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Binary Classifier:

Assuming I have built a binary classifier and decided on an operating point. And made the classifier live on production data. This classifier returns the probability score for each of the two classes.

Is it safe to say, for production/out-of-sample instances where the classifier returns a probability score close to the operating point, the classifier is confused for those instances?

Moreover, if the I collect those instances where the classifier scores are close to the operating point. And compare it with my training data. There could be two cases:

  1. The "confusing" instances have significantly different distribution as opposed to the training data. In which case, my classifier is not faulty. And If possible I should manually label these instances and refit the classifier.

  2. The "confusing" instances have similar distribution to my training data. In which case my classifier is at fault. What could be the implications of this case? But I believe this case would have been captured while training itself. Such instances would be very less in cardinality.

If the above mentioned thought process is correct. How can we extend this to multi-class classifier?

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The more accurate term would be "uncertain", but you are correct in your line of thought. Your classifier (based on learned or engineered features distributions) can't determine with certainty which class to assign to this merginal cases. It isn't necessary a case where they have a completely different distribution, more likelely that they are part of the same distribution but are located on its tail close to the tail of the distribution of the Second class (think 2 gaussians that at some area share similar density values).

Depending on the amount of such cases, you should examine them and attempt to trace the source of confusion. Maybe some clever preprocessing could help or different features (and maybe these are just outliers).

In the multi class case, you would probably get similar behavior, but each time on a subset of all classes. I.E. the model is certain that the sample is one of 2-3 classes (out of 10 total classes for example) but it can't be certain from which specific class. So you will get probabilities of similar values for these classes and very small probabilities for the rest.

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  • $\begingroup$ Thanks for highlighting the overlapping tail case. $\endgroup$
    – swe
    Dec 24 '18 at 7:08

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