Question about the paper (Bayesian rule)

[Alexander Zhang]

The paper is neat and novel compared to active learning, which only focuses on the unlabeled scenario. However, I cannot understand the Bayesian process. In my understanding, it should be:

Thank you for your valuable advice!

[Zichun Yu]

Yeah, I am also curious about it. Can you explain it? Thank you!

[SoerenMind]

Hi, What you wrote down is Starting with Bayes rule: P(A | B) = P(B | A)*P(A) / P(B) Maybe the easiest way to understand it is by first considering a simplified version of the problem in a setting without any x or D_t: P(y_ho | y) = P(y | y_ho)*P(y_ho) / P(y) Importantly in the above you can condition on some variable V. V does nothing except stay in the conditional everywhere: P(y_ho | y, V) = P(y | y_ho, V)*P(y_ho | V) / P(y | V) (You could alternatively write P(y_ho | y, V) = P(y, V | y_ho)*P(y_ho) / P(y, V). I think what you did is some variant of that. This is correct and the line above is also correct.) In our case that variable V is V = x, x_ho, Dt so we can substitute it in: P(y_ho | y, Dt, x, x_ho) = P(y | y_ho, x, x_ho, Dt)*P(y_ho | x, x_ho, Dt) / P(y | x, x_ho, Dt) Sorry if I made any mistakes in writing this, it happens easily with so many variables. Best, Sören

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[Alexander Zhang]

Thank you for your detailed answer, I think i can figure out what it means. Great job & work for online data selection.