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July 1

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

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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)[reply]

Good question. I'm not too sure of the answer.
You could assign a prior probability to each of models A and B, where X denotes A or B.
Then update the probabilities using Bayes's theorem
Then calculate a probability that you voted for Johnson (J), say, weighting the prediction of each model with the probability of each model. . This could be regarded as an "ensemble model".
Now suppose, for example, and . 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)[reply]