Hastie, Tibshirani and Friedman (2009), The Elements of Statistical
Learning, 2nd ed., Springer, Section 2.8.3, book p. 36 (PDF p. 55):
f_theta(x) = sum_m beta_m sigma(alpha_m' x + b_m) (2.45), where
sigma(x) = 1/(1 + e^-x) is the activation function.
Usage
Nnet1lay(X, alpha, b, beta = NULL, y = NULL)
Arguments
- X
N-by-p design.
- alpha
p-by-M matrix whose columns are the directions alpha_m.
- b
M-vector of bias terms.
- beta
optional M-vector of output weights.
- y
optional N-vector; refits beta by least squares.
Value
list: estimate, fitted, hidden, beta, rss, n, p, M, method.
Details
With alpha and b fixed this is a linear basis expansion, so given y the
output weights beta follow in closed form by least squares on the hidden
activations; alpha and b are inputs rather than being invented.
Examples
Nnet1lay(cbind(c(0, 0)), cbind(c(1)), 0, beta = 2)$fitted
#> [1] 1 1
