---
title: "SuSiE with L0Learn initialization example"
author: "Kaiqian Zhang"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{SuSiE with L0Learn initialization example}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE,comment = "#")
```

`susieR` allows for a customized initialization. In this vignette we
deomonstrate how to use
[`L0Learn`](https://github.com/hazimehh/L0Learn) fit to initialize
susieR.

```{r, warning=FALSE}
library(susieR)
library(L0Learn)
```

## Simulate data

First, we simulate data from the minimal example.

```{r}
set.seed(1)
n = 1000
p = 1000
beta = rep(0,p)
beta[c(1,2,300,400)] = 1
X = matrix(rnorm(n*p),nrow=n,ncol=p)
y = X %*% beta + rnorm(n)
```

## Fit L0Learn 

We start with fitting a L0-regularized model to the simulated data. 

```{r}
set.seed(1)
L0fit = L0Learn.cvfit(X, y, penalty = "L0")
```

Let's choose the penalty strength parameter that minimizes the
cross-validation error.

```{r}
lambdaIndex = which.min(L0fit$cvMeans[[1]]) 
L0coef = as.numeric(coef(L0fit$fit, lambda = L0fit$fit$lambda[[1]][lambdaIndex]))
effect.beta = L0coef[which(L0coef!=0)][-1]
effect.index = (which(L0coef!=0)-1)[-1] 
length(effect.beta)
effect.beta[1:10]
effect.index[1:10]
```

The L0Learn model finds `r length(effect.beta)` effects, which will be
used to initialize susie.

## Build an initialization object

We create an initialization from `l0learn` coefficients using
`susie_init_coef` function,

```{r}
set.seed(1)
s.init = susie_init_coef(effect.index, effect.beta, p)
```

## Run susieR with initialization

Now, we use `effect.index` and `effect.beta` obtained from L0Learn fit
to create an `s.init` object. We then run susie with this
initialization.

```{r}
susieL0.fit = susie(X,y,model_init=s.init)
susieL0.fit$sets$cs
```

## References

1. Hussein Hazimeh and Rahul Mazumder. (2018). Fast Best Subset
Selection: Coordinate Descent and Local Combinatorial Optimization
Algorithms.