do.lasso | R Documentation |
LASSO is a popular regularization scheme in linear regression in pursuit of sparsity in coefficient vector that has been widely used. The method can be used in feature selection in that given the regularization parameter, it first solves the problem and takes indices of estimated coefficients with the largest magnitude as meaningful features by solving
\textrm{min}_{β} ~ \frac{1}{2}\|Xβ-y\|_2^2 + λ \|β\|_1
where y is response
in our method.
do.lasso(X, response, ndim = 2, lambda = 1)
X |
an (n\times p) matrix whose rows are observations and columns represent independent variables. |
response |
a length-n vector of response variable. |
ndim |
an integer-valued target dimension. |
lambda |
sparsity regularization parameter in (0,∞). |
a named Rdimtools
S3 object containing
an (n\times ndim) matrix whose rows are embedded observations.
a length-ndim vector of indices with highest scores.
a (p\times ndim) whose columns are basis for projection.
name of the algorithm.
Kisung You
tibshirani_regression_1996Rdimtools
## generate swiss roll with auxiliary dimensions ## it follows reference example from LSIR paper. set.seed(1) n = 123 theta = runif(n) h = runif(n) t = (1+2*theta)*(3*pi/2) X = array(0,c(n,10)) X[,1] = t*cos(t) X[,2] = 21*h X[,3] = t*sin(t) X[,4:10] = matrix(runif(7*n), nrow=n) ## corresponding response vector y = sin(5*pi*theta)+(runif(n)*sqrt(0.1)) ## try different regularization parameters out1 = do.lasso(X, y, lambda=0.1) out2 = do.lasso(X, y, lambda=1) out3 = do.lasso(X, y, lambda=10) ## visualize opar <- par(no.readonly=TRUE) par(mfrow=c(1,3)) plot(out1$Y, main="LASSO::lambda=0.1") plot(out2$Y, main="LASSO::lambda=1") plot(out3$Y, main="LASSO::lambda=10") par(opar)
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