An Example of Model Composition

Example Bayesian Network

@0, @4 continuous; @1, @2, @3 discrete (Boolean).

CSE454 2004 : This document is online at   http://www.csse.monash.edu.au/~lloyd/tilde/CSC4/CSE454/   and contains hyper-links to other resources - Lloyd Allison ©.

Friedman N., & Goldszmidt, M.. Learning Bayesian networks with local structure. UAI'96, pp.252-262, 1996

-- first suggested using classification trees instead of CPTs in the nodes of Bayesian Networks.

Oh good, we just happen to have an MML [classification tree], in Haskell.

Net:[
{CTleaf N(1.0,0.41)(+-0.1),_,_,_,_},          -- @0 ~ N(1,0.4)

{CTleaf _,mState[0.5,0.5],_,_,_},             -- @1

{CTfork @0<|>=1.4[                            -- @2 | @0,@1
  {CTleaf _,_,mState[0.99,0.01],_,_},           -- @0<1.4
  {CTfork @1=False|True[                        -- @0>=1.4
    {CTleaf _,_,mState[0.98,0.02],_,_},           -- @1 = False
    {CTleaf _,_,mState[0.02,0.98],_,_}]}]},       -- @1 = True

{CTleaf _,_,_,mState[0.5,0.5],_},             -- @3, independent

{CTfork @2=False|True[                        -- @4 | @0, @2
  {CTfork @0<|>=1.0[                          -- @2=False
    {CTleaf _,_,_,_,N(0.55,0.2)(+-0.1)},        -- @0 < 1.0
    {CTfork @0<|>=1.4[                          -- @0 >= 1.0
      {CTleaf _,_,_,_,N(1.0,0.2)(+-0.1)},         -- @0 [1.0,1.4)
      {CTleaf _,_,_,_,N(1.45,0.2)(+-0.1)}]}]},    -- @0 >= 1.4
   {CTleaf _,_,_,_,N(3.45,0.2)(+-0.1)}]} ]     -- @2=True

Lost Person Data

data Tipe = Alzheimers | Child | Despondent |
            Hiker | Other | Retarded | Psychotic
            deriving (Eq, Enum, Read, Show, Bounded)

type Age  = Double

data Race = White | Black  deriving ...

data Gender  = Male | Female  deriving ...

data Topography = Mountains | Piedmont | Tidewater  deriving ...

data Urban = Rural | Suburban | Urban  deriving ...

type HrsNt   = Double  -- hours notified

type DistIPP = Double  -- distance

Network Inferred.

Net:[

@1 Age:
{CTleaf _,(Maybe 50:50,N(40.6,27.5)(+-0.5)),...},

@2 Race:
{CTleaf _,_,(Maybe 50:50,mState[0.66,0.34]),...},

@3 Gender:
{CTleaf _,_,_,(Maybe 50:50,mState[0.72,0.28]),...},

@0 Tipe:
{CTfork @1(<|>=19.0|?)[  ... uses @1, @2 and @3, ... ]

@4 Topography:
{CTleaf _,_,_,_,(Maybe 50:50,mState[0.17,0.52,0.31]),...},

@5 Urban:
{CTfork @4(=Mountains..Tidewater|?)[
  {CTleaf _,_,_,_,_,(Maybe 50:50,mState[0.93,0.04,0.04]),...},
  {CTleaf _,_,_,_,_,(Maybe 50:50,mState[0.70,0.19,0.11]),...},
  {CTleaf _,_,_,_,_,(Maybe 50:50,mState[0.38,0.02,0.6 ]),...},
  {CTleaf _,_,_,_,_,(Maybe 50:50,mState[0.73,0.2 ,0.07]),...}]},

@6 HrsNT:
{CTfork @1(<|>=62.0|?)[
  {CTleaf _,_,_,_,_,_,(Maybe 50:50,N( 8.7, 7.6)(+-0.5)),...},
  {CTleaf _,_,_,_,_,_,(Maybe 50:50,N(21.4,26.3)(+-0.5)),...},
  {CTleaf _,_,_,_,_,_,(Maybe 50:50,N(20.0,...1-case...),...}]},

@7 DistIP:
{CTfork @6(<|>=1.0|?)[
  {CTleaf _,_,_,_,_,_,_,(Maybe 50:50,N( ...no-cases... ),...},
  {CTleaf _,_,_,_,_,_,_,(Maybe 50:50,N(0.59,0.6)(+-0.2)),...},
  {CTleaf _,_,_,_,_,_,_,(Maybe 50:50,N(1.52,2.8)(+-0.2)),...}]}]

network: 115.1 nits, data: 5396.6 nits
null:   5935.6 nits (@0..@7)                       [30/4/2004]

Reading

• Allison, L. Types and classes of machine learning and data mining. 26th Australasian Computer Science Conference (ACSC), Adelaide, pp.207-215, Feb 2003.
• Comley, J. and Dowe, D. L. General Bayesian networks and asymmetric languages. Hawaii Int. Conf. Statistics and Related Fields (HICS-2), June 2003.
• Friedman, N. & Goldszmidt, M. Learning Bayesian networks with local structure. UAI'96, pp.252-262, 1996.
• Koester, R. J., Virginia dataset on lost-person behaviour. 2001. Authors' [www site].
• Twardy, C. R. SARbayes: Predicting lost person behavior. Presented to the National Association of Search and Rescue (NASAR), Charlotte, NC. 2002.