Our analysis sheds light on the behavior of that loss function and explains its superior performance on binary labeled data over data with graded relevance. In particular, we show that ListNet's loss bounds Mean Reciprocal Rank as well as Normalized Discounted Cumulative Gain. If you’re working on a classification problem where there are more than two prediction outcomes, however, sparse categorical cross-entropy is a more suitable loss function. In our churn example, we were predicting one of two outcomes: either a customer will churn or not. In fact, we establish an analytical connection between softmax cross entropy and two popular ranking metrics in a learning-to-rank setup with binary relevance labels. Binary cross-entropy is most useful for binary classification problems. In this work, however, we show that the above statement is not entirely accurate. This loss was designed to capture permutation probabilities and as such is considered to be only loosely related to ranking metrics. In fact, we establish an analytical connection between softmax cross entropy and two popular ranking metrics in a learning-to-rank setup with binary relevance. Because of this even if the predicted values are equal to the actual values your loss will not be equal to 0. One such loss ListNet's which measures the cross entropy between a distribution over documents obtained from scores and another from ground-truth labels. Logistic Regression: Can fit either a line, or polynomial with sigmoid activation minimizing the binary cross-entropy loss for each datapoint. Binary cross entropy loss assumes that the values you are trying to predict are either 0 and 1, and not continuous between 0 and 1 as in your example. This gap has given rise to a large body of research that reformulates the problem to fit into existing machine learning frameworks or defines a surrogate, ranking-appropriate loss function. One of the challenges of learning-to-rank for information retrieval is that ranking metrics are not smooth and as such cannot be optimized directly with gradient descent optimization methods.
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