SemiMultiPose: A Semi-supervised Multi-animal Pose Estimation Framework

Multi-animal pose estimation is essential for studying animals' social behaviors in neuroscience and neuroethology. Advanced approaches have been proposed to support multi-animal estimation and achieve state-of-the-art performance. However, these models rarely exploit unlabeled data during training even though real world applications have exponentially more unlabeled frames than labeled frames. Manually adding dense annotations for a large number of images or videos is costly and labor-intensive, especially for multiple instances. Given these deficiencies, we propose a novel semi-supervised architecture for multi-animal pose estimation, leveraging the abundant structures pervasive in unlabeled frames in behavior videos to enhance training, which is critical for sparsely-labeled problems. The resulting algorithm will provide superior multi-animal pose estimation results on three animal experiments compared to the state-of-the-art baseline and exhibits more predictive power in sparsely-labeled data regimes.

Attentive Clustering Processes

Amortized approaches to clustering have recently received renewed attention thanks to novel objective functions that exploit the expressiveness of deep learning models. In this work we revisit a recent proposal for fast amortized probabilistic clustering, the Clusterwise Clustering Process (CCP), which yields samples from the posterior distribution of cluster labels for sets of arbitrary size using only O(K) forward network evaluations, where K is an arbitrary number of clusters. While adequate in simple datasets, we show that the model can severely underfit complex datasets, and hypothesize that this limitation can be traced back to the implicit assumption that the probability of a point joining a cluster is equally sensitive to all the points available to join the same cluster. We propose an improved model, the Attentive Clustering Process (ACP), that selectively pays more attention to relevant points while preserving the invariance properties of the generative model. We illustrate the advantages of the new model in applications to spike-sorting in multi-electrode arrays and community discovery in networks. The latter case combines the ACP model with graph convolutional networks, and to our knowledge is the first deep learning model that handles an arbitrary number of communities.

A zero-inflated gamma model for deconvolved calcium imaging traces

Calcium imaging is a critical tool for measuring the activity of large neural populations. Much effort has been devoted to developing "pre-processing" tools for calcium video data, addressing the important issues of e.g., motion correction, denoising, compression, demixing, and deconvolution. However, statistical modeling of deconvolved calcium signals (i.e., the estimated activity extracted by a pre-processing pipeline) is just as critical for interpreting calcium measurements, and for incorporating these observations into downstream probabilistic encoding and decoding models. Surprisingly, these issues have to date received significantly less attention. In this work we examine the statistical properties of the deconvolved activity estimates, and compare probabilistic models for these random signals. In particular, we propose a zero-inflated gamma (ZIG) model, which characterizes the calcium responses as a mixture of a gamma distribution and a point mass that serves to model zero responses. We apply the resulting models to neural encoding and decoding problems. We find that the ZIG model outperforms simpler models (e.g., Poisson or Bernoulli models) in the context of both simulated and real neural data, and can therefore play a useful role in bridging calcium imaging analysis methods with tools for analyzing activity in large neural populations.

Disentangled sticky hierarchical Dirichlet process hidden Markov model

The Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) has been used widely as a natural Bayesian nonparametric extension of the classical Hidden Markov Model for learning from sequential and time-series data. A sticky extension of the HDP-HMM has been proposed to strengthen the self-persistence probability in the HDP-HMM. However, the sticky HDP-HMM entangles the strength of the self-persistence prior and transition prior together, limiting its expressiveness. Here, we propose a more general model: the disentangled sticky HDP-HMM (DS-HDP-HMM). We develop novel Gibbs sampling algorithms for efficient inference in this model. We show that the disentangled sticky HDP-HMM outperforms the sticky HDP-HMM and HDP-HMM on both synthetic and real data, and apply the new approach to analyze neural data and segment behavioral video data.

General linear-time inference for Gaussian Processes on one dimension

Gaussian Processes (GPs) provide a powerful probabilistic framework for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we prove that for data sampled on one dimension (e.g., a time series sampled at arbitrarily-spaced intervals), approximate GP inference at any desired level of accuracy requires computational effort that scales linearly with the number of observations; this new theorem enables inference on much larger datasets than was previously feasible. To achieve this improved scaling we propose a new family of stationary covariance kernels: the Latent Exponentially Generated (LEG) family, which admits a convenient stable state-space representation that allows linear-time inference. We prove that any continuous integrable stationary kernel can be approximated arbitrarily well by some member of the LEG family. The proof draws connections to Spectral Mixture Kernels, providing new insight about the flexibility of this popular family of kernels. We propose 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.

Discrete Neural Processes

Many data generating processes involve latent random variables over discrete combinatorial spaces whose size grows factorially with the dataset. In these settings, existing posterior inference methods can be inaccurate and/or very slow. In this work we develop methods for efficient amortized approximate Bayesian inference over discrete combinatorial spaces, with applications to random permutations, probabilistic clustering (such as Dirichlet process mixture models) and random communities (such as stochastic block models). The approach is based on mapping distributed, symmetry-invariant representations of discrete arrangements into conditional probabilities. The resulting algorithms parallelize easily, yield iid samples from the approximate posteriors, and can easily be applied to both conjugate and non-conjugate models, as training only requires samples from the generative model.

Amortized Bayesian inference for clustering models

We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed, symmetry-invariant representations of cluster arrangements into conditional probabilities. The method parallelizes easily, yields iid samples from the approximate posterior of cluster assignments with the same computational cost of a single Gibbs sampler sweep, and can easily be applied to both conjugate and non-conjugate models, as training only requires samples from the generative model.

A Novel Variational Family for Hidden Nonlinear Markov Models

Latent variable models have been widely applied for the analysis and visualization of large datasets. In the case of sequential data, closed-form inference is possible when the transition and observation functions are linear. However, approximate inference techniques are usually necessary when dealing with nonlinear dynamics and observation functions. Here, we propose a novel variational inference framework for the explicit modeling of time series, Variational Inference for Nonlinear Dynamics (VIND), that is able to uncover nonlinear observation and transition functions from sequential data. The framework includes a structured approximate posterior, and an algorithm that relies on the fixed-point iteration method to find the best estimate for latent trajectories. We apply the method to several datasets and show that it is able to accurately infer the underlying dynamics of these systems, in some cases substantially outperforming state-of-the-art methods.

Penalized matrix decomposition for denoising, compression, and improved demixing of functional imaging data

Calcium imaging has revolutionized systems neuroscience, providing the ability to image large neural populations with single-cell resolution. The resulting datasets are quite large, which has presented a barrier to routine open sharing of this data, slowing progress in reproducible research. State of the art methods for analyzing this data are based on non-negative matrix factorization (NMF); these approaches solve a non-convex optimization problem, and are effective when good initializations are available, but can break down in low-SNR settings where common initialization approaches fail. Here we introduce an approach to compressing and denoising functional imaging data. The method is based on a spatially-localized penalized matrix decomposition (PMD) of the data to separate (low-dimensional) signal from (temporally-uncorrelated) noise. This approach can be applied in parallel on local spatial patches and is therefore highly scalable, does not impose non-negativity constraints or require stringent identifiability assumptions (leading to significantly more robust results compared to NMF), and estimates all parameters directly from the data, so no hand-tuning is required. We have applied the method to a wide range of functional imaging data (including one-photon, two-photon, three-photon, widefield, somatic, axonal, dendritic, calcium, and voltage imaging datasets): in all cases, we observe ~2-4x increases in SNR and compression rates of 20-300x with minimal visible loss of signal, with no adjustment of hyperparameters; this in turn facilitates the process of demixing the observed activity into contributions from individual neurons. We focus on two challenging applications: dendritic calcium imaging data and voltage imaging data in the context of optogenetic stimulation. In both cases, we show that our new approach leads to faster and much more robust extraction of activity from the data.

Reparameterizing the Birkhoff Polytope for Variational Permutation Inference

Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation, but fully Bayesian inference poses a severe challenge in this high-dimensional, discrete space. To surmount this challenge, we start with the usual step of relaxing a discrete set (here, of permutation matrices) to its convex hull, which here is the Birkhoff polytope: the set of all doubly-stochastic matrices. We then introduce two novel transformations: first, an invertible and differentiable stick-breaking procedure that maps unconstrained space to the Birkhoff polytope; second, a map that rounds points toward the vertices of the polytope. Both transformations include a temperature parameter that, in the limit, concentrates the densities on permutation matrices. We then exploit these transformations and reparameterization gradients to introduce variational inference over permutation matrices, and we demonstrate its utility in a series of experiments.