`YFIT = predict(B,X)`

[YFIT,stdevs] = predict(B,X)

[YFIT,scores] = predict(B,X)

[YFIT,scores,stdevs] = predict(B,X)

Y = predict(B,X,'param1',val1,'param2',val2,...)

`YFIT = predict(B,X)`

computes the predicted
response of the trained ensemble `B`

for predictors `X`

.
By default, `predict`

takes a democratic (nonweighted)
average vote from all trees in the ensemble. In `X`

,
rows represent observations and columns represent variables. `YFIT`

is
a cell array of strings for classification and a numeric array for
regression.

For regression, `[YFIT,stdevs] = predict(B,X)`

also
returns standard deviations of the computed responses over the ensemble
of the grown trees.

For classification, `[YFIT,scores] = predict(B,X)`

returns
scores for all classes. `scores`

is a matrix with
one row per observation and one column per class. For each observation
and each class, the score generated by each tree is the probability
of this observation originating from this class computed as the fraction
of observations of this class in a tree leaf. `predict`

averages
these scores over all trees in the ensemble.

`[YFIT,scores,stdevs] = predict(B,X)`

also
returns standard deviations of the computed scores for classification. `stdevs`

is
a matrix with one row per observation and one column per class, with
standard deviations taken over the ensemble of the grown trees.

`Y = predict(B,X,'param1',val1,'param2',val2,...)`

specifies
optional parameter name/value pairs:

`'Trees'` | Array of tree indices to use for computation of responses.
Default is `'all'` . |

`'TreeWeights'` | Array of `NTrees` weights for weighting votes
from the specified trees. |

`'UseInstanceForTree'` | Logical matrix of size `Nobs` -by-`NTrees` indicating
which trees to use to make predictions for each observation. By default
all trees are used for all observations. |

For regression problems, the predicted response for an observation is the weighted average of the predictions using selected trees only. That is,

$${\widehat{y}}_{\text{bag}}=\frac{1}{{\displaystyle \sum _{t=1}^{T}{\alpha}_{t}I(t\in S)}}{\displaystyle \sum _{t=1}^{T}{\alpha}_{t}{\widehat{y}}_{t}I(t\in S)}.$$

$${\widehat{y}}_{t}$$ is the prediction from tree

*t*in the ensemble.*S*is the set of indices of selected trees that comprise the prediction (see`'`

`Trees`

`'`

and`'`

`UseInstanceForTree`

`'`

). $$I(t\in S)$$ is 1 if*t*is in the set*S*, and 0 otherwise.*α*is the weight of tree_{t}*t*(see`'`

`TreeWeights`

`'`

).

For classification problems, the predicted class for an observation is the class that yields the largest weighted average of the class posterior probabilities (i.e., classification scores) computed using selected trees only. That is,

For each class

*c*∊*C*,`predict`

estimates the posterior probability of class*c*given observation*x*, $${\widehat{P}}_{t}\left(c|x\right)$$, using each tree,*t*= 1,...,*T*.*C*is the set of all distinct classes in the training data. For more details on classification tree posterior probabilities, see`fitctree`

and`predict`

.`predict`

computes the weighted average of the class posterior probabilities over the selected trees.$${\widehat{P}}_{\text{bag}}\left(c|x\right)=\frac{1}{{\displaystyle \sum _{t=1}^{T}{\alpha}_{t}I(t\in S)}}{\displaystyle \sum _{t=1}^{T}{\alpha}_{t}{\widehat{P}}_{t}\left(c|x\right)I(t\in S)}.$$

The predicted class is the class that yields the largest weighted average.

$${\widehat{y}}_{\text{bag}}=\underset{c\in C}{\mathrm{arg}\mathrm{max}}\left\{{\widehat{P}}_{\text{bag}}\left(c|x\right)\right\}.$$

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