Decision Tree Improvements

[varunagrawal]

1. Unique is now bottom-up, since I found another test case where it was incorrect and this fixes it.
2. Print the number of assignments inside square brackets when printing a DecisionTree.
3. Change GTSAM_DT_NO_PRUNING to GTSAM_DT_MERGING so it disambiguates from Hybrid pruning.
4. Expose GTSAM_DT_MERGING via CMake.

[dellaert]

LGTM but see my question. email me when I should look again

[dellaert]

Why do all these have a Unique now? That was not detailed in the PR comment

[varunagrawal]

Okay I undid that. Looks like it was a remnant of debugging.

[varunagrawal]

TODO(Varun): Elaborate more on how this works.

[varunagrawal]

@dellaert so I am really struggling with implementing this function correctly in the decision tree

// Applying binary operator to two leaves results in a leaf
  NodePtr apply_g_op_fL(const Leaf& fL, const Binary& op) const override {
    // fL op gL
    // TODO(Varun) Is the nrAssignments setting correct?
    NodePtr h(new Leaf(op(fL.constant_, constant_), fL.nrAssignments()));
    return h;
  }

I only need nrAssignments for pruning in the DecisionTreeFactor, so I replaced that with a loop over all the assignments in the cartesian product (which is a bit slower)

auto allValues = DiscreteValues::CartesianProduct(this->discreteKeys());
for (auto&& val : allValues) {
  double prob = (*this)(val);
  probabilities.push_back(prob);
}

It seems that there is no time improvement, since the test case is now taking 131.93 seconds compared to 117 seconds with the cartesian product taking up 12.8236 seconds (which accounts for the time difference).

My conclusion is that perhaps the DecisionTreeFactor is inherently non-scalable, which means I should perhaps move to the TableFactor.

[varunagrawal]

I am contemplating removing the nrAssignments variable since I introduced it just for pruning and it is not being correctly computed. :(