Binomial evidence

[D Reeves]

Hello,

Thank you very much for creating this library. Its been really useful in my research so far and I really appreciate the level of documentation provided. I am interested in using libDAI to perform inference on a large discrete DAG. I need to learn the conditional probabilities of this graph which I want to learn using EM. In order to test out the API on a simpler example, I have implemented a toy example based on the problem detailed here:

http://ai.stanford.edu/~chuongdo/papers/em_tutorial.pdf

The implementation works, however, I am running into some scaling issues when moving to a more complex problem using a larger graph. I am wondering if I can reduce the number of calculations in the sum product algorithm by supplying the evidence as a binomial random variable rather than a set of categorical variables. The code below is how I currently define a single run of belief propagation in the case where the factor values are known and do not need to be learned. 

  std::vector<Var> Xs;

  for (int i=0; i<11; i++){

    Xs.push_back(Var(i,2));

  }

  std::vector<Factor> CoinFactors = {Factor(Xs[0])};

  CoinFactors[0].set(0, 0.5);

  CoinFactors[0].set(1, 0.5);

  for (int i=1; i < Xs.size(); i++) {

    Factor factor( VarSet(Xs[0], Xs[i]) );

    factor.set(0, 0.6);

    factor.set(1, 0.5);

    factor.set(2, 0.4);

    factor.set(3, 0.5);

    CoinFactors.push_back( factor );

  }

  FactorGraph fg( CoinFactors );

  fg.clamp(1, 0);

  fg.clamp(2, 1);

  fg.clamp(3, 1);

  fg.clamp(4, 1);

  fg.clamp(5, 0);

  fg.clamp(6, 0);

  fg.clamp(7, 1);

  fg.clamp(8, 0);

  fg.clamp(9, 1);

  fg.clamp(10,0);

  PropertySet opts;

  opts.set("inference", string("SUMPROD"));

  opts.set("updates",string("PARALL"));

  opts.set("logdomain", true);

  opts.set("tol", 1e-9);

  opts.set("maxiter", string("1"));

  opts.set("verbose", string("2"));

  BP bp = BP( fg, opts );

  bp.init();

  bp.run();

This code corresponds to learning the posterior probability of the first coin chosen being A or B given that from a single set of coin flips 5 heads and 5 tails are observed (the first outcome in the linked example). I achieve this by defining each of the 10 flips to be a categorical random variable and clamp them to a specific state (H=0, T=1). I wonder if there is any possibility of me defining a single binomial variable where I set state 0 to 5, set state 1 to 5 and then run BP. My larger problem involves evidence as multinomial random variables but understanding how I can implement the binomial case will provide the guidance that I need.

Any ideas on how I can achieve this with libDAI?

Thanks!

[Joris Mooij]

Hi D,

libDAI does not distinguish binary from multinomial/categorical variables.

Best, Joris

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