[Paper Review] Online Neural Connectivity Estimation with Noisy Group Testing

Anne Draelos, John Pearson|arXiv (Cornell University)|Jan 1, 2020

SARS-CoV-2 detection and testing4 citations

TL;DR

This paper proposes a noisy group testing framework to efficiently infer binary neural connectivity in large, sparse networks using holographic photostimulation. By stimulating neuron ensembles instead of individuals, the method reduces required tests to logarithmic scale with population size and frames connectivity estimation as a convex optimization problem equivalent to variational Bayesian inference, enabling real-time, streaming connectivity inference for networks of tens of thousands of neurons.

ABSTRACT

One of the primary goals of systems neuroscience is to relate the structure of neural circuits to their function, yet patterns of connectivity are difficult to establish when recording from large populations in behaving organisms. Many previous approaches have attempted to estimate functional connectivity between neurons using statistical modeling of observational data, but these approaches rely heavily on parametric assumptions and are purely correlational. Recently, however, holographic photostimulation techniques have made it possible to precisely target selected ensembles of neurons, offering the possibility of establishing direct causal links. A naive method for inferring functional connections is to stimulate each individual neuron multiple times and observe the responses of cells in the local network, but this approach scales poorly with the number of neurons. Here, we propose a method based on noisy group testing that drastically increases the efficiency of this process in sparse networks. By stimulating small ensembles of neurons, we show that it is possible to recover binarized network connectivity with a number of tests that grows only logarithmically with population size under minimal statistical assumptions. Moreover, we prove that our approach, which reduces to an efficiently solvable convex optimization problem, is equivalent to Variational Bayesian inference on the binary connection weights, and we derive rigorous bounds on the posterior marginals. This allows us to extend our method to the streaming setting, where continuously updated posteriors allow for optional stopping, and we demonstrate the feasibility of inferring connectivity for networks of up to tens of thousands of neurons online.

Motivation & Objective

• Address the challenge of inferring functional neural connectivity in large populations of neurons during behavior, where traditional methods are limited by scalability and reliance on parametric assumptions.
• Overcome the inefficiency of stimulating neurons individually by leveraging group testing to reduce the number of required stimulations.
• Develop a method that operates under minimal statistical assumptions while enabling causal inference through targeted photostimulation.
• Enable real-time, streaming connectivity estimation with optional stopping by deriving time-evolving posterior marginals.
• Scale connectivity inference to networks of tens of thousands of neurons using a computationally efficient, convex optimization formulation.

Proposed method

• Formulate neural connectivity estimation as a noisy group testing problem, where neuron ensembles are stimulated and response patterns are used to infer binary synaptic connections.
• Model the connection weights as latent binary variables and use variational Bayesian inference to approximate the posterior distribution over these weights.
• Reduce the inference problem to a convex optimization problem that can be efficiently solved using standard numerical methods.
• Derive rigorous analytical bounds on the posterior marginals of connection weights, enabling confidence quantification and optional stopping in streaming settings.
• Integrate the method into a streaming framework where new stimulation-response data continuously update the posterior, allowing online connectivity estimation.
• Leverage the sparsity of neural networks to ensure that the number of required tests grows logarithmically with population size, not linearly.

Experimental results

Research questions

• RQ1 Can group testing principles be applied to neural connectivity estimation to drastically reduce the number of required stimulations in large-scale neural circuits?
• RQ2 How can a method be designed to infer binary connectivity with minimal statistical assumptions while maintaining computational efficiency?
• RQ3 To what extent can variational Bayesian inference be used to derive analytically tractable posteriors for connection weights in neural networks?
• RQ4 Can the method support real-time, streaming inference with optional stopping based on confidence in connectivity estimates?
• RQ5 What is the scalability of the approach in terms of population size, and can it handle networks of tens of thousands of neurons?

Key findings

• The proposed method reduces the number of required stimulations to grow logarithmically with network size, enabling scalable inference in large neural populations.
• The method is equivalent to variational Bayesian inference on binary connection weights, providing a principled probabilistic framework for connectivity estimation.
• Rigorous analytical bounds on posterior marginals are derived, enabling confidence quantification and support for optional stopping in online settings.
• The inference problem reduces to a convex optimization problem, ensuring computational efficiency and numerical stability.
• The method is demonstrated to be feasible for online connectivity inference in networks of up to tens of thousands of neurons.
• The approach enables direct causal inference through targeted photostimulation, overcoming the purely correlational limitations of prior statistical methods.