A.1 List of Neural Topic Modeling Works used in our Meta-Analysis In Table 6, we report the forty publications used in our meta-analysis (Section 3), which are sourced from a survey of neural topic models (Zhao et al., 2021b). A.2 Preprocessing Details Our steps are delineated in our implementation,22 but we list our choices here for easy reference. Corpus statistics are in Table 7. We use the default en-core-web-smspaCy model (Honnibal et al., 2020), version 3.0.5, Document processing - We do not process documents with fewer than 25 whitespace-separated tokens.

State-space graphical models and the variational autoencoder framework provide a principled apparatus for learning dynamical systems from data. State-of-the-art probabilistic approaches are often able to scale to large problems at the cost of flexibility of the variational posterior or expressivity of the dynamics model. However, those consolidations can be detrimental if the ultimate goal is to learn a generative model capable of explaining the spatiotemporal structure of the data and making accurate forecasts. We introduce a low-rank structured variational autoencoding framework for nonlinear Gaussian state-space graphical models capable of capturing dense covariance structures that are important for learning dynamical systems with predictive capabilities. Our inference algorithm exploits the covariance structures that arise naturally from sample based approximate Gaussian message passing and low-rank amortized posterior updates -- effectively performing approximate variational smoothing with time complexity scaling linearly in the state dimensionality. In comparisons with other deep state-space model architectures our approach consistently demonstrates the ability to learn a more predictive generative model. Furthermore, when applied to neural physiological recordings, our approach is able to learn a dynamical system capable of forecasting population spiking and behavioral correlates from a small portion of single trials.

We introduce the variational filtering EM algorithm, a simple, general-purpose method for performing variational inference in dynamical latent variable models using information from only past and present variables, i.e. filtering. The algorithm is derived from the variational objective in the filtering setting and consists of an optimization procedure at each time step. By performing each inference optimization procedure with an iterative amortized inference model, we obtain a computationally efficient implementation of the algorithm, which we call amortized variational filtering. We present experiments demonstrating that this general-purpose method improves inference performance across several recent deep dynamical latent variable models.

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For decades, the dominant paradigm for approximate Bayesian inferencep(z|x) = p(z,x)/p(x) has been Markov-Chain Monte-Carlo (MCMC) algorithms, which estimate the evidencep(x) = R p(z,x)dz via sampling. However, since sampling tends to be a slow and computationally intensive process, these sampling-based approximate inference methods fadewhendealing withthemodern probabilistic machine learning problems that usually involveverycomplexmodels, high-dimensional feature spaces andlargedatasets.