Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems.

We further give "active local" versions of these heuristics: given atest pointx?,we show how the labelT(x?) With this information, we may decide thathwould not have been of much utility anyway, thereby saving ourselves the resources and effort to label the entire datasetS (and to runA).

We obtain our algorithm via a connection to the problem of implicitly learning decision trees.

We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG)and Chow-Liu Recursive Grouping (CLRG)without theassumption thattheeffectivedepth isbounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization inCLRG greatly reduces the sample complexity ofRG from being exponential in the diameter of the tree to onlylogarithmic inthediameter forthehidden Markovmodel (HMM).

Our method is able to routinely handle large data-sets with more than 7,000 sample points and outperform heuristics methods and other MIP based techniques.