cvxreg.models.PCR

cvxreg.models.PCR(*, c=1.0, shape='convex', monotonic=None, fit_intercept=True, solver='ecos')

Penalized Convex Regression (PCR) model.

PCR fit a convex function with coefficients \(\boldsymbol{\xi}_1,\ldots,\boldsymbol{\xi}_n\) from the data. \(\boldsymbol{\xi}_i\) is d-dimensional vector and n is the number of observations. The optimization problem is:

\[\begin{split}\min_{\boldsymbol{\xi}_1,\ldots,\boldsymbol{\xi}_n; \boldsymbol{\theta}} & \frac{1}{2}\sum_{i=1}^n (y_i-\theta_i)^2 + c * \sum_{i=1}^n \|\boldsymbol{\xi}_i\|_2^2 \\\\ s.t. & \theta_i + \boldsymbol{\xi}_i^T (\boldsymbol{x}_j - \boldsymbol{x}_i) \geq \theta_j, i,j=1,\ldots,n\end{split}\]

where \(\boldsymbol{x}_i\) is the i-th observation, \(y_i\) is the i-th target value, \(\theta_i\) is the value of \(f(\boldsymbol{x}_i)\), \(\boldsymbol{\xi}_i\) is the coefficient at the i-th observation, and \(c\) is the regularization parameter.

Parameters

Parameters

Options

c

Float, default: 1.0. c must be non-negative Float, i.e. in \([0, inf)\).

The regularization parameter.

shape

Selection: {convex, concave}, default: convex

The shape of the function to be fitted.

monotonic

Selection: {increasing, decreasing}, default: None

Whether to constrain the function to be monotonic.

fit_intercept

Boolean, default: True

Whether to fit the intercept.

solver

Selection: {ecos, osqp, scs, cvxopt, mosek, gurobi, cplex, copt}, default: ecos

The solver to use. There three open-source solvers: ecos, osqp, scs, and five commercial solvers: cvxopt, mosek, gurobi, cplex, copt.

To use commercial solvers, you need to install them first, see Install.

Attributes

Attributes

Type

coef_

numpy.ndarray

The coefficients of the fitted function.

intercept_

numpy.ndarray

The intercept of the fitted function.

Examples

import numpy as np
from cvxreg.models import PCR
X = np.array([[1, 1], [1, 2], [2, 2]])
y = [1, 2, 3]
pcr = PCR()
pcr.fit(X, y)
print(pcr.coef_)
# [[-2.80851372e-06 -4.48428251e-06]
#   [ 2.02631940e-07  1.89185893e-01]
#   [ 3.51352926e-01  1.89185893e-01]]
print(pcr.intercept_)
# [1.75676572 1.56757233 1.21621961]

Methods

Methods

Type

fit(X, y)

Fit model with solver.

X of shape (n_samples, n_features)

y of shape (n_samples,)

predict(X)

Predict using the convex regression model.

X of shape (n_samples, n_features)

See examples: Examples.