MML

java.lang.Object
- mml.MML

```
public class MML
extends java.lang.Object
```
The class of Minimum Message Length [MML] tools for statistical and inductive inference, and machine learning. The main business is in (fully parameterised) Model, FunctionModel and SeriesModel. Each of these may be created by an UnParameterised Model or its Estimator.
Also see package mml's README, [the book] and the [home page].

Field Summary

Fields
Modifier and Type	Field and Description
`static BetaUPM`	`Beta` The UnParameterised `Beta` Model.
`static ExponentialUPM`	`Exponential` The UnParameterised `Exponential` Model.
`static GammaUPM`	`Gamma` The UnParameterised `Gamma` Model.
`static Geometric0UPM`	`Geometric0` The UnParameterised Geometric Model (distribution) over integers in [0, ∞), capable of `estimating` a fully parameterised `Geometric` Model.
`static double`	`invLog2` 1 / log_e(2)
`static Model`	`Known` A Model of given, known, common knowledge.
`static UPModel`	`KnownUPM` The unParameterised Model version of `Known`.
`static LaplaceUPM`	`Laplace` The UnParameterised Laplace probability distribution.
`static Linear1`	`Linear1` The `instance` of the UnParameterised `Linear1` FunctionModel; (Cts→Cts, linear regression).
`static double`	`log2` log_e(2)
`static double`	`log2PI` log_e(2π).
`static Continuous`	`logNormal` The UnParameterised `Transformed` Model that is the `log`–`Normal` Model.
`static double`	`logPI` log_e(π)
`static LogStar0UPM.M`	`logStar0` The fully (trivially) parameterised log^* Model, or "universal" probability distribution, for integers n ≥ 0.
`static LogStar0UPM`	`logStar0upm` The UnParameterised log^* Model for integers n ≥ 0.
`static NormalUPM.M`	`N01` The fully parameterised Normal Model, N_{⟨μ=0,σ=1⟩}; it might be useful.
`static NormalUPM`	`Normal` The UnParameterised `Normal` Model (Gaussian distribution) capable of `estimating` both μ and σ together to give a fully parameterised Normal `M Model`.
`static NormalMu`	`NormalMu0` The UnParameterised `NormalMu` Model with μ = 0, given, and σ unset.
`static Poisson0UPM`	`Poisson0` The UnParameterised Poisson Model (distribution) over integers in [0, ∞), capable of `estimating` a fully parameterised `Poisson` Model.
`static java.util.Random`	`RNG` Standard practice is for those Models that do implement `Model.random()` to use RNG so that a run can be repeated by setting RNG's `seed` to a known value.
`static vMF`	`vMF3` The `UnParameterised` von Mises - Fisher Model (distribution) of Directions in R³.
`static WallaceInt0UPM.M`	`WallaceInt0` The fully (trivially) parameterised Wallace Model for integers n ≥ 0.
`static WallaceInt0UPM`	`WallaceInt0upm` The UnParameterised Wallace Model for integers n ≥ 0.

Constructor Summary

Constructors
Constructor and Description

MML()

Constructors
Constructor and Description
`MML()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`informativeIncrement(int D)` See p.180 Wallace (2005), the informative explanation (D parameters estimated) versus the uninformative explanation, I1 - I0 = (D/2)(1 + log(2 π k[D])), nits.
`static double`	`latticeConstant(int D)` latticeConstant(D) (aka κ(D)), the lattice constant for D dimensions, D ≥ 1, i.e., D parameters, [www].
`static void`	`main(java.lang.String[] argv)` Runs `Test`.main(argv).

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

- Field Detail
  - log2
```
public static final double log2
```
    log_e(2)
  - invLog2
```
public static final double invLog2
```
    1 / log_e(2)
  - logPI
```
public static final double logPI
```
    log_e(π)
  - log2PI
```
public static final double log2PI
```
    log_e(2π).
  - RNG
```
public static final java.util.Random RNG
```
    Standard practice is for those Models that do implement Model.random() to use RNG so that a run can be repeated by setting RNG's seed to a known value.
  - Known
```
public static final Model Known
```
    A Model of given, known, common knowledge. That is, pr(d)=1, nlPr(d)=0, for all data d.
  - KnownUPM
```
public static final UPModel KnownUPM
```
    The unParameterised Model version of Known.
  - WallaceInt0upm
```
public static final WallaceInt0UPM WallaceInt0upm
```
    The UnParameterised Wallace Model for integers n ≥ 0. WallaceInt0 is fully (trivially) parameterised.
  - WallaceInt0
```
public static final WallaceInt0UPM.M WallaceInt0
```
    The fully (trivially) parameterised Wallace Model for integers n ≥ 0. If needed, WallaceInt0upm is UnParameterised.
  - logStar0upm
```
public static final LogStar0UPM logStar0upm
```
    The UnParameterised log^* Model for integers n ≥ 0. logStar0 is fully (trivially) parameterised. Also see WallaceInt0upm.
  - logStar0
```
public static final LogStar0UPM.M logStar0
```
    The fully (trivially) parameterised log^* Model, or "universal" probability distribution, for integers n ≥ 0. Note, the Model has infinite mean – does your data source? If needed, logStar0upm is UnParameterised. Also see WallaceInt0.
  - Geometric0
```
public static final Geometric0UPM Geometric0
```
    The UnParameterised Geometric Model (distribution) over integers in [0, ∞), capable of estimating a fully parameterised Geometric Model. Also see [www].
  - Poisson0
```
public static final Poisson0UPM Poisson0
```
    The UnParameterised Poisson Model (distribution) over integers in [0, ∞), capable of estimating a fully parameterised Poisson Model. Also see [www].
  - Laplace
```
public static final LaplaceUPM Laplace
```
    The UnParameterised Laplace probability distribution. If you really want its class, that is here. Also see fully parameterised, M_μ,b.
  - Exponential
```
public static final ExponentialUPM Exponential
```
    The UnParameterised Exponential Model.
  - Gamma
```
public static final GammaUPM Gamma
```
    The UnParameterised Gamma Model.
  - Beta
```
public static final BetaUPM Beta
```
    The UnParameterised Beta Model.
  - Normal
```
public static final NormalUPM Normal
```
    The UnParameterised Normal Model (Gaussian distribution) capable of estimating both μ and σ together to give a fully parameterised Normal M Model. Also see NormalMu, and [www].
  - N01
```
public static final NormalUPM.M N01
```
    The fully parameterised Normal Model, N_{⟨μ=0,σ=1⟩}; it might be useful.
  - NormalMu0
```
public static final NormalMu NormalMu0
```
    The UnParameterised NormalMu Model with μ = 0, given, and σ unset. This is a reasonably common, useful special case. Also see N_0,1.
  - logNormal
```
public static final Continuous logNormal
```
    The UnParameterised Transformed Model that is the log–Normal Model. It is for Cts data in (0, ∞) whose log follows a Normal distribution. Its statistical parameters and the parameters of its estimator are as per the Normal.
  - Linear1
```
public static final Linear1 Linear1
```
    The instance of the UnParameterised Linear1 FunctionModel; (Cts→Cts, linear regression). Also see the fully parameterised Linear1.M.
  - vMF3
```
public static final vMF vMF3
```
    The UnParameterised von Mises - Fisher Model (distribution) of Directions in R³.
- Constructor Detail
  - MML
```
public MML()
```
- Method Detail
  - latticeConstant
```
public static double latticeConstant(int D)
```
    latticeConstant(D) (aka κ(D)), the lattice constant for D dimensions, D ≥ 1, i.e., D parameters, [www].
  - informativeIncrement
```
public static double informativeIncrement(int D)
```
    See p.180 Wallace (2005), the informative explanation (D parameters estimated) versus the uninformative explanation, I1 - I0 = (D/2)(1 + log(2 π k[D])), nits. This begins (1/2)log(2 π e / 12) when D=1, and note that (1 + log(2 π k[D]) ≥ 0 for all D>0. There is a small price to pay for stating an opinion about the value of a Model's parameter(s) compared to a message that does not state any such opinion.
  - main
```
public static void main(java.lang.String[] argv)
```
    Runs Test.main(argv).

Class MML

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

log2

invLog2

logPI

log2PI

RNG

Known

KnownUPM

WallaceInt0upm

WallaceInt0

logStar0upm

logStar0

Geometric0

Poisson0

Laplace

Exponential

Gamma

Beta

Normal

N01

NormalMu0

logNormal

Linear1

vMF3

Constructor Detail

MML

Method Detail

latticeConstant

informativeIncrement

main