# bridge.EM: Bridge Regression - Expectation Maximization In BayesBridge: Bridge Regression

## Description

Expectation Maximization for bridge regression.

## Usage

 ```1 2 3 4 5``` ```bridge.EM (y, X, alpha=0.5, ratio=1.0, lambda.max=1e9*ratio, tol=1e-9, max.iter=30, use.cg=FALSE, ret.solves=FALSE) bridge.EM.R(y, X, alpha, ratio=1.0, lambda.max=1e9*ratio, tol=1e-9, max.iter=30, init=NULL) ```

## Arguments

 `y` An N dimensional vector of data. `X` An N x P dimensional design matrix. `ratio` The ratio tau/sigma. `alpha` A parameter. `lambda.max` A cut-off used to determine when a variable vanishes. `tol` The threshold at which the algorithm terminates. `max.iter` The maximum number of iterations to use. `use.cg` Use the conjugate gradient method. `ret.solves` Return the number of times a linear system is solved. `init` Initial value.

## Details

Bridge regression is a regularized regression in which the regression coefficient's prior is an exponential power distribution. Specifically, inference on the regression coefficient beta is made using the model

y = X β + ε, ε \sim N(0, σ^2 \; I),

p(β) \propto \exp(∑_j -(|β_j|/τ)^{α}).

This procedure calculates the posterior mode of beta, given ratio=τ/σ and alpha using the expectation maximization algorithm.

## References

Nicolas G. Poslon, James G. Scott, and Jesse Windle. The Bayesian Bridge. http://arxiv.org/abs/1109.2279.

`bridge.reg`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# Load the diabetes data... data(diabetes, package="BayesBridge"); cov.name = colnames(diabetes\$x); y = diabetes\$y; X = diabetes\$x; # Center the data. y = y - mean(y); mX = colMeans(X); for(i in 1:442){ X[i,] = X[i,] - mX; } # Expectation maximization. bridge.EM(y, X, 0.5, 1.0, 1e8, 1e-9, 30, use.cg=TRUE); ```

### Example output

```Using conjugate gradient method.
age         sex         bmi         map          tc         ldl
-9.784325 -239.774890  519.864326  324.296617 -788.022455  473.628865
hdl         tch         ltg         glu
98.900975  176.127557  749.828649   67.542089
```

BayesBridge documentation built on May 29, 2017, 10:40 a.m.