<p>See <a href="https://github.com/mlpack/mlpack/issues/809" class="issue-link js-issue-link" data-url="https://github.com/mlpack/mlpack/issues/809" data-id="187261339" data-error-text="Failed to load issue title" data-permission-text="Issue title is private">#809</a> for the discussion that led to this ticket.</p>
<p>Currently, the <code>DiscreteDistribution</code> class in <code>src/mlpack/core/dists/</code> only supports single-dimension discrete inputs (like <code>(1)</code>, <code>(2)</code>, <code>(5)</code>, etc.).  It would be very useful if it instead supported multi-dimensional discrete inputs (like <code>(1, 2, 3)</code>, <code>(3, 5, 8)</code>, <code>(1, 7, 5)</code>).  So the <code>DiscreteDistribution</code> class can easily be extended to support that case.  Right now, in the single dimension case, the probability of some input X is simply stored as P(X).  Now, with multi-dimensional inputs x_1, x_2, ..., x_d, the probability should be P(x_1) P(x_2) ... P(x_d) (just single-dimension probabilities multiplied).</p>
<p>When we close this ticket it should be possible to train multi-dimensional discrete HMMs with the <code>mlpack_hmm_train</code> program, and there should also be tests for the multi-dimensional support in <code>src/mlpack/tests/distribution_test.cpp</code>.</p>

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