Ensemble methods; mixing predictions from simple learners to get sophisticated predictions.

Fast to train, fast to use. Gets you results. May not get you answers. So, like neural networks but from the previous hype cycle.

Jeremy Kun: Why Boosting Doesn’t Overfit:

Boosting, which we covered in gruesome detail previously, has a natural measure of complexity represented by the number of rounds you run the algorithm for. Each round adds one additional “weak learner” weighted vote. So running for a thousand rounds gives a vote of a thousand weak learners. Despite this, boosting doesn’t overfit on many datasets. In fact, and this is a shocking fact, researchers observed that Boosting would hit zero training error, they kept running it for more rounds, and the generalization error kept going down! It seemed like the complexity could grow arbitrarily without penalty. […] this phenomenon is a fact about voting schemes, not boosting in particular.

## Questions

- In a different context, I’ve run into model averaging; How does this relate to voting algorithms?
- How do you phrase ensemble algorithms in a Bayesian context? If it were Bayesian model averaging, this would be easy, but where the learners are all ill-posed?

## Randoms trees, forests, jungles

- Awesome Random Forests
- how to do machine vision using random forests brought to you by the folks behind Kinect.

## Implementations

## Refs

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- Balog, M., & Teh, Y. W.(2015) The Mondrian Process for Machine Learning.
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- CrSK11
- Criminisi, A., Shotton, J., & Konukoglu, E. (2011) Decision Forests for Classification, Regression, Density Estimation, Manifold Learning and Semi-Supervised Learning (No. MSR-TR-2011-114). . Microsoft Research
- CrSK12
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*The Annals of Statistics*, 28(2), 337–407. DOI. - GaLe13
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- JoZh14
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*IEEE Transactions on Pattern Analysis and Machine Intelligence*, 36(5), 942–954. DOI. - LaRT14
- Lakshminarayanan, B., Roy, D. M., & Teh, Y. W.(2014) Mondrian Forests: Efficient Online Random Forests. In Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, & K. Q. Weinberger (Eds.), Advances in Neural Information Processing Systems 27 (pp. 3140–3148). Curran Associates, Inc.
- RaRe09
- Rahimi, A., & Recht, B. (2009) Weighted Sums of Random Kitchen Sinks: Replacing minimization with randomization in learning. In Advances in neural information processing systems (pp. 1313–1320). Curran Associates, Inc.
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*The Annals of Statistics*, 26(5), 1651–1686. DOI. - Scor14
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- Scornet, E., Biau, G., & Vert, J.-P. (2014) Consistency of Random Forests.
*arXiv:1405.2881 [math, Stat]*. - SSKN13
- Shotton, J., Sharp, T., Kohli, P., Nowozin, S., Winn, J., & Criminisi, A. (2013) Decision Jungles: Compact and Rich Models for Classification. In Proc. NIPS.