There are two different guidelines on using customized loss function in xgboost.
If predicted probability ‘p’ = sigmoid(z)
In https://github.com/dmlc/xgboost/blob/master/demo/guide-python/custom_objective.py 1, line#25 mentions that gradient of customized loss function should be taken w.r.t 'z’
2 . In https://xgboost.readthedocs.io/en/latest/tutorials/custom_metric_obj.html 1, gradient is w.r.t 'p’
Which is correct?
To keep this as general as possible, you need to calculate the gradient of the total loss function w.r.t changing the current predicted values. Normally, your loss function will be of the form $L = \sum_{i=1}^{N} \ell (y_{i}, \hat{y_{i}})$, in which $y_{i}$ is the label of the $i^{th}$ datapoint and $\hat{y_{i}}$ is your prediction (in the binary classification case, you might choose to define it such that $y_{i}$ are the binary labels, and $\hat{y_{i}}$ are the probabilities the classifier assigns to the label being one of the classes).
You then need to calculate $\frac{\partial\ell}{\hat{y_{i}}}\big|{y{i}}$
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I implement a model with a custom training loop and custom loss function. Loss function return a float value. But while calculate gradient tf.gradient(loss,model.trainable_weights), It gives None gradient. I know the issue is way of calculate loss. I tried with custom mse loss. It works fine. I want to implement loss function like count_predition_0's+count_predition_1's/label_0's+label_1's. It's a binary classification problem. I set batch size is 100. So model return 100 batch output. I only consider few batch eg out of 100 batch i only consider or filter it out 40 based on input. Both label and prediction in same shape that is not issue here. That label and prediction pass to custom_loss function.
Notebook link
I have a data-set without labels, but I do have a way to get pairs of examples with opposite labels, that is given a pair x,z I know that their true labels are either 0,1 or 1,0.
So, I am building a model that accepts pairs of samples as input, and learns to classify them with opposite labels. Assuming I have an arbitrary model for predicting a single sample, y_hat = f(x), I am building a model with Keras that accepts pairs of samples (x,z) and outputs pairs of predictions, f(x), f(z). I then use a custom loss function that drives the model towards the correct direction: Given that a regular binary classifier is trained using the Binary Cross Entropy (BCE) to make the predicted and desired output "close", I use the negative BCE. Also, since BCE is not symmetric, I symmetrize it. So, the loss function I give the model.compile method is:
from tensorflow import keras
bce = keras.losses.BinaryCrossentropy()
def neg_sym_bce(y1, y2):
return (- 0.5 * (bce(y1, y2) + bce(y2, y1)))
My problem is, this model fails to learn to classify even a single pair of my data (I get f(x)~=f(z)~=0.5), and if I try to train it with synthetic "easy" data, it takes hundreds of epochs to converge (also on a single pair).
This made me suspect that it has to do with a "vanishing gradient" problem. Indeed, when I plot (see below) the loss for a single pair, which is a function of 2 variables (the 2 outputs), it is evident that there is a wide plateau around the 0.5, 0.5 point. It is also evident that the global minima is, as expected, around the points 0,1 and 1,0.
So, is there a way to deal with the vanishing gradient here? I read about the problem but the references I found deal with vanishing gradient in the network, not in the loss itself.
Or, is there another loss that can drive the model to predict opposite labels?
Think if your labels are always either 0,1 or 1,1 just use categorical_crossentropy for the loss.
I have written my custom training loop using tf.GradientTape(). My data has 2 classes. The classes are not balanced; class1 data contributes almost 80% and class2 contributes remaining 20%. Therefore in order to remove this imbalance I was trying to write custom loss function which will take into account this imbalance and apply the corresponding class weights and calculate the loss. i.e. I want to use the class_weights = [0.2, 0.8]. I am not able to find similar examples.
However all the examples I am seeing are using model.fit approach where its easier to pass the class_weights. I am not able to find out the example which uses class_weights with custom training loop using tf.GradientTape.
I did go through the suggestions of using sample_weight, however I don't have the data where in I can specify the weights for samples, therefore my preference is to use class weight.
I am using BinaryCrossentropy loss as loss function but I want to change the loss based on the class_weights. That's where I am stuck, how to tell BinaryCrossentropy to consider the class_weights.
Is my approach of using custom loss function correct or there is better way to make use of class_weights while training with custom training loop (not using model.fit)?
you can write your own loss function. in that loss function call BinaryCrossentropy and then multiply the result in the weight you want and return that
Here's an implementation that should work for n classes instead of just 2.
For your example of 80:20 split, calculate weights as below (assuming 100 samples in total).
Weight calculation (ref: Handling Class Imbalance: TensorFlow):
weight_class_0 = (1/count_for_class_0) * (total_samples / num_classes) # (80%) 0.625
weight_class_1 = (1/count_for_class_1) * (total_samples / num_classes) # (20%) 2.5
class_wts = tf.constant([weight_class_0, weight_class_1])
Loss function: Requires labels to be sparse and logits unscaled (no activations applied).
# Example logits=[[-3.2, 2.0], [1.2, 0.5], ...], (sparse)labels=[0, 1, ...]
def weighted_sparse_categorical_crossentropy(labels, logits, weights):
loss = tf.nn.sparse_softmax_cross_entropy_with_logits(labels, logits)
class_weights = tf.gather(weights, labels)
return tf.reduce_mean(class_weights * loss)
You can supply this loss function to custom training loops.
I built a CNN model on images one-class classification.
The output tensor is a list which has 65 elements. I make this tensor input to Softmax Function, and got the classified result.
I think the max value in this output tensor is the classified result, why not use this way to do classification task? Just the Softmax Function can be taken the derivative easily?
Softmax is used for multi-class classification. In multi-class class classification the model is expected to classify the input to single class with higher probability. Predicting with high probability enforces probabilities for other classes to be low.
As you stated one of the reason why one uses Softmax over max function is the softmax function is diffrential over Real Numbers and max function is not.
Edit:
There are some other properties of softmax function that makes it suitable to use for neural networks compared to max. Firstly it is soft version of max function. Let's say the logits of neural network has 4 outputs of [0.5, 0.5, 0.69, 0.7]. Hard max returns 1 for maximum index(in this case for 4th index) and 0 for other indexes. This results information loss.
Second important property of softmax is the output of sofmax function are in interval [0,1] and the sum of these values is equal to 1. For this reason the output of softmax function can be interpreted as probability. This means output can be considered as the confidence of the model to classify inputs to one of each output classes.
I'm trying to know which loss function uses XGBoost for multi-class classification. I found in this question the loss function for logistic classification in the binary case.
I had though that for the multi-class case it might be the same as in GBM (for K classes) which can be seen here, where y_k=1 if x's label is k and 0 in any other case, and p_k(x) is the softmax function. However, I have made the first and second order gradient using this loss function and the hessian doesn't match the one defined in the code here (in function GetGradient in SoftmaxMultiClassObj) by a constant 2.
Could you please tell me which is the loss function used?
Thank you in advance.
The loss function used for multiclass is, as you suspect, the softmax objective function. As of now the only options for multiclass are shown in the quote below, the multi:softprob returning all probabilities instead of just those of the most likely class.
“multi:softmax” –set XGBoost to do multiclass classification using the softmax objective, you also need to set num_class(number of classes)
“multi:softprob” –same as softmax, but output a vector of ndata * nclass, which can be further reshaped to ndata, nclass matrix. The result contains predicted probability of each data point belonging to each class.
See https://xgboost.readthedocs.io/en/latest//parameter.html#learning-task-parameters.