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Given a multiclass classification model, with n features, how can I measure the uncertainty of the model for that particular classification?

Let's say that for some class the model accuracy is amazing, but for another it's not. I would like to find a metric that will let me decide if, for a particular sample, I would like to "listen" to the model or not.

I thought about using prediction intervals, but am not sure how to calculate them.

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Alternatively to the accepted answer, another way to estimate the uncertainty of a specific prediction is to combine the probabilities returned by the model for each class using a certain function. This is a common practice in "Active learning", where given a trained model you select a subset of unlabelled instances to label (to augment the initial training dataset) based on some sort of uncertainty estimation. The three most common functions used (called sampling strategies [1] in the literature) are:

  • Shannon entropy: you simply apply Shannon entropy to the probabilities returned by the model for each class. The highest the entropy the highest the uncertainty.

  • Least confident: you simply look at the highest probability returned by the model among all classes. Intuitively the certainty level is lower for a test instance with a 'low' highest probability (e.g. [.6, .35, .05] --> .6) compared to a 'high' highest probability (eg. [.9, .05, .05] --> .9).

  • Margin Sampling: you subtract form the highest probability the second-highest probability (e.g. [.6, .35, .05] --> .6-.35=.25). It is conceptually similar to the least confident strategy, but a bit more reliable since you're looking at the distance between two probabilities rather than a single raw value. Also, in this case, a small difference means a high uncertainty level.

Another more interesting way to estimate the uncertainty level for a test instance that is applicable to deep models with dropout layers is instead deep active learning [2]. Basically, by leaving dropout active while doing predictions you can bootstrap a set of different outcomes (in terms of probabilities for each class) from which you can estimate mean and variance. The variance, in this case, tells you how much the model is uncertain about that instance.

Anyway, consider that these are just crude approximations, using a model that specifically estimates the uncertainty of a particular prediction as suggested in the accepted answer is surely the best option. Nevertheless, these estimations can be useful because they are potentially applicable to every model that returns probabilities (and there are also adaptations for models like SVM).

[1] http://www.robotics.stanford.edu/~stong/papers/tong_thesis.pdf

[2] https://arxiv.org/abs/1808.05697

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In the model, you will decide how best to get uncertainty. If you used Bayesian optimization (that's a great package for it in Python), for example, you get a covariance matrix along with your expected values, and so inherently get an uncertainty measure. In this case, you can make predictions as to the underlying function of your data, and the (co-)variance will provide levels of uncertainty, as shown by the width of the green bands around the line below:

enter image description here

So the red points show where we have some sample data... notice that we have none e.g. at X = 4 and X = -1, which is why we have high uncertainty; the 95% confidence interval is very large.


If you use a standard deep neural network TPO perform classification, for example, there is no inherent measure of uncertainty. All you really have is your test accuracy, to let you know how well the model performs on hold-out data. I cannot remember where it is explained, but I believe it is not actually feasible to interpret the class prediction values in terms of uncertainty.

For example, if you are predicting cat or dog for an image, and the two classes receive (normalized) logit values [0.51, 0.49] respectively, you cannot assume this means very low certainty.

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Though it does not exactly measure uncertainty for a classification model, you can give a look at trust scores.

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My answer is wrong, but I keep it because other people may make my mistake and the comments below my answer are valuable

I think you looking for

model.predict_prob()

in python lots of models have it. and with this function, you can calculate how strong the model sure about its answer.

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    $\begingroup$ Given a sample , you receive a array of probabilities from the model , the real label is X and the model tells you that in probability of 0.73 it is X , how do you compare it to other samples or other classes? probability is not a measure of certainty $\endgroup$
    – Latent
    Jul 29 '18 at 7:22
  • $\begingroup$ if you convert your label to dummy variable you can see the probability for each class. $\endgroup$
    – parvij
    Jul 29 '18 at 10:32
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    $\begingroup$ Probability not equal uncertainty $\endgroup$
    – Latent
    Jul 29 '18 at 11:00
  • $\begingroup$ model.predict_prob() will give you the expected probabilty, but for a given probabilty you might have a higher variance (in other words a higher uncertainty). $\endgroup$
    – Tanguy
    Jun 16 '21 at 21:31

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