The Ridge model sets up and solves the Ridge (or Tikhonov) least squares problem:
$$\text{minimize } || Ax+\eta-b ||_2 + \alpha || \Delta x_i ||_2$$ $$\text{subject to } x_i \ge 0$$
where A is the a basis matrix, b is an observation, x is a vector of coefficients, and eta is a constant background term. Alpha is a hyperparameter that specifies the weight given to the smoothness regularization term.
Ridge differs from Quadratic in that it gives defined the problem in terms of cvxpy’s norm2() function,
and lets it handle the appropriate factorizations.
kemitter.model.Ridge(alpha)¶Solves and stores results of cvxpy ridge regression solver, implemented by the cvxpy.norm2() function.
name¶str – “RIDGE” (constant)
alpha¶float – the regularization parameter for the smoothness penalty
See also
run(bases, observation, verbose=True)¶Runs the model calculations.
Bases and observations are loaded into proper polarized data sets. In this step,
arguments are checked to ensure polarization angles match in value and order. Any bases that have not been
built already are built with their corresponding build() method.
Bases and observations of multiple polarizations are then concatenated and given to cvxpy and MOSEK for solving.
Results are returned and processed in inherited Model attributes.
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