Source
Van Gael, Saatci, Teh and Ghahramani (2008), LIT-1622, read in full in NOTE-1204: §5.1 (two synthetic designs), §5.2 (well-log data) and §5.3 (Alice in Wonderland).
What was actually shown
- On the almost cyclic synthetic sequence, the beam sampler “discovers the underlying structure much faster” in Hamming error after greedy matching, averaged over 20 runs, and its curve does not move with the hyperprior, while Gibbs gets worse as the prior is strengthened (Figure 3).
- With uninformative emissions, as self-transition rises from 0.75 to 0.999, “the beam sampler mixes increasingly well, the Gibbs sampler suffers from slow random walk behavior” (Figure 4, 60 starts).
- On 4050 well-log measurements with a Cauchy likelihood, after 10,000 iterations Gibbs “hasn’t discovered any structure while the beam sampler has” (Figure 6, by eye).
- After about 20 iterations the beam sampler sums over “a little more than one state” per step on the first synthetic set (Figure 3, bottom).
- On text, both converge to the same performance; the paper says that experiment does not compare the samplers.
What would settle it
Numbers per unit of computation on persistent sequences, as stated in promote_when. The paper reports neither timings nor effective sample sizes.
Connections
- THEORY-1037. The exactness of the sampler is settled; this is the separate claim about speed.
- LIT-1577. The infinite factorial HMM’s experiments rely on a sampler of this kind and report two single runs (NOTE-1199); they add no evidence on mixing.