Minimal models of multidimensional computations.
Minimal models of multidimensional computations.
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DOI：
10.1371/journal.pcbi.1001111
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发表时间：
2011-03
影响因子：
4.3
通讯作者：
Sharpee TO
中科院分区：
文献类型：
--
作者：
Fitzgerald JD;Sincich LC;Sharpee TO
由许多生物系统执行的多维计算通常以关于输入和输出之间的相关性的有限信息为特征。考虑到这一限制，我们的方法是构造系统的最大噪声熵响应函数，从而得到与输入/输出矩的给定约束集一致的封闭形式和最小偏差模型;结果等同于机器学习的条件随机场模型。对于具有二进制输出的系统，例如编码感官刺激的神经元，最大噪声熵模型是其参数取决于约束的逻辑函数。对平均输出的约束将二进制最大噪声熵模型变成最小互信息模型，允许计算约束的信息内容和系统计算的信息论表征。我们使用这种方法来分析猕猴视网膜和丘脑的非线性输入/输出功能，虽然这些系统以前已被证明是响应于两个输入维度，在这个减少的空间中的响应函数的函数形式还没有明确确定。一个二阶模型的基础上的逻辑函数被发现是必要的和足够的，以准确地描述自然刺激的神经反应，占平均93%的互信息与少量的参数。因此，尽管刺激是高度非高斯的，但神经响应中的绝大多数信息与一阶和二阶相关性有关。我们的研究结果提出了一种原则性和无偏的方式来建模多维计算，并确定被编码在输出中的输入的统计数据。从分子到生态系统的许多尺度的生物系统都可以被视为信息处理器，检测其环境中的重要事件并将其转化为行动。在存在噪声和其他重叠事件的情况下检测感兴趣的事件通常需要使用输入的非线性变换。投入和产出之间关系的非线性性质，使得很难通过实验来描述它们的特性，因为数据收集受到了限制。在这里，我们讨论如何最小模型的非线性输入/输出关系的信息处理系统可以通过最大化的数量称为噪声熵。所提出的方法可以用来“聚焦”可用的数据，确定输入/输出的相关性是重要的，并创建与这些相关性一致的最小偏差模型。我们希望这种方法能够帮助探索复杂生物系统进行的计算，并扩展我们对生物世界基本现象的理解。
The multidimensional computations performed by many biological systems are often characterized with limited information about the correlations between inputs and outputs. Given this limitation, our approach is to construct the maximum noise entropy response function of the system, leading to a closed-form and minimally biased model consistent with a given set of constraints on the input/output moments; the result is equivalent to conditional random field models from machine learning. For systems with binary outputs, such as neurons encoding sensory stimuli, the maximum noise entropy models are logistic functions whose arguments depend on the constraints. A constraint on the average output turns the binary maximum noise entropy models into minimum mutual information models, allowing for the calculation of the information content of the constraints and an information theoretic characterization of the system's computations. We use this approach to analyze the nonlinear input/output functions in macaque retina and thalamus; although these systems have been previously shown to be responsive to two input dimensions, the functional form of the response function in this reduced space had not been unambiguously identified. A second order model based on the logistic function is found to be both necessary and sufficient to accurately describe the neural responses to naturalistic stimuli, accounting for an average of 93% of the mutual information with a small number of parameters. Thus, despite the fact that the stimulus is highly non-Gaussian, the vast majority of the information in the neural responses is related to first and second order correlations. Our results suggest a principled and unbiased way to model multidimensional computations and determine the statistics of the inputs that are being encoded in the outputs. Biological systems across many scales, from molecules to ecosystems, can all be considered information processors, detecting important events in their environment and transforming them into actions. Detecting events of interest in the presence of noise and other overlapping events often necessitates the use of nonlinear transformations of inputs. The nonlinear nature of the relationships between inputs and outputs makes it difficult to characterize them experimentally given the limitations imposed by data collection. Here we discuss how minimal models of the nonlinear input/output relationships of information processing systems can be constructed by maximizing a quantity called the noise entropy. The proposed approach can be used to “focus” the available data by determining which input/output correlations are important and creating the least-biased model consistent with those correlations. We hope that this method will aid the exploration of the computations carried out by complex biological systems and expand our understanding of basic phenomena in the biological world.
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DOI：
10.1364/josaa.11.002350
发表时间：
1994-09-01
影响因子：
1.9
作者：
CHUBB, C;ECONOPOULY, J;LANDY, MS
通讯作者：
LANDY, MS
影响因子：
2.9
作者：
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影响因子：
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作者：
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影响因子：
2.5
作者：
Fairhall, Adrienne L.;Burlingame, C. Andrew;Berry, Michael J., II
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DOI：
10.1073/pnas.0706938104
发表时间：
2007-11-27
影响因子：
11.1
作者：
Chen, Xiaodong;Han, Feng;Dan, Yang
通讯作者：
Dan, Yang