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.
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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). |
beta |
The estimated parameter b. |
s |
The value of s. |
impmin |
The value of impmin. |
K |
The value of K. |
Pierre Alquier <alquier@ensae.fr>
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.
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