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.

See also the advanced usage example for more information about limitations and workarounds for more complex objetives: Advanced Usage of Custom Objectives

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

\[\frac{1}{2}[\log(pred + 1) - \log(label + 1)]^2\]

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

\[\sqrt{\frac{1}{N}[\log(pred + 1) - \log(label + 1)]^2}\]

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-identity 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:

\[g = \frac{\partial{objective}}{\partial{pred}} = \frac{\log(pred + 1) - \log(label + 1)}{pred + 1}\]

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

\[h = \frac{\partial^2{objective}}{\partial{pred}^2} = \frac{ - \log(pred + 1) + \log(label + 1) + 1}{(pred + 1)^2}\]

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 custom_metric parameter:

xgb.train({'tree_method': 'hist', 'seed': 1994,
           'disable_default_eval_metric': 1},
          dtrain=dtrain,
          num_boost_round=10,
          obj=squared_log,
          custom_metric=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 identity 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 receive 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. Also, see Intercept for some more explanation.

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)