Package org.pepstock.charba.client.ml

Class RobustPolynomialRegression

java.lang.Object

org.pepstock.charba.client.ml.RobustPolynomialRegression

All Implemented Interfaces:

IsRegression

public final class RobustPolynomialRegression
extends Object

Robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods.
Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable. Certain widely used methods of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results if those assumptions are not true; thus ordinary least squares is said to be not robust to violations of its assumptions.
Robust regression methods are designed to be not overly affected by violations of assumptions by the underlying data-generating process.

In particular, least squares estimates for regression models are highly sensitive to outliers.
While there is no precise definition of an outlier, outliers are observations that do not follow the pattern of the other observations.
This is not normally a problem if the outlier is simply an extreme observation drawn from the tail of a normal distribution, but if the outlier results from non-normal measurement error or some other violation of standard ordinary least squares assumptions, then it compromises the validity of the regression results if a non-robust regression technique is used.
The Polynomial Regression equation is given below:

y = b₀ + b₁x₁ + b₂x₁² + b₂x₁³ +...... b_nx₁ⁿ

Author:

Andrea "Stock" Stocchero

Field Summary

Fields

Modifier and Type	Field	Description
static int	DEFAULT_DEGREE	Default degree, 2.
static int	DEFAULT_FORMULA_PRECISION	Default precision to get the formula, 2.

Method Summary

Modifier and Type	Method	Description
List<Double>	getCoefficients()	Returns all calculated coefficients as an array, in increasing order of power (from 0 to degree).
int	getDegree()	Returns the maximum degree of the polynomial.
RegressionDescriptor	getDescriptor()	Returns the regression descriptor.
List<Double>	getPowers()	Returns the powers coefficient.
RegressionType	getType()	Returns the regression type.
boolean	isConsistent()	Returns true if the regression is consistent and usable.
double	predict(double x)	Returns the Y value, calculated by the regression formula at specific X value.
List<Double>	predict(double... xValues)	Returns a list of Y values, calculated by the regression formula for specific X values.
double	predict(Date x)	Returns the Y value, calculated by the regression formula at specific X value.
List<Double>	predict(List<Double> xValues)	Returns a list of Y values, calculated by the regression formula for specific X values.
double	predict(DataPoint dataPoint)	Returns the Y value, calculated by the regression formula at specific X value.
double	predict(TimeSeriesItem item)	Returns the Y value, calculated by the regression formula at specific X value.
List<Double>	predictByDataPoints(List<DataPoint> dataPoints)	Returns a list of Y values, calculated by the regression formula for specific X values.
List<Double>	predictByDataPoints(DataPoint... dataPoints)	Returns a list of Y values, calculated by the regression formula for specific X values.
List<Double>	predictByDates(Date... xValues)	Returns a list of Y values, calculated by the regression formula for specific X values.
List<Double>	predictByDates(List<Date> xValues)	Returns a list of Y values, calculated by the regression formula for specific X values.
List<Double>	predictByTimeSeriesItems(List<TimeSeriesItem> items)	Returns a list of Y values, calculated by the regression formula for specific X values.
List<Double>	predictByTimeSeriesItems(TimeSeriesItem... items)	Returns a list of Y values, calculated by the regression formula for specific X values.
RegressionScore	score(List<Double> y)	Evaluates the regression formula if the model fits enough. X values are creating starting from 0 with increment of 1.
RegressionScore	score(List<Double> y, double starting)	Evaluates the regression formula if the model fits enough. X values are creating starting from passed argument with increment of 1.
RegressionScore	score(List<Double> y, double starting, double increment)	Evaluates the regression formula if the model fits enough. X values are creating starting from passed argument with increment of passed argument.
RegressionScore	score(List<Double> x, List<Double> y)	Evaluates the regression formula if the model fits enough.
RegressionScore	scoreByDataPoints(List<DataPoint> dataPoints)	Evaluates the regression formula if the model fits enough.
RegressionScore	scoreByDate(List<Date> x, List<Double> y)	Evaluates the regression formula if the model fits enough.
RegressionScore	scoreByTimeSeriesItems(List<TimeSeriesItem> items)	Evaluates the regression formula if the model fits enough.
String	toFormula()	Returns the formula of the regression.
String	toFormula(int precision)	Returns the formula of the regression, using the requested precision.
String	toLaTeX()	Returns the formula of the regression.
String	toLaTeX(int precision)	Returns the formula of the regression, using the requested precision.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_DEGREE

public static final int DEFAULT_DEGREE

Default degree, 2.

See Also:

Constant Field Values

DEFAULT_FORMULA_PRECISION

public static final int DEFAULT_FORMULA_PRECISION

Default precision to get the formula, 2.

See Also:

Constant Field Values

Method Detail

getDegree

public final int getDegree()

Returns the maximum degree of the polynomial.

Returns:

the maximum degree of the polynomial

getPowers

public final List<Double> getPowers()

Returns the powers coefficient.

Returns:

the powers coefficient

getCoefficients

public final List<Double> getCoefficients()

Returns all calculated coefficients as an array, in increasing order of power (from 0 to degree).

Returns:

all calculated coefficients as an array

getType

public final RegressionType getType()

Returns the regression type.

Specified by:

getType in interface IsRegression

Returns:

the regression type

getDescriptor

public final RegressionDescriptor getDescriptor()

Returns the regression descriptor.

Specified by:

getDescriptor in interface IsRegression

Returns:

the regression descriptor

isConsistent

public final boolean isConsistent()

Description copied from interface: IsRegression

Returns true if the regression is consistent and usable.

Specified by:

isConsistent in interface IsRegression

Returns:

true if the regression is consistent and usable

predict

public final double predict(double x)

Description copied from interface: IsRegression

Returns the Y value, calculated by the regression formula at specific X value.

Specified by:

predict in interface IsRegression

Parameters:

x - value to use to get the predicted value

Returns:

the Y value, calculated by the regression formula at specific X value

predict

public final double predict(Date x)

Description copied from interface: IsRegression

Returns the Y value, calculated by the regression formula at specific X value.

Specified by:

predict in interface IsRegression

Parameters:

x - value to use to get the predicted value

Returns:

the Y value, calculated by the regression formula at specific X value

predict

public final double predict(DataPoint dataPoint)

Description copied from interface: IsRegression

Returns the Y value, calculated by the regression formula at specific X value.

Specified by:

predict in interface IsRegression

Parameters:

dataPoint - value to use to get the predicted value

Returns:

the Y value, calculated by the regression formula at specific X value

predict

public final double predict(TimeSeriesItem item)

Description copied from interface: IsRegression

Returns the Y value, calculated by the regression formula at specific X value.

Specified by:

predict in interface IsRegression

Parameters:

item - value to use to get the predicted value

Returns:

the Y value, calculated by the regression formula at specific X value

predict

public final List<Double> predict(double... xValues)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predict in interface IsRegression

Parameters:

xValues - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predict

public final List<Double> predict(List<Double> xValues)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predict in interface IsRegression

Parameters:

xValues - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predictByDates

public final List<Double> predictByDates(Date... xValues)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predictByDates in interface IsRegression

Parameters:

xValues - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predictByDates

public final List<Double> predictByDates(List<Date> xValues)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predictByDates in interface IsRegression

Parameters:

xValues - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predictByDataPoints

public final List<Double> predictByDataPoints(DataPoint... dataPoints)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predictByDataPoints in interface IsRegression

Parameters:

dataPoints - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predictByDataPoints

public final List<Double> predictByDataPoints(List<DataPoint> dataPoints)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predictByDataPoints in interface IsRegression

Parameters:

dataPoints - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predictByTimeSeriesItems

public final List<Double> predictByTimeSeriesItems(TimeSeriesItem... items)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predictByTimeSeriesItems in interface IsRegression

Parameters:

items - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

predictByTimeSeriesItems

public final List<Double> predictByTimeSeriesItems(List<TimeSeriesItem> items)

Description copied from interface: IsRegression

Returns a list of Y values, calculated by the regression formula for specific X values.

Specified by:

predictByTimeSeriesItems in interface IsRegression

Parameters:

items - values to use to get the predicted values

Returns:

a list of Y values, calculated by the regression formula for specific X values

score

public final RegressionScore score(List<Double> y)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.
X values are creating starting from 0 with increment of 1.

Specified by:

score in interface IsRegression

Parameters:

y - Y values to use for evaluation

Returns:

the score of the regression

score

public final RegressionScore score(List<Double> y,
                                   double starting)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.
X values are creating starting from passed argument with increment of 1.

Specified by:

score in interface IsRegression

Parameters:

y - Y values to use for evaluation

starting - starting value to create X values

Returns:

the score of the regression

score

public final RegressionScore score(List<Double> y,
                                   double starting,
                                   double increment)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.
X values are creating starting from passed argument with increment of passed argument.

Specified by:

score in interface IsRegression

Parameters:

y - Y values to use for evaluation

starting - starting value to create X values

increment - increment to apply to the starting value

Returns:

the score of the regression

score

public final RegressionScore score(List<Double> x,
                                   List<Double> y)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.

Specified by:

score in interface IsRegression

Parameters:

x - X values to use for evaluation

y - Y values to use for evaluation

Returns:

the score of the regression

scoreByDate

public final RegressionScore scoreByDate(List<Date> x,
                                         List<Double> y)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.

Specified by:

scoreByDate in interface IsRegression

Parameters:

x - X values to use for evaluation

y - Y values to use for evaluation

Returns:

the score of the regression

scoreByDataPoints

public final RegressionScore scoreByDataPoints(List<DataPoint> dataPoints)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.

Specified by:

scoreByDataPoints in interface IsRegression

Parameters:

dataPoints - X and Y values to use for evaluation

Returns:

the score of the regression

scoreByTimeSeriesItems

public final RegressionScore scoreByTimeSeriesItems(List<TimeSeriesItem> items)

Description copied from interface: IsRegression

Evaluates the regression formula if the model fits enough.

Specified by:

scoreByTimeSeriesItems in interface IsRegression

Parameters:

items - X and Y values to use for evaluation

Returns:

the score of the regression

toFormula

public final String toFormula()

Description copied from interface: IsRegression

Returns the formula of the regression.

Specified by:

toFormula in interface IsRegression

Returns:

the formula of the regression

toFormula

public final String toFormula(int precision)

Description copied from interface: IsRegression

Returns the formula of the regression, using the requested precision.

Specified by:

toFormula in interface IsRegression

Parameters:

precision - precision to apply to the numbers of the formula

Returns:

the formula of the regression

toLaTeX

public final String toLaTeX()

Description copied from interface: IsRegression

Returns the formula of the regression.

Specified by:

toLaTeX in interface IsRegression

Returns:

the formula of the regression

toLaTeX

public final String toLaTeX(int precision)

Description copied from interface: IsRegression

Returns the formula of the regression, using the requested precision.

Specified by:

toLaTeX in interface IsRegression

Parameters:

precision - precision to apply to the numbers of the formula

Returns:

the formula of the regression