Training function of Sparse Additive Logistic Regression

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Description

The logistic model is learned using training data.

Usage

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samLL(X, y, p=3, lambda = NULL, nlambda = NULL, 
lambda.min.ratio = 0.1, thol=1e-5, max.ite = 1e5)

Arguments

X

The n by d design matrix of the training set, where n is sample size and d is dimension.

y

The n-dimensional label vector of the training set, where n is sample size. Labels must be coded in 1 and 0.

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 (d*p+1 by length of lambda) with each column corresponding to a regularization parameter. Since we use the basis expansion with the intercept, the length of each column is d*p+1.

df

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

knots

The p-1 by d matrix. Each column contains the knots applied to the corresponding variable.

Boundary.knots

The 2 by d matrix. Each column contains the boundary points applied to the corresponding variable.

func_norm

The functional norm matrix (d by length of lambda) with each column corresponds to a regularization parameter. Since we have d input variabls, the length of each column is d.

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

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## 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)