogate splits for the <em>cyl in {8, 6}</em> split are used to predict those two tuples (<em>id = 9</em> and <em>id = 18</em>). The splits are used in descending order till a surrogate variable is found that is not NULL. In this case, the two tuples have non-NULL values for <em>disp</em>, hence the <em>disp &gt; 146.7</em> split is used to make the prediction. If all the surrogate variables had been NULL then the majority branch would have been followed.</dd></dl>
<ol type="1">
<li>Predict regression output for the same data and compare with original. <pre class="example">
DROP TABLE IF EXISTS prediction_results;
SELECT madlib.tree_predict('train_output',
'mt_cars',
'prediction_results',
'response');
SELECT s.id, mpg, estimated_mpg FROM prediction_results p, mt_cars s where s.id = p.id;
</pre> Result: <pre class="result">
id | mpg | estimated_mpg
----+------+------------------
1 | 18.7 | 16.84
2 | 21 | 19.7428571428571
3 | 24.4 | 22.58
4 | 21 | 19.7428571428571
5 | 17.8 | 19.7428571428571
6 | 16.4 | 16.84
7 | 22.8 | 22.58
8 | 17.3 | 13.325
9 | 21.4 | 19.7428571428571
10 | 15.2 | 13.325
11 | 18.1 | 19.7428571428571
12 | 32.4 | 30.0666666666667
13 | 14.3 | 14.78
14 | 22.8 | 22.58
15 | 30.4 | 30.0666666666667
16 | 19.2 | 19.7428571428571
17 | 33.9 | 30.0666666666667
18 | 15.2 | 16.84
19 | 10.4 | 13.325
20 | 27.3 | 30.0666666666667
21 | 10.4 | 13.325
22 | 26 | 30.0666666666667
23 | 14.7 | 16.84
24 | 30.4 | 30.0666666666667
25 | 21.5 | 22.58
26 | 15.8 | 14.78
27 | 15.5 | 14.78
28 | 15 | 14.78
29 | 13.3 | 14.78
30 | 19.2 | 16.84
31 | 19.7 | 19.7428571428571
32 | 21.4 | 22.58
(32 rows)
</pre></li>
</ol>
<p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd>[1] Breiman, Leo; Friedman, J. H.; Olshen, R. A.; Stone, C. J. (1984). Classification and regression trees. Monterey, CA: Wadsworth &amp; Brooks/Cole Advanced Books &amp; Software.</dd></dl>
<p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl>
<p>File <a class="el" href="decision__tree_8sql__in.html">decision_tree.sql_in</a> documenting the training function</p>
<p><a class="el" href="group__grp__random__forest.html">Random Forest</a></p>
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