incline.LocalPolynomial

class incline.LocalPolynomial(bandwidth=0.2, degree=2, kernel='gaussian')

Local polynomial regression with kernel weights.

Fits a weighted least squares polynomial around every point and reads the derivative off the coefficients.

Variables:

• bandwidth (float) – Kernel width as a fraction of the series span.

• degree (int) – Degree of the local polynomial.

• kernel (str) – 'gaussian', 'epanechnikov' or 'uniform'.

Parameters:

• bandwidth (float)

• degree (int)

• kernel (str)

__init__(bandwidth=0.2, degree=2, kernel='gaussian')

Parameters:

• bandwidth (float)

• degree (int)

• kernel (str)

Return type:

None

Methods

__init__([bandwidth, degree, kernel])
analytic_operators(axis, order)	Emit the operator rows from the same weighted least squares solve.
evaluate(axis, y, order)	Fit a weighted local polynomial at every point.
fit(axis, y[, order, se, noise, ...])	Estimate the trend and, optionally, its uncertainty.
native_posterior(axis, y, order, ...)	Uncertainty from the smoother's own probability model.
operators(axis, order)	The smoothing and derivative operators for this configuration.
params()	Report bandwidth, degree and kernel.
scale_of(axis)	Bandwidth as a fraction of the span.
with_scale(scale, axis)	Set the kernel bandwidth to scale of the span.

Attributes

bandwidth
degree
has_native_posterior
is_linear	Whether the derivative is a fixed linear map of the data.
kernel
linear
name
requires_regular_grid
supported_orders

name: ClassVar[str] = 'local_poly'

linear: ClassVar[bool] = True

bandwidth: float = 0.2

degree: int = 2

kernel: str = 'gaussian'

evaluate(axis, y, order)

Fit a weighted local polynomial at every point.

Parameters:

• axis (TimeAxis)

• y (npt.NDArray[np.float64])

• order (int)

Return type:

Evaluation

analytic_operators(axis, order)

Emit the operator rows from the same weighted least squares solve.

Each point’s estimate is e_k' (X'WX)^-1 X'W y; the row vector in front of y is that point’s operator row. Building it costs one extra solve against an identity block rather than n full evaluations.

Parameters:

• axis (TimeAxis)

• order (int)

Return type:

tuple[npt.NDArray[np.float64], npt.NDArray[np.float64]] | None

with_scale(scale, axis)

Set the kernel bandwidth to scale of the span.

Parameters:

• scale (float)

• axis (TimeAxis)

Return type:

Self

scale_of(axis)

Bandwidth as a fraction of the span.

Parameters:

axis (TimeAxis)

Return type:

float

params()

Report bandwidth, degree and kernel.

Return type:

dict[str, Any]