load(l,
k,
g,
beta,
M,
e,
mu,
snr=None,
shape=None)
| source code
|
Returns data generated such that we know the exact solution.
The data generated by this function is fit to the Linear regression + L1 +
L2 + Smoothed total variation function, i.e.:
f(b) = (1 / 2).|Xb - y|² + l.L1mu(b) + (k / 2).|b|² + g.TVmu(b),
where L1mu is the smoothed L1 norm, |.|² is the squared L2 norm and TVmu is
the smoothed total variation penalty.
Parameters
----------
l : The L1 regularisation parameter.
k : The L2 regularisation parameter.
g : The total variation regularisation parameter.
beta : The regression vector to generate data from.
M : The matrix to use when building data. This matrix carries the desired
correlation structure of the generated data. The generated data
will be a column-scaled version of this matrix.
e : The error vector e = Xb - y. This vector carries the desired
distribution of the residual.
mu : The Nesterov smoothing regularisation parameter.
snr : Signal-to-noise ratio between model and residual.
shape : The underlying dimension of the regression vector, beta. E.g. the
beta may represent an underlying 3D image. In that case the shape
is a three-tuple with dimensions (Z, Y, X). If shape is not
provided, the shape is set to (p,) where p is the dimension of
beta.
Returns
-------
X : The generated X matrix.
y : The generated y vector.
beta : The regression vector with the correct snr.
|