# automatic statistician (wip)

*27 February 2017*

notes on (Duvenaud, Lloyd, Grosse, Tenenbaum, & Ghahramani, n.d.) and (Lloyd, Duvenaud, Grosse, Tenenbaum, & Ghahramani, 2014).
these papers are part of the automatic statistician project.

## summary

understanding: 5/10

code: https://github.com/jamesrobertlloyd/gp-structure-search, https://github.com/jamesrobertlloyd/gpss-research

the problem: find good kernels for GPs.

kernels are closed under addition and multiplication.
we form a generative grammar for kernel construction:
\begin{align}
\mathcal S &\to \mathcal S + \mathcal B \\
\mathcal S &\to \mathcal S \times \mathcal B \\
\mathcal B &\to \mathcal B’
\end{align}
where is a subexpression (e.g. ) and is a base kernel; one of (exponentiated square difference), (periodic), (linear), (rational quadratic).

how do we search over expressions?
we use greedy search: at each stage, we choose the highest scoring kernel and expand it by applying all possible operators.

how do we score kernels?
using the bayesian information criterion:
\begin{align}
\mathrm{BIC}(M) = -2 \log p(D \given M) + |M| \log n.
\end{align}
here, is kernel, is data, is number of data points is number of kernel parameters, is the evidence.

? this is some sort of approximation to if we had a prior on .

## references

- Duvenaud, D., Lloyd, J. R., Grosse, R., Tenenbaum, J. B., & Ghahramani, Z. Structure Discovery in Nonparametric Regression through Compositional Kernel Search. In
*30th International Conference on Machine Learning (June 2013)*. International Machine Learning Society.
@inproceedings{duvenaud2013structure,
title = {Structure Discovery in Nonparametric Regression through Compositional Kernel Search},
author = {Duvenaud, David and Lloyd, James Robert and Grosse, Roger and Tenenbaum, Joshua B and Ghahramani, Zoubin},
booktitle = {30th International Conference on Machine Learning (June 2013)},
organization = {International Machine Learning Society}
}

- Lloyd, J. R., Duvenaud, D., Grosse, R., Tenenbaum, J., & Ghahramani, Z. (2014). Automatic Construction and Natural-Language Description of Nonparametric Regression Models. In
*Twenty-Eighth AAAI Conference on Artificial Intelligence*.
@inproceedings{lloyd2014automatic,
title = {Automatic Construction and Natural-Language Description of Nonparametric Regression Models},
author = {Lloyd, James Robert and Duvenaud, David and Grosse, Roger and Tenenbaum, Joshua and Ghahramani, Zoubin},
booktitle = {Twenty-Eighth AAAI Conference on Artificial Intelligence},
year = {2014}
}

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