Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
Neural Comput. 2020 Apr;32(4):794-828. doi: 10.1162/neco_a_01267. Epub 2020 Feb 18.
Optimality principles have been useful in explaining many aspects of biological systems. In the context of neural encoding in sensory areas, optimality is naturally formulated in a Bayesian setting as neural tuning which minimizes mean decoding error. Many works optimize Fisher information, which approximates the minimum mean square error (MMSE) of the optimal decoder for long encoding time but may be misleading for short encoding times. We study MMSE-optimal neural encoding of a multivariate stimulus by uniform populations of spiking neurons, under firing rate constraints for each neuron as well as for the entire population. We show that the population-level constraint is essential for the formulation of a well-posed problem having finite optimal tuning widths and optimal tuning aligns with the principal components of the prior distribution. Numerical evaluation of the two-dimensional case shows that encoding only the dimension with higher variance is optimal for short encoding times. We also compare direct MMSE optimization to optimization of several proxies to MMSE: Fisher information, maximum likelihood estimation error, and the Bayesian Cramér-Rao bound. We find that optimization of these measures yields qualitatively misleading results regarding MMSE-optimal tuning and its dependence on encoding time and energy constraints.
最优性原理在解释生物系统的许多方面都很有用。在感觉区域的神经编码背景下，最优性自然可以在贝叶斯框架中表述为最小化平均解码误差的神经调谐。许多工作优化 Fisher 信息，它近似于最优解码器的最小均方误差 (MMSE)，对于长编码时间是有效的，但对于短编码时间可能会产生误导。我们研究了在每个神经元和整个神经元群体的 firing rate 约束下，通过具有固定发放率的神经元群体对多元刺激进行 MMSE 最优神经编码。我们表明，群体水平的约束对于形成具有有限最优调谐宽度的良好问题公式是必不可少的，并且最优调谐与先验分布的主成分一致。对二维情况的数值评估表明，对于短编码时间，只对具有更高方差的维度进行编码是最优的。我们还将直接 MMSE 优化与 MMSE 的几个代理优化进行了比较：Fisher 信息、最大似然估计误差和贝叶斯克拉美罗界。我们发现，这些措施的优化在 MMSE 最优调谐及其对编码时间和能量约束的依赖方面产生了定性上的误导结果。
