rdetools (version 1.0)

estnoise: Estimate noise level

Description

Estimates the noise level for a label vector 'y' and a denoised version of this label vector 'yh'. Which loss function is used to estimate the noise level depends on the kind of problem (regression problem or classification problem).

Usage

estnoise(y, yh, regression = FALSE, nmse = TRUE)

Arguments

y

a label vector containg only -1 and 1 for a classification problem, and real numbers in case of regression

yh

a denoised version of y which can be obtained by using e.g. rde

regression

FALSE in case of a classification problem, TRUE in case of a regression problem

nmse

if 'nmse' is TRUE and this is a regression problem, the mean squared error will be normalized

Value

• Estimated noise level

Details

In case of a classification problem, the 0-1-loss is used to estimate the noise level: $$y = (y_1, ..., y_n)$$ $$L_{01}(y, \hat{y}) = \frac{1}{n}\sum_{i=1}^{n}{\mathbf{I}_{{y_i \neq \hat{y}_i}}}$$ In case of a regression problem, the mean squared error (mse) or the normalized mean squared error (nmse) is used, depending on whether 'nmse' is FALSE (mse) or TRUE (nmse): $$L_{mse}(y, \hat{y}) = \frac{1}{n}\sum_{i=1}^{n}{(y_i - \hat{y}_i)^2}$$ $$L_{nmse}(y, \hat{y}) = \frac{L_{mse}(y, \hat{y})}{\frac{1}{n}\sum_{i=1}^{n}{(y_i - \frac{1}{n}\sum_{j=1}^{n}{y_j})^2}}$$

See Also

sincdata, rde_loocv, rde_tcm, rbfkernel, drawkpc

Examples

## estimate noise of sinc data explicitly
d <- sincdata(100, 0.7) # generate sinc data
K <- rbfkernel(d$X) # calculate rbf kernel matrix
r <- rde(K, d$y, est_y = TRUE) # estimate relevant dimension
noise <- estnoise(d$y, r$yh, regression = TRUE) # estimate noise level

## estimate noise of sinc data implicitly (via rde_loocv)
d <- sincdata(100, 0.7) # generate sinc data
K <- rbfkernel(d$X) # calculate rbf kernel matrix
r <- rde(K, d$y, est_y = TRUE) # estimate relevant dimension AND estimate noise
r$noise # estimated noise level