Iterative Selection of Blocks of Features - isbf

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Description

isbfperforms estimation in the model Y = b + e where the unknown parameter b is sparse, or sparse and constant by blocks. Y is a vector of size p, b a vector of size p and e is the noise.

When b is sparse and constant by blocks, one can use isbf(Y,K=...) where K is the expected maximal size for a block. The method used is Iterative Selection of Blocks of Features procedure of Alquier (2010). When b is only sparse, one can use isbf(Y), as the default value for K is 1. Of course, one can always set K=p, but be careful, the computation time and the memory used is directly proportional to p*K.

NOTE: one can used isbfReg(X,Y) with X the identity matrix instead, but isbf(Y) is really faster.

Usage

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isbf(Y, epsilon = 0.05, K = 1, impmin = 1/100,
s = NULL, v = NULL)

Arguments

Y

The data. A vector of size p.

epsilon

The confidence level. The theoretical guarantees in Alquier (2010) is that each iteration of the ISBF procedure gets closer to the real parameter b with probability at least 1-epsilon. When epsilon is very small, the procedure becomes very conservative. When epsilon is too large, there is a risk of overfitting. If not specified, epsilon = 5%.

K

The maximal length of blocks. If not specified, K=1, this means we seek for a sparse (not constant by block) parameter b. One should take a larger K is b is really expected to be constant by blocks. If p is quite small (up to 1000), K=p is a reasonnable choice. For larger values of p, please take into account that the computation time and the memory used is directly proportional to p*K.

impmin

Criterion for the end of the iterations. When no more iteration can provide an improvement of Xb larger than impmin, the algorithm stops. If not speficied, impmin=1/100.

s

The threshold used in the iterations. If not specified, the theoretical value of Alquier (2010) is used: s = sqrt(2*v*log(p*K/epsilon)).

v

The variance of e, if it is known. If not specified, estimated on the data (by a MA(10)-smoothing).

Value

beta

The estimated parameter b.

s

The value of s.

impmin

The value of impmin.

K

The value of K.

Author(s)

Pierre Alquier <alquier@ensae.fr>

References

P. Alquier, An Algorithm for Iterative Selection of Blocks of Features, Proceedings of ALT'10, 2010, M. Hutter, F. Stephan, V. Vovk and T. Zeugmann Eds., Lecture Notes in Artificial Intelligence, pp. 35-49, Springer.

Examples

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# generating data
b = c(rep(0,100),rep(2,40),rep(0,60))
e = rnorm(200,0,0.3)
Y = b + e

# call of isbf
A = isbf(Y,K=200,v=0.3)

# visualization of the results
plot(Y)
lines(A$beta,col="red")