io.improbable.keanu.distributions.continuous

Class SmoothUniform

java.lang.Object

io.improbable.keanu.distributions.continuous.SmoothUniform

All Implemented Interfaces:

ContinuousDistribution, Distribution<DoubleTensor>

public class SmoothUniform
extends java.lang.Object
implements ContinuousDistribution

The Smooth Uniform distribution is the usual Uniform distribution with the edges at max and min smoothed by attaching a sigmoid as shoulders.

Math:

let sigmoid shoulder function be f(x), Sw be shoulder width, Bw be base (max-min) width, and h be the bodyHeight of the base.

f(x) = Ax^3 + Bx^2 f'(x) = 3Ax^2 + 2Bx integral f = Ax^4/4 + Bx^3/3

f(Sw) = h integral of f from 0 to Sw = 1 (area under the curve must be 1) f'(Sw) = 0

yields:

| 0 3Sw^2 2Sw | | h | | 0 | | -1 Sw^3 Sw^2 | * | A | = | 0 | | Bw Sw/4 2Sw/3 | | B | | 1 |

therefore:

h = 1 / (Sw + Bw) A = -2 / (Sw^3 * (Sw + Bw)) B = 3 / (Sw^3 * Sw^2*Bw)

Method Summary

Modifier and Type	Method and Description
Diffs	dLogProb(DoubleTensor x)
DoubleTensor	logProb(DoubleTensor x)
static DoubleVertex	logProbOutput(LogProbGraph.DoublePlaceholderVertex x, LogProbGraph.DoublePlaceholderVertex xMin, LogProbGraph.DoublePlaceholderVertex xMax, double edgeSharpness)
DoubleTensor	sample(long[] shape, KeanuRandom random)
static ContinuousDistribution	withParameters(DoubleTensor xMin, DoubleTensor xMax, double edgeSharpness) Will return samples between xMin and xMax as well as samples from the left and right shoulder.

Methods inherited from class java.lang.Object

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

Method Detail

withParameters

public static ContinuousDistribution withParameters(DoubleTensor xMin,
                                                    DoubleTensor xMax,
                                                    double edgeSharpness)

Will return samples between xMin and xMax as well as samples from the left and right shoulder. The width of the shoulder is determined by the edgeSharpness as a percentage of the body width, which is (xMax - xMin).

Parameters:

xMin - min value from body

xMax - max value from body

edgeSharpness - sharpness as a percentage of the body width

Returns:

a new ContinuousDistribution object

sample

public DoubleTensor sample(long[] shape,
                           KeanuRandom random)

Specified by:

sample in interface Distribution<DoubleTensor>

logProb

public DoubleTensor logProb(DoubleTensor x)

Specified by:

logProb in interface Distribution<DoubleTensor>

logProbOutput

public static DoubleVertex logProbOutput(LogProbGraph.DoublePlaceholderVertex x,
                                         LogProbGraph.DoublePlaceholderVertex xMin,
                                         LogProbGraph.DoublePlaceholderVertex xMax,
                                         double edgeSharpness)

dLogProb

public Diffs dLogProb(DoubleTensor x)

Specified by:

dLogProb in interface ContinuousDistribution