Inference on a game graph : how to visualise? (Migrated from community.research.microsoft.com)

All replies

• 

  

  0

  Sign in to vote

  jwinn replied on 06-09-2010 1:29 PM

  A great explanation of the TrueSkill model (which doesn't use Infer.NET unfortunately!) is on this page:
  http://www.moserware.com/2010/03/computing-your-skill.html
  It has lots of detailed explanation and visualisations and should help understand how the model works.

  Best,
  John W.

  Friday, June 3, 2011 5:47 PM
• 

  

  0

  Sign in to vote

  alexjames replied on 06-14-2010 8:19 AM

  Thanks john, that's great, just what I wanted. However, I was interested in experimenting with infer.net, so i wonder if i could ask afurther question. 

  Is there a way of representing a ranking inference algorithm without using a Gaussian model? For example, using observed variables that specify if one agent has won or not, as opposed to a pair of agents in which one has won and one has lost, and linking to Bernoulli distributins in some way?

  best

  alex

  Friday, June 3, 2011 5:47 PM
• 

  

  0

  Sign in to vote

  jwinn replied on 06-14-2010 10:17 AM

  I think the main thing you need is to have some continuous latent variable in order to be able to rank players.  This could have a Beta distribution (e.g. over the probability of winning) instead of a Gaussian distribution, but it would be difficult to design a model without such an underlying continuous variable. However, if you come up with one, please share it here!

  Why are you keen for the model not to be Gaussian?

  Best,
  John W.

   

  Friday, June 3, 2011 5:47 PM
• 

  

  0

  Sign in to vote

  alexjames replied on 06-14-2010 10:44 AM

  Hello John

  I was keen to see how to implement the model in infer.net by way of a comparison with the gaussian model (and to familiarise myself with infer.net), as per Stern's Go model which has two different implementations of a ranking model, which i also note has a beta latent variable like you suggest, but bernoulli for the observations: 

  http://research.microsoft.com/pubs/67955/p873-stern.pdf

  "The full Bayesian ranking model can
  infer a global ranking from these pairs. In contrast,
  the Independent Bernoulli model cannot infer a global
  ranking for the chain. It would learn the probabilities
  fA;B;C;Dg = f1=1; 1=2; 1=2; 0=1g where each fraction
  is (times played)/(total times seen). In the second
  graph the data do not provide enough information
  to learn a global ranking."

  I wonder if you could point me in the right direction re. an implementation of the latter?

  Best

  alex

  Friday, June 3, 2011 5:47 PM
• 

  

  0

  Sign in to vote

  alexjames replied on 06-15-2010 5:13 AM

  Hello John

  I have found the below as a starting point for experimentation with inferring beta ranks from bernoulli, from a separate post 'learning a beta. 

  thanks again

  best

  alex

   

  (http://community.research.microsoft.com/forums/p/2779/4456.aspx#4456)

   #light

  // Reference the Infer.NET DLLs

  #r @"C:\Program Files\Microsoft Research\Infer.NET 2.2\bin\Release\Infer.Compiler.dll"
  #r @"C:\Program Files\Microsoft Research\Infer.NET 2.2\bin\Release\Infer.Runtime.dll"

  open MicrosoftResearch.Infer
  open MicrosoftResearch.Infer.Models
  open MicrosoftResearch.Infer.Distributions
  open MicrosoftResearch.Infer.Factors

  let data =
  [|
      [|true;true;false;true;true;false|];
      [|true;true;true;false;true|]
  |]

  // Sizes of the inner arrays

  let sizes = data |> Array.map (fun d -> d.Length)

  // Outer range

  let uRange = Range(sizes.Length)

  // The sizes as a variable array

  let sizesVar = Variable.Constant(sizes, uRange)

  // The inner variable range

  let sRange = Range(sizesVar.[uRange])

  // The Bernoulli parameters

  let epsilon = Variable.Array<double>(uRange)
  epsilon.[uRange] <- Variable.Beta(1.0,1.0).ForEach(uRange)

  // The draws from the Bernoullis

  let e = Variable.Array<_>(Variable.Array<bool>(sRange), uRange)
  e.[uRange].[sRange] <- Variable.Bernoulli(epsilon.[uRange]).ForEach(sRange)

  // The observations:

  e.ObservedValue <- data
  let ie = InferenceEngine(VariationalMessagePassing())
  ie.ShowProgress = false
  let epsPosteriors = Distribution< >.ToArray<Beta[>(ie.Infer< >(epsilon))
  let epsPosteriorMeans = epsPosteriors |> Array.map (fun post -> post.GetMean())
  printf "Epsilon posterior means: %A" epsPosteriorMeans
  ()

  Friday, June 3, 2011 5:47 PM
• 

  

  0

  Sign in to vote

  alexjames replied on 06-15-2010 5:16 AM

  Hello John

  I thnk the below gives me a startig point. 

  Best

  alex

   

   #light

  // Reference the Infer.NET DLLs

  #r @"C:\Program Files\Microsoft Research\Infer.NET 2.2\bin\Release\Infer.Compiler.dll"
  #r @"C:\Program Files\Microsoft Research\Infer.NET 2.2\bin\Release\Infer.Runtime.dll"

  open MicrosoftResearch.Infer
  open MicrosoftResearch.Infer.Models
  open MicrosoftResearch.Infer.Distributions
  open MicrosoftResearch.Infer.Factors

  let data =
  [|
      [|true;true;false;true;true;false|];
      [|true;true;true;false;true|]
  |]

  // Sizes of the inner arrays

  let sizes = data |> Array.map (fun d -> d.Length)

  // Outer range

  let uRange = Range(sizes.Length)

  // The sizes as a variable array

  let sizesVar = Variable.Constant(sizes, uRange)

  // The inner variable range

  let sRange = Range(sizesVar.[uRange])

  // The Bernoulli parameters

  let epsilon = Variable.Array<double>(uRange)
  epsilon.[uRange] <- Variable.Beta(1.0,1.0).ForEach(uRange)

  // The draws from the Bernoullis

  let e = Variable.Array<_>(Variable.Array<bool>(sRange), uRange)
  e.[uRange].[sRange] <- Variable.Bernoulli(epsilon.[uRange]).ForEach(sRange)

  // The observations:

  e.ObservedValue <- data
  let ie = InferenceEngine(VariationalMessagePassing())
  ie.ShowProgress = false
  let epsPosteriors = Distribution< >.ToArray<Beta[>(ie.Infer< >(epsilon))
  let epsPosteriorMeans = epsPosteriors |> Array.map (fun post -> post.GetMean())
  printf "Epsilon posterior means: %A" epsPosteriorMeans
  ()

  Friday, June 3, 2011 5:47 PM
• 

  

  0

  Sign in to vote

  jwinn replied on 06-17-2010 3:06 PM

  Hi Alex,

  Glad you're making progress - post again if you have particular questions on anything.

  Best,
  John W.

  • Marked as answer by Microsoft Research Friday, June 3, 2011 5:47 PM

  Friday, June 3, 2011 5:47 PM