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Which is the best loss function for MSE?
The Huber Loss Function. The Huber Loss offers the best of both worlds by balancing the MSE and MAE together. We can define it using the following piecewise function: What this equation essentially says is: for loss values less than delta, use the MSE; for loss values greater than delta, use the MAE.
Is the MSE loss function for logistic regression convex?
Now we mathematically show that the MSE loss function for logistic regression is non-convex. For simplicity, let’s assume we have one feature “x” and “binary labels” for a given dataset.
When to use MSE or Mae in machine learning?
What this equation essentially says is: for loss values less than delta, use the MSE; for loss values greater than delta, use the MAE. This effectively combines the best of both worlds from the two loss functions! Using the MAE for larger loss values mitigates the weight that we put on outliers so that we still get a well-rounded model.
Why is MSE not good for binary classification?
Here we have shown that MSE is not a good choice for binary classification problems. But the same can be extended for multi-class classification problems given that target values are one-hot encoded. MSE and problem of Non-Convexity in Logistic Regression.
Why do we use Mae for larger loss values?
Using the MAE for larger loss values mitigates the weight that we put on outliers so that we still get a well-rounded model. At the same time we use the MSE for the smaller loss values to maintain a quadratic function near the centre. This has the effect of magnifying the loss values as long as they are greater than 1.
Which is the output of the loss function?
The output of the loss function is called the loss which is a measure of how well our model did at predicting the outcome. A high value for the loss means our model performed very poorly. A low value for the loss means our model performed very well.
How does the MSE assess the quality of a predictor?
The MSE assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable ), or an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).