goclemens / regression

simple regression library

Regression

Summary

The Regression Object can be used to calculate an analytic approximation of a given set of value pairs. The result is a linear combination of chosen basis functions which fit the given values the best. The calculated parameters are saved within the Regression object. The resulting function is a fit of the given value pairs. The function, its first or second derivative can be evaluated at any given position or sampled over a given interval.

The implementation is losly based on

http://bl.ocks.org/jonahwilliams/62be9996afe5c2531625

Tryout at https://goclemens.github.io/Regression/example/smoothingSplines.html

This example is in the example folder of the repository

Usage

Example

Given is a dataset with points in 2D space in the form of x-coordinates X and corresponding y-coordinates Y. The input data needs to be sorted by x-value. As basis we choose a truncated power basis (basically cubic splines) and as regualizer for the linear regression problem the squared second derivative (sq2ndDer).

var data = {
  X: [0.1,0.4,1,1.5,1.9,2.1,2.8,3,4.2,4.9,5.7,6.8,7.3,8.2,8.4,9.2,9.8],
  Y: [1,2,1,2,1,1,2,3,4,5,6,7,8,8,9,6,5]
};

var options = {
  data: data,
  basis: "trunc-power",
  regualizer: "Sq2ndDer",
  lambda: 0.1
};

var regression = new Regression(options);
regression.calcRegression();

var fittedValues = regression.sample([-0.1,10],100);

Plot of the given data and the sampled values of the regression function fittedValues (done with d3.js).

Options

• data: Object { X: Array, Y: Array }

  The value pairs have to be presorted by x-value from smaller to higher. The data object must contain at least two value pairs.

• basis: String

  • "trunc-power" (default)

    basically a cubic polynomial basis

  • "linear"

    a linear and a constant basis function

• regualizer: String

  • "Sq2ndDer" (default)
  • "ridge"
  • "none"

• knots: Array or false (default false)

  Positions for the knots for the basis functions. False will result in an automatic choose for the knots (usully the point positions itself)

• lambda: Number >0 (default 0.01)

  prefactor for the regualizer, works as a smoothing parameter

All Methods

• Regression.setBasis(basisId)

  Sets the used basis for the linear regression to basisId.

• Regression.calcRegression(options)

  Triggers the calculation of the regression and overides the existing options with options (optional).

• Regression.sample(interval,resolution)

  Samples the regression function for the given interval with the given resolution. Triggers Regression.calcRegression() if not done yet.

• Regression.sampleDer(interval,resolution)

  Samples the 1st derivative of the regression function for the given interval with the given resolution. Triggers Regression.calcRegression() if not done yet.

• Regression.sample2ndDer(interval,resolution)

  Samples the 2nd derivative of the regression function for the given interval with the given resolution. Triggers Regression.calcRegression() if not done yet.

• Regression.eval(position)

  Evaluates the regression function at the given position. Triggers Regression.calcRegression() if not done yet.

• Regression.evalDer(postion)

  Evaluates the 1st derivative of the regression function at the given position. Triggers Regression.calcRegression() if not done yet.

• Regression.eval2ndDer(position)

  Evaluates the 2nd derivative of the regression function at the given position. Triggers Regression.calcRegression() if not done yet.

• Regression.evalIntegral(interval)

  Evaluates the definite integral of the regression function over the given interval. Triggers Regression.calcRegression() if not done yet.

• Regression.roots()

  Gives the roots of the regression function.

• Regression.rootsDer()

  Gives the roots of the derivative of the regression function.

• Regression.roots2ndDer()

  Gives the roots of the second derivative of the regression function.

• Regression.extrema()

  Returns an object containing the minima, maxima and saddlepoints of the regression function.

  {
      min: [],
      max: [],
      saddle: []
  }

• Regression.analyticString() !experimental!

  Returns a string which represents the analytic function given by the regression.