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You are given two arrays, one with predicted scores from a logistic regression based classifier and another with true class labels. Note that, the scores from the classifier can be converted to the conditional probability of the class label being 1 given an input x using the sigmoid function (defined below for your reference). Given a threshold value t, we consider the predicted value to be 1 if the predicted probability is greater than t and 0 otherwise. You need to write a function to compute accuracy, precision and recall of the classifier, given a threshold.

For reference, here are the definitions of accuracy, precision and recall and here is the definition of the sigmoid function.

In other words, Accuracy: fraction of data points where the predicted label and the true label agree relative to all data points. Precision: fraction of data points where the predicted label and the true label agree relative to data points where the predicted label is 1. Recall: fraction of data points where the predicted label and the true label agree relative to data points where the true label is 1.

Finally, given a score s, we get the P(=1x)=11+esP(label=1x)=1+es1 (i.e. the sigmoid function)

• [execution time limit] 4 seconds (py)

• [input] array.float scores

  Predicted scores from the logistic regression based classifier

• [input] array.integer binary_labels

  True labels (each entry is either 1 or 0)

• [input] float threshold

  Threshold probability

• [output] array.float

  Array of length 3 where the first index is accuracy, second index is precision, third index is recall