We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over multiple samples, for little more computational cost than drawing a single additional collapsed Gibbs sample. Our approach can be understood as adapting the soft clustering methodology of Collapsed Variational Bayes (CVB0) to CGS parameter estimation, in order to get the best of both techniques. Our estimators can straightforwardly be applied to the output of any existing implementation of CGS, including modern accelerated variants. We perform extensive empirical comparisons of our estimators with those of standard collapsed inference algorithms on real-world data for both unsupervised LDA and Prior-LDA, a supervised variant of LDA for multi-label classification. Our results show a consistent advantage of our approach over traditional CGS under all experimental conditions, and over CVB0 inference in the majority of conditions. More broadly, our results highlight the importance of averaging over multiple samples in LDA parameter estimation, and the use of efficient computational techniques to do so.

A central goal of cognitive neuroscience is to decode human brain activity-that is, to infer mental processes from observed patterns of whole-brain activation. Previous decoding efforts have focused on classifying brain activity into a small set of discrete cognitive states. To attain maximal utility, a decoding framework must be open-ended, systematic, and context-sensitive-that is, capable of interpreting numerous brain states, presented in arbitrary combinations, in light of prior information. Here we take steps towards this objective by introducing a probabilistic decoding framework based on a novel topic model-Generalized Correspondence Latent Dirichlet Allocation-that learns latent topics from a database of over 11,000 published fMRI studies. The model produces highly interpretable, spatially-circumscribed topics that enable flexible decoding of whole-brain images. Importantly, the Bayesian nature of the model allows one to "seed" decoder priors with arbitrary images and text-enabling researchers, for the first time, to generate quantitative, context-sensitive interpretations of whole-brain patterns of brain activity.

This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.