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題名 | 類神經網路模型結構選取--廣義統計自由度的使用=Using Equivalent Degree of Freedom to Determine the Structure for Neural Models |
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作 者 | 林財川; | 書刊名 | 統計與資訊評論 |
卷期 | 8 民94.12 |
頁次 | 頁1-15 |
分類號 | 511.2 |
關鍵詞 | 類神經網路模型; 隱藏節點數選取; 過度擬合; Artificial neural networks; Number of nodes; Over-fitting; |
語文 | 中文(Chinese) |
中文摘要 | 本文旨在建構一個具有精煉類神經網路模型演算法。因相較於一般的統計分析方法,過度擬合的問題更可能經由類神經網路模型的複雜轉換而產生。精煉的類神經網路模型架構之研究,包括顯著輸入變數的選取及隱藏層的數目及每層的節點數等問題。如何測量類神經網路之複雜度或自由度乃解決選模問題之關鍵。本文使用資料擾動法計算廣義自由度的測量;接著以此廣義自由度定義一個交叉驗證函數分數用以逐步地求出顯著的輸入變數及隱藏節點數。有限樣本之模擬選模結果發現含單層隱藏層模型架構與原已知模型吻合,且權重估計亦相當接近原設定參數。 |
英文摘要 | This research aims to propose an algorithm to the parsimonious artificial neural network (ANN) structure. There are many different ways to construct and implement neural networks for forecasting. However, most works use ANN directly, without seeking an appropriate ANN structure. The issue of finding a parsimonious ANN model for a real problem is critical. Because that the problem of over-fitting is more likely to occur with ANNs. The parsimonious ANN model not only has the recognition ability, but also has more important generalization capability. This study aims to determine the significant input variables and the number of hidden layers and hidden nodes. In fact, to measure the degree of an ANN models play key roles in recent research of ANN. Applying the idea of counting the number of parameter in linear model into the nonlinear setup will course the problem of over-fitting. However the problem of degree of freedom in nonlinear and nonparametric model still open. While no universal answer can be expected, a data perturbation is used to assess and adjust the impact of nonlinearity. Sequentially, we define a so-called GCV to choose the significant input variables and the number of nodes in hidden layer simultaneously. Trough simulation we assess the performance of this proposed method of finding parsimonious ANN structure. Through simulation, we find that for ANN with single hidden layer the resulting structure and estimated weights are quit close to the given model. Under finite sample simulations, we find such method have a good performance. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。