We propose a scalable algorithm for model selection in sigmoid belief networks (SBNs), based on the factorized asymptotic Bayesian (FAB) framework. We derive the corresponding generalized factorized information criterion (gFIC) for the SBN, which is proven to be statistically consistent with the marginal log-likelihood. To capture the dependencies within hidden variables in SBNs, a recognition network is employed to model the variational distribution. The resulting algorithm, which we call FABIA, can simultaneously execute both model selection and inference by maximizing the lower bound of gFIC. On both synthetic and real data, our experiments suggest that FABIA, when compared to state-of-the-art algorithms for learning SBNs, $(i)$ produces a more concise model, thus enabling faster testing; $(ii)$ improves predictive performance; $(iii)$ accelerates convergence; and $(iv)$ prevents overfitting.

Neural Information Processing Systems http://nips.cc/

We propose a scalable algorithm for model selection in sigmoid belief networks (SBNs), based on the factorized asymptotic Bayesian (FAB) framework. We derive the corresponding generalized factorized information criterion (gFIC) for the SBN, which is proven to be statistically consistent with the marginal log-likelihood. To capture the dependencies within hidden variables in SBNs, a recognition network is employed to model the variational distribution. The resulting algorithm, which we call FABIA, can simultaneously execute both model selection and inference by maximizing the lower bound of gFIC. On both synthetic and real data, our experiments suggest that FABIA, when compared to state-of-the-art algorithms for learning SBNs, $(i)$ produces a more concise model, thus enabling faster testing; $(ii)$ improves predictive performance; $(iii)$ accelerates convergence; and $(iv)$ prevents overfitting.

The factorized asymptotic Bayesian ( FAB) approach has recently been shown as a scalable model-selection framework for latent variable models.

Neural Information Processing Systems http://nips.cc/

Designing flexible probabilistic models over tree topologies is important for developing efficient phylogenetic inference methods.

Deep dynamic generative models are developed to learn sequential dependencies in time-series data. The multi-layered model is designed by constructing a hierarchy of temporal sigmoid belief networks (TSBNs), defined as a sequential stack of sigmoid belief networks (SBNs). Each SBN has a contextual hidden state, inherited from the previous SBNs in the sequence, and is used to regulate its hidden bias. Scalable learning and inference algorithms are derived by introducing a recognition model that yields fast sampling from the variational posterior. This recognition model is trained jointly with the generative model, by maximizing its variational lower bound on the log-likelihood. Experimental results on bouncing balls, polyphonic music, motion capture, and text streams show that the proposed approach achieves state-of-the-art predictive performance, and has the capacity to synthesize various sequences.

Kernelized attention extends the attention mechanism by modeling sequence correlations through kernel functions, making significant progresses in optimizing attention. Under the guarantee of harmonic analysis theory, kernel functions can be expanded with basis functions, inspiring random feature-based approaches to enhance the efficiency of kernelized attention while maintaining predictive performance. However, current random feature-based works are limited to the Fourier basis expansions under Bochner's theorem. We propose Schoenberg's theorem-based attention (SchoenbAt), which approximates dot-product kernelized attention with the polynomial basis under Schoenberg's theorem via random Maclaurin features and applies a two-stage regularization to constrain the input space and restore the output scale, acting as a drop-in replacement of dot-product kernelized attention. Our theoretical proof of the unbiasedness and concentration error bound of SchoenbAt supports its efficiency and accuracy as a kernelized attention approximation, which is also empirically validated under various random feature dimensions. Evaluations on real-world datasets demonstrate that SchoenbAt significantly enhances computational speed while preserving competitive performance in terms of precision, outperforming several efficient attention methods.

In this paper the authors propose an efficient method for tree probability estimation (given a collection of trees) that relies on the description of trees as subsplit Bayesian networks. Through this representation, the authors relax the classic conditional clade distribution - which assumes that given their parent, sister clades are independent - and assume instead that given their parent subsplit, sister subsplits are independent, thus allowing more dependence structure on sister clades. The authors first present a simple maximum likelihood estimation algorithm for rooted trees, and then propose two alternatives to generalize their work to unrooted trees. They finally illustrate their method on both simulated and real-data experiments. I think this paper is very well written, in particular I have greatly appreciated the Background and SBN description sections that make use of a simple though not trivial example to introduce new notions and provide useful insights on the assumptions.