Wikipedia:Reference desk/Archives/Mathematics/2018 July 1

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

July 1

"If you disagree, you're probably both wrong in the same direction" in ensemble learning

I've tried to ask this question before, but I don't think I worded it clearly, so I'm trying again. What ensemble learning models, if any, could make inferences that would translate in English to ones like the following?

• "Model A says you probably voted for Donald Trump, and Model B says you voted for Hillary Clinton. But if you were a Trump voter or a Clinton voter, then the training data says both models would almost certainly agree about that; and most of the voters whom A and B disagree about in our training data, actually voted for Gary Johnson."
• "Estimator A says X is 50 ± 2. Estimator B says X is 60 ± 3. But when their estimates are incompatible, they're usually both too low, and in this case the ensemble estimate is 75 ± 10."

NeonMerlin 00:17, 1 July 2018 (UTC)

Good question. I'm not too sure of the answer.

You could assign a prior probability to each of models A and B, $P(X)$ where X denotes A or B.

Then update the probabilities using Bayes's theorem $P(X|data)={\frac {P(data|X)P(X)}{P(data|A)P(A)+P(data|B)P(B)}}$

Then calculate a probability that you voted for Johnson (J), say, weighting the prediction of each model with the probability of each model. $P(J)=P(J|A)P(A|data)+P(J|B)P(B|data)$. This could be regarded as an "ensemble model".

Now suppose, for example, $P(T|A)>P(J|A)>P(C|A)$ and $P(C|B)>P(J|B)>P(T|B)$. Neither model predicts voting for Johnson. But it's possible the ensemble model does... maybe. I don't know. I'm not sure how the ensemble model would converge as you gather more data points; it's worth investigating at some point. I apologise if my answer is useless. PeterPresent (talk) 06:03, 2 July 2018 (UTC)