Class LinearRegressionData

source code

   object --+    
            |    
SimulatedData --+
                |
               LinearRegressionData

Returns data for linear regression that is 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_2 + sum_{i=1}^N l_i.P_i(b),

where the P_i(.) are penalty functions.

Parameters
----------
penalties : List or tuple. The penalties to add to the linear regression
        function.

X0 : Numpy array (n-by-p). The initial 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 : Numpy array (n-by-1). The error vector e = Xb - y. This vector carries
        the desired distribution of the residual.

snr : Positive float. Signal-to-noise ratio between model and residual.

intercept : Boolean. Whether or not to include an intercept variable. This
        variable is not penalised. Note that if intercept is True, then e
        will be centred.

Returns
-------
X : Numpy array (n-by-p). The generated X matrix.

y : Numpy array (n-by-1). The generated y vector.

beta : Numpy array (p-by-1). The regression vector with the correct snr (if
        snr is given).

Generate the simulated data.

Parameters
----------
beta : Numpy array (p-by-1). The regression vector to generate data
        from.