| 摘要: | 本文主要發展用來判別神經元網路資訊流向的統計分析方法。格蘭傑因果關係 (Granger causality, GC) 是個用來估計時間序列訊號間因果交互作用相當流行且有效的概念。在過去的二十年來，GC 已成為一個可用來偵測多種不同類型神經活動資料間因果關聯的強大分析方法。然而，在實際運用GC到神經科學領域時，有三個主要問題尚須進一步的研究與釐清：第一，原始的GC測度被設計成非負實數的形式，因此缺乏用來區分神經元間興奮性與抑制性因果關聯的有效特徵。第二，雖然GC已大量被使用，但估算出的因果強度與實際神經元之間突觸權重的關聯仍不清楚。第三，GC 無法直接用來解析大尺度的神經元資料，因為其中的變數數量經常遠遠超過所紀錄到的時間序列樣本數。對於上述前兩個問題，我們利用原始GC的架構並根據一個最佳線性預測子（best linear predictor, BLP）的假設，提出了能夠有效解析神經元網路間突觸權重的計算方法。在BLP的假設下，GC 可被擴展以同時測量神經元間興奮性與抑制性作用。我們設計了三種不同類型的模擬神經元網路來測試所提的新方法，包含從簡單的線性與近線性網路結構至複雜的非線性網路結構。這些模擬例子驗證了BLP假設的正當性以及計算方法的正確性。此方法也被示範性的用來分析大腦前扣帶皮層（ACC）與紋狀體（STR）真實的神經元活動資料。分析結果顯示，在注射 D2 多巴胺受體刺激劑的狀態下，ACC 當中以及由 ACC 投射至 STR 存在顯著的興奮性作用，而 STR 當中存在顯著的抑制作用。
實務上，從腦中擷取大尺度紀錄之神經訊號間的因果交互作用對於腦部特定功能之完整解析與可靠推論來說相當重要。然而，在大尺度訊號中，神經元的數量往往嚴重大過紀錄到的訊號長度；此過大的變數與樣本比值對於大多數現存的統計分析方法來說都會造成相當大的阻礙，甚至使分析方法在數學計算上完全失效。本文接著介紹一個三階段的變數選擇方法，它能夠有效地將一個大尺度變數集合調降成一個只包含有相關性變數的較小變數集，進而讓GC能夠應用到此調降的變數集合上。此方法使用（1）正交向前選擇解釋變量，（2）一停止準則以終止前向納入變量，和（3）進一步向後修剪消除不相關變量。對於上段提到的第三個問題，我們以此三階段方法為核心提出一個變量選擇演算法使得GC能夠被用來解析大尺度的時間序列資料。我們設計了一個以電位閾值激發的大尺度神經元網路模型來試驗所提方法的一致性。此方法應用在大鼠的行為資料分析中也得到全新的發現。這些框架提供了真實神經元網路分析的新方向。;This thesis is devoted to developing statistical methods for identifying the information flow of neuronal networks. Granger causality (GC) is a very popular and also useful
concept for estimating causal interactions between time-series signals. Over the past two decades, GC has emerged as a powerful analytical method for detecting the causal relationship among various types of neural activity data. However, three problems encountered when GC was used in the field of neuroscience remain not very clear and
further researches are needed. Firstly, the GC measure is designed to be nonnegative in its original form, lacking of the trait for differentiating the effects of excitations
and inhibitions between neurons. Secondly, how is the estimated causality related to the underlying neuronal synaptic weights? Thirdly, GC can not be applied to large-scale neuronal data, in which the number of variables is far greater than the length of time series. For the first two problems, we propose, under a best linear predictor (BLP) assumption, a computational algorithm for analyzing neuronal networks by estimating the synaptic weights among them. Under the BLP assumption, the GC analysis can be extended to measure both excitatory and inhibitory effects between neurons. The method was examined by three sorts of simulated networks: those with linear, almost linear, and
nonlinear network structures. The method was also illustrated to analyze real spike train data from the anterior cingulate cortex (ACC) and the striatum (STR). The results showed, under the quinpirole administration, the significant existence of excitatory effects inside the ACC, excitatory effects from the ACC to the STR, and inhibitory
effects inside the STR.
Extracting causal interactions from a large-scale recording of neural ensemble in the brain is very important to a comprehensive understanding or a reliable inference of
certain brain functions. However, the oversized ratio between neuron number and signal length causes great difficulty to most of existing statistical methods. This thesis also introduces a three-stage variable selection approach that can be used to effectively reduce the large-scale variable set to a small but relevant one and enables GC to be applied to the reduced set. The method uses (1) an orthogonal greedy algorithm to include variables in a forward manner (2) a stopping criterion to terminate the forward inclusion of variables, and (3) a backward elimination to further trim irrelevant variables. For the third problem, we propose a computational algorithm
which wraps the above selection approach as its core, enabling GC to work on large-scale time-series data. The method was examined by a large-scale simulated threshold spiking neuron model, and real data were used to demonstrate that our method is also useful in monitoring neural connectivity for general network. These frameworks give an insight into the analysis of real neuronal networks. |
