Documentation
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Overview ¶
Package fit provides functions for fitting models to data.
Index ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func LOESS ¶
LOESS computes the locally-weighted least squares polynomial regression to the data (xs[i], ys[i]). 0 < span <= 1 is the smoothing parameter, where smaller values fit the data more tightly. Degree is typically 2 and span is typically between 0.5 and 0.75.
The regression is "local" because the weights used for the polynomial regression depend on the x at which the regression function is evaluated. The weight of observation i is W((x-xs[i])/d(x)) where d(x) is the distance from x to the span*len(xs)'th closest point to x and W is the tricube weight function W(u) = (1-|u|³)³ for |u| < 1, 0 otherwise. One consequence of this is that only the span*len(xs) points closest to x affect the regression at x, and that the effect of these points falls off further from x.
References ¶
Cleveland, William S., and Susan J. Devlin. "Locally weighted regression: an approach to regression analysis by local fitting." Journal of the American Statistical Association 83.403 (1988): 596-610.
http://www.itl.nist.gov/div898/handbook/pmd/section1/dep/dep144.htm
func LinearLeastSquares ¶
func LinearLeastSquares(xs, ys, weights []float64, terms ...func(xs, termOut []float64)) (params []float64)
LinearLeastSquares computes the least squares fit for the function
f(x) = Β₀terms₀(x) + Β₁terms₁(x) + ...
to the data (xs[i], ys[i]). It returns the parameters Β₀, Β₁, ... that minimize the sum of the squares of the residuals of f:
∑ (ys[i] - f(xs[i]))²
If weights is non-nil, it is used to weight these residuals:
∑ weights[i] × (ys[i] - f(xs[i]))²
The function f is specified by one Go function for each linear term. For efficiency, the Go function is vectorized: it will be passed a slice of x values in xs and must fill the slice termOut with the value of the term for each value in xs.
Note that this is called a "linear" least squares fit because the fitted function is linear in the computed parameters. The function need not be linear in x.
Types ¶
type PolynomialRegressionResult ¶
type PolynomialRegressionResult struct {
// Coefficients is the coefficients of the fitted polynomial.
// Coefficients[i] is the coefficient of the x^i term.
Coefficients []float64
// F evaluates the fitted polynomial at x.
F func(x float64) float64
}
PolynomialRegressionResult is the resulting polynomial from a PolynomialRegression.
TODO: Should this just be a least squares regression result? We have the terms functions, so we can construct F, though it won't be very efficient.
func PolynomialRegression ¶
func PolynomialRegression(xs, ys, weights []float64, degree int) PolynomialRegressionResult
PolynomialRegression performs a least squares regression with a polynomial of the given degree. If weights is non-nil, it is used to weight the residuals.
func (PolynomialRegressionResult) String ¶
func (r PolynomialRegressionResult) String() string
Source Files