Class PolynomialRegression

machine_learning/polynomial_regression.py:41–180

class PolynomialRegression:
    __slots__ = "degree", "params"

    def __init__(self, degree: int) -> None:
        """
        @raises ValueError: if the polynomial degree is negative
        """
        if degree < 0:
            raise ValueError("Polynomial degree must be non-negative")

        self.degree = degree
        self.params = None

    @staticmethod
    def _design_matrix(data: np.ndarray, degree: int) -> np.ndarray:
        """
        Constructs a polynomial regression design matrix for the given input data. For
        input data x = (x₁, x₂, ..., xₙ) and polynomial degree m, the design matrix is
        the Vandermonde matrix

            |1  x₁  x₁² ⋯ x₁ᵐ|
        X = |1  x₂  x₂² ⋯ x₂ᵐ|
            |⋮  ⋮   ⋮   ⋱ ⋮  |
            |1  xₙ  xₙ² ⋯  xₙᵐ|

        Reference: https://en.wikipedia.org/wiki/Vandermonde_matrix

        @param data:    the input predictor values x, either for model fitting or for
                        prediction
        @param degree:  the polynomial degree m
        @returns:       the Vandermonde matrix X (see above)
        @raises ValueError: if input data is not N x 1

        >>> x = np.array([0, 1, 2])
        >>> PolynomialRegression._design_matrix(x, degree=0)
        array([[1],
               [1],
               [1]])
        >>> PolynomialRegression._design_matrix(x, degree=1)
        array([[1, 0],
               [1, 1],
               [1, 2]])
        >>> PolynomialRegression._design_matrix(x, degree=2)
        array([[1, 0, 0],
               [1, 1, 1],
               [1, 2, 4]])
        >>> PolynomialRegression._design_matrix(x, degree=3)
        array([[1, 0, 0, 0],
               [1, 1, 1, 1],
               [1, 2, 4, 8]])
        >>> PolynomialRegression._design_matrix(np.array([[0, 0], [0 , 0]]), degree=3)
        Traceback (most recent call last):
        ...
        ValueError: Data must have dimensions N x 1
        """
        _rows, *remaining = data.shape
        if remaining:
            raise ValueError("Data must have dimensions N x 1")