i have a classification problem where i am predicting likelihood of client defaulting on loan. i plotted the predicted probabilities from my model, and then plotted against the label '1' for default or 0 for non-default.

enter image description here

it is cut out here but y axis is the density. am i right to reason that this shows an exponential distribution, or that the fact the class 1 curve has a fat tail it shows that default is an extreme / unexpected event? woud you say class 1 is following any type of distribution?

compare this to the below:

enter image description here

doesn't the second graph show that the model isn't that good at distinguishing between class 0 and class 1?


In both graph it show that the model will not perform very well on the classification task as the probability distribution of the model overlaps significantly. A good model will have almost seperated curve for each class. Adding more feature will help the model differentiate between curves.

  • $\begingroup$ but can you comment on anything about the likelihood of default, could you say it suggests defaults are extreme $\endgroup$ – Maths12 Jul 1 '20 at 9:48
  • $\begingroup$ Except near the peak of green curve the default will be red class as it has fat tail $\endgroup$ – SrJ Jul 1 '20 at 9:54
  • $\begingroup$ does this indicate a imbalanced problem or not? $\endgroup$ – Maths12 Jul 1 '20 at 10:38
  • $\begingroup$ Yeah partly. But your model should be trained with more dimensions or more differentiable feature so that it can distinguish $\endgroup$ – SrJ Jul 1 '20 at 11:00
  • $\begingroup$ sorry to add do both plots indicate imbalcned probem? what does area under the kde show? $\endgroup$ – Maths12 Jul 1 '20 at 11:01

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