# Training function of Sparse Additive Logistic Regression

### Description

The logistic model is learned using training data.

### Usage

1 2 |

### Arguments

`X` |
The |

`y` |
The |

`p` |
The number of baisis spline functions. The default value is 3. |

`lambda` |
A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care. Do not supply a single value for lambda. Supply instead a decreasing sequence of lambda values. samLL relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit. |

`nlambda` |
The number of lambda values. The default value is 20. |

`lambda.min.ratio` |
Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default is 0.1. |

`thol` |
Stopping precision. The default value is 1e-5. |

`max.ite` |
The number of maximum iterations. The default value is 1e5. |

### Details

We adopt various computational algorithms including the block coordinate descent, fast iterative soft-thresholding algorithm, and newton method. The computation is further accelerated by "warm-start" and "active-set" tricks.

### Value

`p` |
The number of baisis spline functions used in training. |

`X.min` |
A vector with each entry corresponding to the minimum of each input variable. (Used for rescaling in testing) |

`X.ran` |
A vector with each entry corresponding to the range of each input variable. (Used for rescaling in testing) |

`lambda` |
A sequence of regularization parameter used in training. |

`w` |
The solution path matrix ( |

`df` |
The degree of freedom of the solution path (The number of non-zero component function) |

`knots` |
The |

`Boundary.knots` |
The |

`func_norm` |
The functional norm matrix ( |

### Author(s)

Tuo Zhao, Xingguo Li, Han Liu, Kathryn Roeder

Maintainers: Tuo Zhao<tourzhao@gmail.com>

### References

P. Ravikumar, J. Lafferty, H.Liu and L. Wasserman. "Sparse Additive Models", *Journal of Royal Statistical Society: Series B*, 2009.

T. Zhao and H.Liu. "Sparse Additive Machine", *International Conference on Artificial Intelligence and Statistics*, 2012.

### See Also

`SAM`

,`plot.samLL,print.samLL,predict.samLL`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
## generating training data
n = 200
d = 100
X = 0.5*matrix(runif(n*d),n,d) + matrix(rep(0.5*runif(n),d),n,d)
y = sign(((X[,1]-0.5)^2 + (X[,2]-0.5)^2)-0.06)
## flipping about 5 percent of y
y = y*sign(runif(n)-0.05)
y = sign(y==1)
## Training
out.trn = samLL(X,y)
out.trn
## plotting solution path
plot(out.trn)
## generating testing data
nt = 1000
Xt = 0.5*matrix(runif(nt*d),nt,d) + matrix(rep(0.5*runif(nt),d),nt,d)
yt = sign(((Xt[,1]-0.5)^2 + (Xt[,2]-0.5)^2)-0.06)
## flipping about 5 percent of y
yt = yt*sign(runif(nt)-0.05)
yt = sign(yt==1)
## predicting response
out.tst = predict(out.trn,Xt)
``` |