For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of variational objective due to the mass-covering property of its minimizer. However, minimizing this objective is challenging. A popular existing approach, Reweighted Wake-Sleep (RWS), suffers from heavily biased gradients and a circular pathology that results in highly concentrated variational distributions. As an alternative, we propose SMC-Wake, a procedure for fitting an amortized variational approximation that uses likelihood-tempered sequential Monte Carlo samplers to estimate the gradient of the inclusive KL divergence. We propose three gradient estimators, all of which are asymptotically unbiased in the number of iterations and two of which are strongly consistent. Our method interleaves stochastic gradient updates, SMC samplers, and iterative improvement to an estimate of the normalizing constant to reduce bias from self-normalization. In experiments with both simulated and real datasets, SMC-Wake fits variational distributions that approximate the posterior more accurately than existing methods.

Amortized variational inference is an often employed framework in simulation-based inference that produces a posterior approximation that can be rapidly computed given any new observation. Unfortunately, there are few guarantees about the quality of these approximate posteriors. We propose Conformalized Amortized Neural Variational Inference (CANVI), a procedure that is scalable, easily implemented, and provides guaranteed marginal coverage. Given a collection of candidate amortized posterior approximators, CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. CANVI ensures that the resulting predictor constructs regions that contain the truth with a user-specified level of probability. CANVI is agnostic to design decisions in formulating the candidate approximators and only requires access to samples from the forward model, permitting its use in likelihood-free settings. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation. Finally, we demonstrate the accurate calibration and high predictive efficiency of CANVI on a suite of simulation-based inference benchmark tasks and an important scientific task: analyzing galaxy emission spectra.

In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound (ELBO), only convergence to a *local* optimum can be guaranteed. In this work, we instead establish the *global* convergence of a particular VI method. This VI method, which may be considered an instance of neural posterior estimation (NPE), minimizes an expectation of the inclusive (forward) KL divergence to fit a variational distribution that is parameterized by a neural network. Our convergence result relies on the neural tangent kernel (NTK) to characterize the gradient dynamics that arise from considering the variational objective in function space. In the asymptotic regime of a fixed, positive-definite neural tangent kernel, we establish conditions under which the variational objective admits a unique solution in a reproducing kernel Hilbert space (RKHS). Then, we show that the gradient descent dynamics in function space converge to this unique function. In ablation studies and practical problems, we demonstrate that our results explain the behavior of NPE in non-asymptotic finite-neuron settings, and show that NPE outperforms ELBO-based optimization, which often converges to shallow local optima.

Cellular barcoding methods offer the exciting possibility of 'infinite-pseudocolor' anatomical reconstruction-i.e., assigning each neuron its own random unique barcoded 'pseudocolor,' and then using these pseudocolors to trace the microanatomy of each neuron. Here we use simulations, based on densely-reconstructed electron microscopy microanatomy, with signal structure matched to real barcoding data, to quantify the feasibility of this procedure. We develop a new blind demixing approach to recover the barcodes that label each neuron, and validate this method on real data with known barcodes. We also develop a neural network which uses the recovered barcodes to reconstruct the neuronal morphology from the observed fluorescence imaging data, 'connecting the dots' between discontiguous barcode amplicon signals. We find that accurate recovery should be feasible, provided that the barcode signal density is sufficiently high. This study suggests the possibility of mapping the morphology and projection pattern of many individual neurons simultaneously, at high resolution and at large scale, via conventional light microscopy.

Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or vector time series sampled at arbitrarily-spaced intervals), for which state-space models are popular due to their linearly-scaling computational costs. It has long been conjectured that state-space models are general, able to approximate any one-dimensional GP. We provide the first general proof of this conjecture, showing that any stationary GP on one dimension with vector-valued observations governed by a Lebesgue-integrable continuous kernel can be approximated to any desired precision using a specifically-chosen statespace model: the Latent Exponentially Generated (LEG) family. This new family offers several advantages compared to the general state-space model: it is always stable (no unbounded growth), the covariance can be computed in closed form, and its parameter space is unconstrained (allowing straightforward estimation via gradient descent). The theorem’s proof also draws connections to Spectral Mixture Kernels, providing insight about this popular family of kernels. We develop parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples.

Modern spatial transcriptomics methods can target thousands of different types of RNA transcripts in a single slice of tissue. Many biological applications demand a high spatial density of transcripts relative to the imaging resolution, leading to partial mixing of transcript rolonies in many voxels; unfortunately, current analysis methods do not perform robustly in this highly-mixed setting. Here we develop a new analysis approach, BARcode DEmixing through Non-negative Spatial Regression (BarDensr): we start with a generative model of the physical process that leads to the observed image data and then apply sparse convex optimization methods to estimate the underlying (demixed) rolony densities. We apply BarDensr to simulated and real data and find that it achieves state of the art signal recovery, particularly in densely-labeled regions or data with low spatial resolution. Finally, BarDensr is fast and parallelizable. We provide open-source code as well as an implementation for the 'NeuroCAAS' cloud platform.

BACKGROUND: A pairings of nucleotide sequences. Given this forbidding free-energy landscape, mechanisms have evolved that contribute to a directed and efficient folding process, including catalytic proteins and error-detecting chaperones. Among structural RNA molecules we make a distinction between "bound" molecules, which are active as part of ribonucleoprotein (RNP) complexes, and "unbound," with physiological functions performed without necessarily being bound in RNP complexes. We hypothesized that unbound molecules, lacking the partnering structure of a protein, would be more vulnerable than bound molecules to kinetic traps that compete with native stem structures. We defined an "ambiguity index"-a normalized function of the primary and secondary structure of an individual molecule that measures the number of kinetic traps available to nucleotide sequences that are paired in the native structure, presuming that unbound molecules would have lower indexes. The ambiguity index depends on the purported secondary structure, and was computed under both the comparative ("gold standard") and an equilibrium-based prediction which approximates the minimum free energy (MFE) structure. Arguing that kinetically accessible metastable structures might be more biologically relevant than thermodynamic equilibrium structures, we also hypothesized that MFE-derived ambiguities would be less effective in separating bound and unbound molecules. RESULTS: We have introduced an intuitive and easily computed function of primary and secondary structures that measures the availability of complementary sequences that could disrupt the formation of native stems on a given molecule-an ambiguity index. Using comparative secondary structures, the ambiguity index is systematically smaller among unbound than bound molecules, as expected. Furthermore, the effect is lost when the presumably more accurate comparative structure is replaced instead by the MFE structure. CONCLUSIONS: A statistical analysis of the relationship between the primary and secondary structures of non-coding RNA molecules suggests that stem-disrupting kinetic traps are substantially less prevalent in molecules not participating in RNP complexes. In that this distinction is apparent under the comparative but not the MFE secondary structure, the results highlight a possible deficiency in structure predictions when based upon assumptions of thermodynamic equilibrium.