Source
Blei, Griffiths and Jordan (2010), LIT-1542, §6.3 and Figs. 9–10, read in full in NOTE-1176 from arXiv 0710.0845v3.
What was actually shown
The JACM corpus (536 abstracts) was split five ways. hLDA was run with infinite depth, and LDA at a range of topic counts around hLDA’s posterior mean, with all hyperparameters given priors and integrated out. For each of 100 posterior samples of the latent variables on the training documents, 800 samples on the held-out documents gave a harmonic-mean estimate of their conditional probability, and these were averaged. The posterior over hLDA’s topic count had its mode near 140. “At each fixed topic cardinality in this range of topics, hLDA provides significantly better predictive performance than LDA.”
The authors frame it as an hLDA-centred test: LDA is “significantly more” flexible, since a document can use any mixture of its topics, so “for large corpora we can expect LDA to dominate hLDA in terms of predictive performance”. The finding is that, in the range near its own size, the single-path constraint helps rather than hurts.
What could have come out otherwise: the flexible model could have won at every topic count, as the authors expect at large ones.
Why it is Proposed
The harmonic-mean estimator of a marginal likelihood (Kass and Raftery, cited by the paper) is unstable, tends to overestimate, and can have infinite variance. The margins in Fig. 9 are large, but no interval on the estimator is given. One corpus was used.
What this does not say
- Not that hierarchies predict better than flat models. The paper expects the reverse when the topic count is free, and says so.
- Not that hLDA’s topics are more interpretable. That is Fig. 10’s separate claim, by eye, against an LDA run with function words left in.
- Not about multiple-path hierarchies. The nested HDP (LIT-002, NOTE-023) is a different comparison.
Connections
- QUESTION-276. T21 asked that a hierarchy be allowed “to lose if it doesn’t provide useful explanatory compression”. This is the original paper’s version of that test: it passes in a range, on one corpus, by an estimator that needs replacing. A hierarchy over members’ activity would need the same test against a flat mixed-membership model, with held-out data the inference did not see.
Note of 2026-10-30: what holds it back
The title states held-out likelihoods that the paper estimated only by the harmonic-mean estimator, which can overestimate and have infinite variance, with no interval given. A re-estimate with a controlled estimator is the missing result. Narrowing to what the paper reports would free nothing, so it is not narrowed (ADR-065 §7).