`Yfit = predict(B,TBLnew)`

Yfit = predict(B,Xnew)

[Yfit,stdevs] = predict(B,TBLnew)

[Yfit,stdevs]
= predict(B,Xnew)

[Yfit,scores] = predict(B,TBLnew)

[Yfit,scores]
= predict(B,Xnew)

[Yfit,scores,stdevs] = predict(B,TBLnew)

[Yfit,scores,stdevs]
= predict(B,Xnew)

Yfit = predict(B,TBLnew,'param1',val1,'param2',val2,...)

Yfit
= predict(B,Xnew,'param1',val1,'param2',val2,...)

`Yfit = predict(B,TBLnew)`

computes the predicted
response of the trained ensemble `B`

for the predictor
data contained in the table `TBLnew`

. By default, `predict`

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

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

is a cell array of strings
for classification and a numeric array for regression. If you trained `B`

using
sample data contained in a table, then the input data for this method
must also be in a table.

`Yfit = predict(B,Xnew)`

computes the predicted
response of the trained ensemble `B`

for predictor
data contained in the matrix `Xnew`

. If you trained `B`

using
sample data contained in a matrix, then the input data for this method
must also be in a matrix.

For regression, `[Yfit,stdevs] = predict(B,TBLnew)`

or ```
[Yfit,stdevs]
= predict(B,Xnew)
```

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

For classification, `[Yfit,scores] = predict(B,TBLnew)`

or ```
[Yfit,scores]
= predict(B,Xnew)
```

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,TBLnew)`

or ```
[Yfit,scores,stdevs]
= predict(B,Xnew)
```

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.

`Yfit = predict(B,TBLnew,'param1',val1,'param2',val2,...)`

or ```
Yfit
= predict(B,Xnew,'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*and each tree*t*= 1,...,*T*,`predict`

computes $${\widehat{P}}_{t}\left(c|x\right)$$, which is the estimated posterior probability of class*c*given observation*x*using tree*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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