eRum 2020

# Ultra fast penalized regressions with package {bigstatsr}

## e-Rum 2020

### Florian Privé (@privefl)
#### postdoc in *Predictive Human Genetics*

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## {bigstatsr} uses memory-mapping

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## Penalized linear regression

with **lasso** ( `$\alpha=1$` ) or **elastic-net** regularization ( `$0 < \alpha < 1$` )

`$$L(\lambda, \alpha) = \underbrace{ ||y - X \beta||_2^2 }_\text{Loss function} + \underbrace{ \lambda \left( \alpha \|\beta\|_1 + (1-\alpha) \frac{\|\beta\|_2^2}{2}  \right) }_\text{Penalisation}$$`

Two hyper-parameters in this model:

- `$\lambda$`

- `$\alpha$`

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## Science and Implementation

### behind the penalized regression framework of {bigstatsr}

- Mostly implemented in **C++**

- Use **strong rules** to discard variables a priori

- Use **early-stopping** to avoid fitting costly models

- Process the hyper-parameter **grid in parallel** (memory-mapping makes it easy and efficient)

.footnote[Strong rules: DOI: [10.1111%2Fj.1467-9868.2011.01004.x](https://doi.org/10.1111/j.1467-9868.2011.01004.x)]

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## Predicting common diseases from genetics

15K `$\times$` 280K (30 GB) in **a few minutes**

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## Predicting height from genetics

350K `$\times$` 560K (1.4 TB) in **one day**

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# package {bigstatsr}
# makes it possible 
# to fit penalized regressions
# on 100s of GB of data

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## Scientific publications

- {bigstatsr}: to be used by any field of research

- {bigsnpr}: algorithms specific to my field of research, Human Genetics

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## Contributions are welcome!

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# Thanks!

#### Go check the package website and the vignette!

[privefl](https://twitter.com/privefl) &nbsp;&nbsp;&nbsp;&nbsp; [privefl](https://github.com/privefl) &nbsp;&nbsp;&nbsp;&nbsp; [F. Privé](https://stackoverflow.com/users/6103040/f-priv%c3%a9)