Esempio n. 1
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  /**
   * {@inheritDoc}
   *
   * <p>Computes KL as follows, where &Gamma;(x) is the gamma function and &psi;(x) is the digamma
   * function.
   *
   * <p>(&alpha;<sub>P</sub>-&alpha;<sub>Q</sub>)&psi;(&alpha;<sub>P</sub>) -
   * ln(&Gamma;(&alpha;<sub>P</sub>)) + ln(&Gamma;(&alpha;<sub>Q</sub>)) +
   * &alpha;<sub>Q</sub>(ln(&beta;<sub>P</sub>/&beta;<sub>Q</sub>)) +
   * &alpha;<sub>P</sub>(&beta;<sub>Q</sub>-&beta;<sub>P</sub>)/&beta;<sub>P</sub>
   *
   * @see <a
   *     href="http://en.wikipedia.org/wiki/Gamma_distribution#Kullback.E2.80.93Leibler_divergence"
   *     >Gamma distribution (Wikipedia)</a>
   */
  @Override
  public double computeKLDivergence(IParameterizedMessage that) {
    if (that instanceof GammaParameters) {
      // KL(P|Q) == (ap-aq)*digamma(ap) - log(gamma(ap)) + log(gamma(aq)) + aq*(log(bp)-log(bq)) +
      // ap*(bq-bp)/bp

      final GammaParameters P = this, Q = (GammaParameters) that;
      final double ap = P.getAlpha(), aq = Q.getAlpha();
      final double bp = P.getBeta(), bq = Q.getBeta();

      double divergence = 0.0;
      if (ap != aq) {
        divergence += (ap - aq) * digamma(ap);
        divergence -= logGamma(ap);
        divergence += logGamma(aq);
      }

      if (bp != bq) {
        divergence += aq * (Math.log(bp) - Math.log(bq)) + ap * ((bq - bp) / bp);
      }

      return divergence;
    }

    throw new IllegalArgumentException(
        String.format("Expected '%s' but got '%s'", getClass(), that.getClass()));
  }