Developer Guide

Contents

Details

Given:
  • n
    feature vectors
    x
    1
    =(
    x
    11
    , ...,
    x
    1
    p
    ), ...,
    x
    n
    =(
    x
    n
    1
    , ...,
    x
    np
    ) of size
    p
  • Their non-negative sample weights
    w
    =(
    w
    1
    , ...,
    w
    n
  • The vector of responses
    y
    =(
    y
    1
    , ...,
    y
    n
    ), where
    y
    i
    R describes the dependent variable for independent variables
    x
    i
    .
The problem is to build a regression decision tree.

Split Criterion

The library provides the decision tree regression algorithm based on the mean-squared error (MSE) [Breiman84]
If sample weights are provided as input, the library will use weighted MSE split criterion.
MSE split criterion (
D
is a set of observations that reach the node):
Without sample weights
With sample weights
To find the best test using MSE, each possible test
is examined using
Where
  • O
    (
    τ
    ) is the set of all possible outcomes of test
    τ
  • D
    v
    is the subset of
    D
    , for which outcome of
    τ
    is
    v
    , for example,
    .
  • operator
    for arbitrary set of observations
    S
    is defined in the table below:
    Without sample weights
    With sample weights
    equivalently the number of elements in
    S
The test used in the node is selected as
. For binary decision tree with "true" and "false" branches,

Training Stage

The regression decision tree follows the algorithmic framework of decision tree training described in Classification and Regression > Decision tree >Training stage.

Prediction Stage

The regression decision tree follows the algorithmic framework of decision tree prediction described in Classification and Regression > Decision tree > Prediction stage.
Given the regression decision tree and vectors
x
1
, …,
x
r
, the problem is to calculate the responses for those vectors.

Product and Performance Information

1

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Notice revision #20110804