vMF

java.lang.Object
- la.la.Value
- - la.la.Function
  - - la.la.Function.Native
    - - mml.UPModel
      - mml.ByPdf
        
        mml.R_D
        
        mml.Direction
        
        mml.vMF

All Implemented Interfaces:

java.lang.Comparable<Value>
```
public class vMF
extends Direction
```
The UnParameterised von Mises - Fisher Model of Directions in R^D. The fully parameterised Model is vMF.M. A Direction is equivalent to a point on the surface of a unit-radius D-ball, so having D-1 degrees of freedom. For the special case of D=3, R³, there is MML.vMF3. (Also see [wikip]['12].)

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

class vMF.M
The fully parameterised von Mises - Fisher Model of Directions in R^D.
- Nested classes/interfaces inherited from class mml.Direction
  Direction.Uniform
- Nested classes/interfaces inherited from class mml.R_D
  R_D.Forest, R_D.ForestSearch, R_D.Independent, R_D.NrmDir, R_D.Transform
- Nested classes/interfaces inherited from class mml.UPModel
  UPModel.Est
- Nested classes/interfaces inherited from class la.la.Function.Native
  Function.Native.WithInverse
- Nested classes/interfaces inherited from class la.la.Function
  Function.Cts2Cts, Function.Cts2Cts2Cts, Function.CtsD2CtsD, Function.HasInverse, Function.Native, Function.Native2, Function.Native3
- Nested classes/interfaces inherited from class la.la.Value
  Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple

Nested Classes
Modifier and Type	Class and Description
`class`	`vMF.M` The fully parameterised von Mises - Fisher Model of Directions in R^D.

Field Summary
- Fields inherited from class mml.UPModel
  dp
- Fields inherited from class la.la.Value
  C, comparator, CR, E, eight, ffalse, five, fiveR, four, fourR, half, negCR, negOne, negOneR, negTenR, nilVal, nine, None, one, oneR, PI, PIby2, point01, point1, point5, point9, quarter, seven, six, ten, tenR, three, threeR, triv, ttrue, two, twoR, zero, zeroR

Constructor Summary

Constructors
Constructor and Description

vMF(Value D)
D, the dimension of R^D.

Constructors
Constructor and Description
`vMF(Value D)` D, the dimension of R^D.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`int`	`D()` D(), the dimension of R^D.
`UPModel.Est`	`estimator(Value t)` Calls the `MML estimator`.
`UPModel.Est`	`estimatorMaxLH(Value t)` The (rough and ready) maximum likelhood estimator for μ and κ; see the `MML estimator`.
`UPModel.Est`	`estimatorMML(Value t)` The MML Estimator for μ and κ.
`double`	`logCD(double kappa)` The `Model's` log normalisation constant.
`double`	`logF(double N, double kappa)` log(F(κ)), log Fisher.
`static void`	`main(java.lang.String[] argv)` Run a few, very(!) simple tests.
`double`	`msg1(double N, double kappa)` Length of the first part of the message.
`double`	`msg2(Vector mu, double kappa, Value ss)` Length of the second part of the message.
`double`	`nlLH(Vector mu, double kappa, Value ss)` Given μ, κ, and statistics, ss = `stats(ds)` of a data-set, ds, return the negative log likelihood of ds.
`double`	`prior_k(double kappa)` Maybe change this(?)-- the prior's pdf on κ is (1+κ)^-2, κ>0.
`vMF.M`	`sp2Model(double msg1, double msg2, Value sp)` Given two-part message lengths, and statistical parameters sp = (μ, κ), return a fully parameterised von Mises - Fisher `Model`.
`Value`	`stats(boolean add, Value ss0, Value ss1)` Combine sufficient statisticses 'ss0' and 'ss1' additively (add=true), or remove ss1 from ss0 (add=false).
`Value`	`stats(Vector ds, int lo, int hi)` Statistics, ss = stats(ds) = (N, R, nlAoM), of a data-set, ds.

Methods inherited from class mml.Direction
K, logArea

Methods inherited from class mml.R_D
ds2L1stats, ds2NorL1stats, ds2Nstats, transform

Methods inherited from class mml.UPModel
apply, defnParams, stats, stats, toString, transform

Methods inherited from class la.la.Function
bOp, fromBop, fromUop, type, uOp

Methods inherited from class la.la.Value
AoM, bOp, compareTo, cons, cts, elt, errMsg, error, force, isTuple, just, n, nElts, nlAoM, pair, print, quad, real, RTE, triple, tuple, UOE, x

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - vMF
```
public vMF(Value D)
```
    D, the dimension of R^D.
- Method Detail
  - D
```
public int D()
```
    D(), the dimension of R^D.
    
    Specified by:
    
    D in class R_D
  - sp2Model
```
public vMF.M sp2Model(double msg1,
                      double msg2,
                      Value sp)
```
    Given two-part message lengths, and statistical parameters sp = (μ, κ), return a fully parameterised von Mises - Fisher Model.
    
    Specified by:
    
    sp2Model in class R_D
  - stats
```
public Value stats(Vector ds,
                   int lo,
                   int hi)
```
    Statistics, ss = stats(ds) = (N, R, nlAoM), of a data-set, ds. All are weighted, N the number of data, Vector R the sum of the (normalised) Directions, and the data total (scaled) nlAoM. More on stats here.
    
    Specified by:
    
    stats in class UPModel
  - stats
```
public Value stats(boolean add,
                   Value ss0,
                   Value ss1)
```
    Description copied from class: UPModel
    
    Combine sufficient statisticses 'ss0' and 'ss1' additively (add=true), or remove ss1 from ss0 (add=false). Also see stats(ds,lo,hi).
    
    Specified by:
    
    stats in class UPModel
  - logF
```
public double logF(double N,
                   double kappa)
```
    log(F(κ)), log Fisher. F = N^D (κ A_D(κ))^D-1 A'_D(κ); see AD. Also see [vMF].
  - msg1
```
public double msg1(double N,
                   double kappa)
```
    Length of the first part of the message.
  - msg2
```
public double msg2(Vector mu,
                   double kappa,
                   Value ss)
```
    Length of the second part of the message.
  - prior_k
```
public double prior_k(double kappa)
```
    Maybe change this(?)-- the prior's pdf on κ is (1+κ)^-2, κ>0. (The prior on the mean Direction μ is Uniform.)
  - estimator
```
public UPModel.Est estimator(Value t)
```
    Calls the MML estimator.
    
    Overrides:
    
    estimator in class UPModel
  - estimatorMML
```
public UPModel.Est estimatorMML(Value t)
```
    The MML Estimator for μ and κ. The maximum likelihood estimate of μ is accepted but its estimate of κ is taken as a starting point (using an R guaranteed that ||R|| < N). The prior on the mean Direction μ is Uniform. See log Fisher and stats(ds). Note, the vMF has D() parameters -- κ, and D()-1 for Direction μ.
  - estimatorMaxLH
```
public UPModel.Est estimatorMaxLH(Value t)
```
    The (rough and ready) maximum likelhood estimator for μ and κ; see the MML estimator. NB. It requires ||R|| < N, Rbar < 1. The prior on the mean Direction μ is Uniform. Note, the vMF has D() parameters -- κ, and D()-1 for Direction μ. Also see stats(ds), estimatorMML.
  - nlLH
```
public double nlLH(Vector mu,
                   double kappa,
                   Value ss)
```
    Given μ, κ, and statistics, ss = stats(ds) of a data-set, ds, return the negative log likelihood of ds. Used by estimator and vMF.M.nlLH(la.la.Value).
  - logCD
```
public double logCD(double kappa)
```
    The Model's log normalisation constant.
    - C_D(κ) = κ^(D/2-1) / {(2π)^D/2 I_D/2-1(κ)},
    - C₃ = κ / {2π(e^κ - e^-κ)}.
    I_α(.) is a modified Bessel function of the first kind.
  - main
```
public static void main(java.lang.String[] argv)
```
    Run a few, very(!) simple tests.

Class vMF

Nested Class Summary

Nested classes/interfaces inherited from class mml.Direction

Nested classes/interfaces inherited from class mml.R_D

Nested classes/interfaces inherited from class mml.UPModel

Nested classes/interfaces inherited from class la.la.Function.Native

Nested classes/interfaces inherited from class la.la.Function

Nested classes/interfaces inherited from class la.la.Value

Field Summary

Fields inherited from class mml.UPModel

Fields inherited from class la.la.Value

Constructor Summary

Method Summary

Methods inherited from class mml.Direction

Methods inherited from class mml.R_D

Methods inherited from class mml.UPModel

Methods inherited from class la.la.Function

Methods inherited from class la.la.Value

Methods inherited from class java.lang.Object

Constructor Detail

vMF

Method Detail

D

sp2Model

stats

stats

logF

msg1

msg2

prior_k

estimator

estimatorMML

estimatorMaxLH

nlLH

logCD

main