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. 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, can be related 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. Finally, we show how our work can be theoretically linked to compressed sensing approaches, and compare results for connectivity inference in different settings.
翻译:系统神经科学的首要目标之一是将神经电路的结构与其功能联系起来,然而,连接模式在从大量人群中记录时很难确定。以前的许多方法都试图利用观测数据的统计模型来估计神经元之间的功能连接。许多先前的方法试图利用观测数据的统计模型来估计神经元之间的功能连接,但这些方法严重依赖参数假设,而且纯粹具有相关性。然而,最近,全息摄影模拟技术使得有可能精确地针对选定的神经元集合,提供了建立直接因果关系的可能性。在这里,我们建议了一种基于噪音群体测试的方法,大大提高了稀疏网络中这一过程的效率。通过刺激神经元的小型聚合,我们表明有可能恢复双子网络的连接,而根据最低统计假设,这些测试只能与人口规模的对数一致增长。此外,我们证明我们的方法,即降低到高效的溶解的锥体优化问题,可以与Variational Bayesian 比较二联结重量的方法有关,我们可以在远处网络上找到严格界限,我们从远端网络上找到精确的精确度,这样可以让我们在直径网络上展示我们的方法。