Predicting probabilities

Binary classification

By default, VW predictions are in the range [-50, +50] (theoretically any real number, but VW truncates it to [-50, +50]). To convert them to {-1, +1}, use --binary – positive predictions are simply mapped to +1, negative to -1. To convert them to [0, +1], use --link=logistic. This uses the logistic function 1/(1 + exp(-x)). If you use --loss_function=logistic, you can interpret the numbers as probabilities of the +1 class. So to output the probability prediction to a file use --loss_function=logistic --link=logistic -p probs.txt.

(For completeness, to convert the predictions to [-1, +1], use --link=glf1. This uses formula 2/(1 + exp(-x)) - 1, i.e. generalized logistic function with limits of 1.)

Multi-class --oaa

By default in oaa, VW predict the label of the most probable class. To get probabilities for each of the 1..N classes, simply use --oaa N --loss_function=logistic --probabilities -p probs.txt. Logistic link function will be used automatically (you should not specify it with --link) and the numbers (probabilities) will be normalized so they sum up to 1. See example usage in test 109.

When using --probabilities during training (or testing with gold costs available), a multi-class logistic loss is reported in addition to the standard zero-one loss. The option --probabilities is stored in the model, so it does not need (actually cannot) be repeated when testing.

Multi-class csoaa_ldf

For cost-sensitive oaa with label-dependent features, use --csoaa_ldf=mc --loss_function=logistic --probabilities -p probs.txt. See example usage in test 110.

TODO

Add command-line examples here (with input data and expected output) instead of linking tests.