# Custom Objective and Evaluation Metric

**Contents**

## Overview

XGBoost is designed to be an extensible library. One way to extend it is by providing our own objective function for training and corresponding metric for performance monitoring. This document introduces implementing a customized elementwise evaluation metric and objective for XGBoost. Although the introduction uses Python for demonstration, the concepts should be readily applicable to other language bindings.

Note

The ranking task does not support customized functions.

Breaking change was made in XGBoost 1.6.

In the following two sections, we will provide a step by step walk through of implementing
the `Squared Log Error (SLE)`

objective function:

and its default metric `Root Mean Squared Log Error(RMSLE)`

:

Although XGBoost has native support for said functions, using it for demonstration provides us the opportunity of comparing the result from our own implementation and the one from XGBoost internal for learning purposes. After finishing this tutorial, we should be able to provide our own functions for rapid experiments. And at the end, we will provide some notes on non-identy link function along with examples of using custom metric and objective with the scikit-learn interface.

If we compute the gradient of said objective function:

As well as the hessian (the second derivative of the objective):

## Customized Objective Function

During model training, the objective function plays an important role: provide gradient
information, both first and second order gradient, based on model predictions and observed
data labels (or targets). Therefore, a valid objective function should accept two inputs,
namely prediction and labels. For implementing `SLE`

, we define:

```
import numpy as np
import xgboost as xgb
from typing import Tuple
def gradient(predt: np.ndarray, dtrain: xgb.DMatrix) -> np.ndarray:
'''Compute the gradient squared log error.'''
y = dtrain.get_label()
return (np.log1p(predt) - np.log1p(y)) / (predt + 1)
def hessian(predt: np.ndarray, dtrain: xgb.DMatrix) -> np.ndarray:
'''Compute the hessian for squared log error.'''
y = dtrain.get_label()
return ((-np.log1p(predt) + np.log1p(y) + 1) /
np.power(predt + 1, 2))
def squared_log(predt: np.ndarray,
dtrain: xgb.DMatrix) -> Tuple[np.ndarray, np.ndarray]:
'''Squared Log Error objective. A simplified version for RMSLE used as
objective function.
'''
predt[predt < -1] = -1 + 1e-6
grad = gradient(predt, dtrain)
hess = hessian(predt, dtrain)
return grad, hess
```

In the above code snippet, `squared_log`

is the objective function we want. It accepts a
numpy array `predt`

as model prediction, and the training DMatrix for obtaining required
information, including labels and weights (not used here). This objective is then used as
a callback function for XGBoost during training by passing it as an argument to
`xgb.train`

:

```
xgb.train({'tree_method': 'hist', 'seed': 1994}, # any other tree method is fine.
dtrain=dtrain,
num_boost_round=10,
obj=squared_log)
```

Notice that in our definition of the objective, whether we subtract the labels from the prediction or the other way around is important. If you find the training error goes up instead of down, this might be the reason.

## Customized Metric Function

So after having a customized objective, we might also need a corresponding metric to
monitor our model’s performance. As mentioned above, the default metric for `SLE`

is
`RMSLE`

. Similarly we define another callback like function as the new metric:

```
def rmsle(predt: np.ndarray, dtrain: xgb.DMatrix) -> Tuple[str, float]:
''' Root mean squared log error metric.'''
y = dtrain.get_label()
predt[predt < -1] = -1 + 1e-6
elements = np.power(np.log1p(y) - np.log1p(predt), 2)
return 'PyRMSLE', float(np.sqrt(np.sum(elements) / len(y)))
```

Since we are demonstrating in Python, the metric or objective need not be a function,
any callable object should suffice. Similar to the objective function, our metric also
accepts `predt`

and `dtrain`

as inputs, but returns the name of the metric itself and a
floating point value as the result. After passing it into XGBoost as argument of `feval`

parameter:

```
xgb.train({'tree_method': 'hist', 'seed': 1994,
'disable_default_eval_metric': 1},
dtrain=dtrain,
num_boost_round=10,
obj=squared_log,
feval=rmsle,
evals=[(dtrain, 'dtrain'), (dtest, 'dtest')],
evals_result=results)
```

We will be able to see XGBoost printing something like:

```
[0] dtrain-PyRMSLE:1.37153 dtest-PyRMSLE:1.31487
[1] dtrain-PyRMSLE:1.26619 dtest-PyRMSLE:1.20899
[2] dtrain-PyRMSLE:1.17508 dtest-PyRMSLE:1.11629
[3] dtrain-PyRMSLE:1.09836 dtest-PyRMSLE:1.03871
[4] dtrain-PyRMSLE:1.03557 dtest-PyRMSLE:0.977186
[5] dtrain-PyRMSLE:0.985783 dtest-PyRMSLE:0.93057
...
```

Notice that the parameter `disable_default_eval_metric`

is used to suppress the default metric
in XGBoost.

For fully reproducible source code and comparison plots, see Demo for defining a custom regression objective and metric.

## Reverse Link Function

When using builtin objective, the raw prediction is transformed according to the objective
function. When a custom objective is provided XGBoost doesn’t know its link function so the
user is responsible for making the transformation for both objective and custom evaluation
metric. For objective with identiy link like `squared error`

this is trivial, but for
other link functions like log link or inverse link the difference is significant.

For the Python package, the behaviour of prediction can be controlled by the
`output_margin`

parameter in `predict`

function. When using the `custom_metric`

parameter without a custom objective, the metric function will receive transformed
prediction since the objective is defined by XGBoost. However, when the custom objective is
also provided along with that metric, then both the objective and custom metric will
recieve raw prediction. The following example provides a comparison between two different
behavior with a multi-class classification model. Firstly we define 2 different Python
metric functions implementing the same underlying metric for comparison,
merror_with_transform is used when custom objective is also used, otherwise the simpler
merror is preferred since XGBoost can perform the transformation itself.

```
import xgboost as xgb
import numpy as np
def merror_with_transform(predt: np.ndarray, dtrain: xgb.DMatrix):
"""Used when custom objective is supplied."""
y = dtrain.get_label()
n_classes = predt.size // y.shape[0]
# Like custom objective, the predt is untransformed leaf weight when custom objective
# is provided.
# With the use of `custom_metric` parameter in train function, custom metric receives
# raw input only when custom objective is also being used. Otherwise custom metric
# will receive transformed prediction.
assert predt.shape == (d_train.num_row(), n_classes)
out = np.zeros(dtrain.num_row())
for r in range(predt.shape[0]):
i = np.argmax(predt[r])
out[r] = i
assert y.shape == out.shape
errors = np.zeros(dtrain.num_row())
errors[y != out] = 1.0
return 'PyMError', np.sum(errors) / dtrain.num_row()
```

The above function is only needed when we want to use custom objective and XGBoost doesn’t know how to transform the prediction. The normal implementation for multi-class error function is:

```
def merror(predt: np.ndarray, dtrain: xgb.DMatrix):
"""Used when there's no custom objective."""
# No need to do transform, XGBoost handles it internally.
errors = np.zeros(dtrain.num_row())
errors[y != out] = 1.0
return 'PyMError', np.sum(errors) / dtrain.num_row()
```

Next we need the custom softprob objective:

```
def softprob_obj(predt: np.ndarray, data: xgb.DMatrix):
"""Loss function. Computing the gradient and approximated hessian (diagonal).
Reimplements the `multi:softprob` inside XGBoost.
"""
# Full implementation is available in the Python demo script linked below
...
return grad, hess
```

Lastly we can train the model using `obj`

and `custom_metric`

parameters:

```
Xy = xgb.DMatrix(X, y)
booster = xgb.train(
{"num_class": kClasses, "disable_default_eval_metric": True},
m,
num_boost_round=kRounds,
obj=softprob_obj,
custom_metric=merror_with_transform,
evals_result=custom_results,
evals=[(m, "train")],
)
```

Or if you don’t need the custom objective and just want to supply a metric that’s not available in XGBoost:

```
booster = xgb.train(
{
"num_class": kClasses,
"disable_default_eval_metric": True,
"objective": "multi:softmax",
},
m,
num_boost_round=kRounds,
# Use a simpler metric implementation.
custom_metric=merror,
evals_result=custom_results,
evals=[(m, "train")],
)
```

We use `multi:softmax`

to illustrate the differences of transformed prediction. With
`softprob`

the output prediction array has shape `(n_samples, n_classes)`

while for
`softmax`

it’s `(n_samples, )`

. A demo for multi-class objective function is also
available at Demo for creating customized multi-class objective function.

## Scikit-Learn Interface

The scikit-learn interface of XGBoost has some utilities to improve the integration with standard scikit-learn functions. For instance, after XGBoost 1.6.0 users can use the cost function (not scoring functions) from scikit-learn out of the box:

```
from sklearn.datasets import load_diabetes
from sklearn.metrics import mean_absolute_error
X, y = load_diabetes(return_X_y=True)
reg = xgb.XGBRegressor(
tree_method="hist",
eval_metric=mean_absolute_error,
)
reg.fit(X, y, eval_set=[(X, y)])
```

Also, for custom objective function, users can define the objective without having to
access `DMatrix`

:

```
def softprob_obj(labels: np.ndarray, predt: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
rows = labels.shape[0]
classes = predt.shape[1]
grad = np.zeros((rows, classes), dtype=float)
hess = np.zeros((rows, classes), dtype=float)
eps = 1e-6
for r in range(predt.shape[0]):
target = labels[r]
p = softmax(predt[r, :])
for c in range(predt.shape[1]):
g = p[c] - 1.0 if c == target else p[c]
h = max((2.0 * p[c] * (1.0 - p[c])).item(), eps)
grad[r, c] = g
hess[r, c] = h
grad = grad.reshape((rows * classes, 1))
hess = hess.reshape((rows * classes, 1))
return grad, hess
clf = xgb.XGBClassifier(tree_method="hist", objective=softprob_obj)
```