<p>In <a href="https://github.com/mlpack/mlpack/pull/751#discussion_r73780816">src/mlpack/core/dists/gamma_distribution.cpp</a>:</p>
<pre style='color:#555'>> @@ -53,6 +64,13 @@ void GammaDistribution::Train(const arma::mat& rdata, const double tol)
> Train(logMeanxVec, meanLogxVec, meanxVec, tol);
> }
>
> +// Fits an alpha and beta parameter according to observation probabilities.
> +void GammaDistribution::Train(const arma::mat& observations,
> + const arma::vec& probabilities,
> + const double tol)
> +{
</pre>
<p>Here's an idea for this. The idea is that we are training the distribution, but we do not know for certain that the points we are training on came from this distribution---we only have an estimate between 0 and 1 of how likely we think it is that the point came from this distribution. So we can train using the probabilities as weights.</p>
<p>We can use each of the probabilities to construct a "weighted" version of <code>meanLogxVec</code>, <code>meanxVec</code>, and <code>logMeanxVec</code>. This means we can't use Armadillo's nice syntax though since we have to implement this ourselves.</p>
<pre><code>arma::vec meanLogxVec(rdata.n_rows, arma::fill::zeros);
arma::vec meanxVec(rdata.n_rows, arma::fill::zeros);
arma::vec logMeanxVec(rdata.n_rows, arma::fill::zeros);
for (size_t i = 0; i < rdata.n_cols; ++i)
{
meanLogxVec += probabilities(i) * std::log(rdata.col(i));
meanxVec += probabilities(i) * rdata.col(i);
}
meanLogxVec /= arma::accu(probabilities);
meanxVec /= arma::accu(probabilities);
logMeanxVec = arma::log(meanxVec);
Train(logMeanxVec, meanLogxVec, meanxVec, tol);
</code></pre>
<p>What do you think?</p>
<p>Testing that could be done by generating points from a Gamma distribution, assigning them a random weight between, e.g., 0.9 and 1, and then generating points from a uniform distribution, and assigning those points a random weight between, e.g, 0.0 and 0.02. Then, call Train() with probabilities, and ensure the resulting trained Gamma distribution is close to the distribution that was used to generate points.</p>
<p>What do you think? I've only outlined ideas here, but I can implement them if you need.</p>
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