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LIT-1626: Infinite Sparse Factor Analysis and Infinite Independent Components Analysis

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Properties7
StatusActive — read 2026-10-27 (NOTE-1209) in full, from the authors' own copy of the ICA 2007 paper; worth reading for infinite sparse factor analysis and infinite ICA, in which an Indian buffet process masks which of unboundedly many sources is active at each data point, the model the infinite factorial HMM's experiments compare against, and for its sampler, whose ratio for a source being on or off shows how far the data can tell an inactive source from an active one at zero (THEORY-1046). Read it knowing that its results are boxplots and a Hinton diagram, that its text and figure caption disagree on the synthetic data's size, and that it misstates the one-parameter IBP's total number of features.
Version2
Tagsprobabilistic-modeling, mathematical-statistics
ExtendsLIT-1623 — Infinite Latent Feature Models and the Indian Buffet Process
Cited as “compared against” byLIT-1577 — The Infinite Factorial Hidden Markov Model
Cited as “paper” byNOTE-1209 — Knowles and Ghahramani — Infinite sparse factor analysis and infinite independent components analysis
Cited as “source” byTHEORY-1046 — In infinite sparse factor analysis, where a binary mask says whether a source is active at a data point and an independent Gaussian value says how strongly, the evidence of that data point for the source being active, with its value integrated out, is σ̂·exp(μ̂²/(2σ̂²)) for the posterior mean μ̂ and standard deviation σ̂ of the value; when the residual has no component along the source's loading the ratio is σ̂, below one, so the data favour an inactive source over an active one at zero by a factor that the prior on the value sets

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Knowles, D. & Ghahramani, Z. (2007). Infinite sparse factor analysis and infinite independent components analysis. In M. E. Davies, C. J. James, S. A. Abdallah & M. D. Plumbley (eds.), Independent Component Analysis and Signal Separation (ICA 2007), LNCS 4666, pp. 381–388. Springer. doi:10.1007/978-3-540-74494-8_48.

Read in full on 2026-10-27 (NOTE-1209). One account was drawn from it: THEORY-1046.

Why this is here

The owner asked on 2026-10-27 to “file the next readings”. The infinite factorial HMM (LIT-1577) measures its Markov IBP prior against this paper’s infinite ICA, which finds nine speakers where the Markov prior finds five (NOTE-1199). Its model, a binary mask times a continuous activation, is the shape of CASE-165’s split between holding a feature (B) and using it (a), and its sampler states exactly what the data say about that split at one data point.

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