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nÃo hà / PropÃe-se nesta tese um mÃtodo de poda de pesos para redes Perceptron Multicamadas (MLP). TÃcnicas clÃssicas de poda convencionais, tais como Optimal Brain Surgeon(OBS) e Optimal Brain Damage(OBD), baseiam-se na anÃlise de sensibilidade de cada peso da rede, o que requer a determinaÃÃo da inversa da matriz Hessiana da funÃÃo-custo. A inversÃo da matriz Hessiana, alÃm de possuir um alto custo computacional, à bastante susceptÃvel a problemas numÃricos decorrentes do mal-condicionamento da mesma. MÃtodos de poda baseados na regularizaÃÃo da funÃÃo-custo, por outro lado, exigem a determinaÃÃo por tentativa-e-erro de um parÃmetro de regularizaÃÃo. Tendo em mente as limitaÃÃes dos mÃtodos de poda supracitados, o mÃtodo proposto baseia-se no "PrincÃpio da MÃxima CorrelaÃÃo dos Erros" (MAXCORE). A idÃia consiste em analisar a importÃncia de cada conexÃo da rede a partir da correlaÃÃo cruzada entre os erros em uma camada e os erros retropropagados para a camada anterior, partindo da camada de saÃda em direÃÃo à camada de entrada. As conexÃes que produzem as maiores correlaÃÃes tendem a se manter na rede podada. Uma vantagem imediata deste procedimento està em nÃo requerer a inversÃo de matrizes, nem um parÃmetro de regularizaÃÃo. O desempenho do mÃtodo proposto à avaliado em problemas de classificaÃÃo de padrÃes e os resultados sÃo comparados aos obtidos pelos mÃtodos OBS/OBD e por um mÃtodo de poda baseado em regularizaÃÃo. Para este fim, sÃo usados, alÃm de dados articialmente criados para salientar caracterÃsticas importantes do mÃtodo, os conjuntos de dados bem conhecidos da comunidade de aprendizado de mÃquinas: Iris, Wine e Dermatology. Utilizou-se tambÃm um conjunto de dados reais referentes ao diagnÃstico de patologias da coluna vertebral. Os resultados obtidos mostram que o mÃtodo proposto apresenta desempenho equivalente ou superior aos mÃtodos de poda convencionais, com as vantagens adicionais do baixo custo computacional e simplicidade. O mÃtodo proposto tambÃm mostrou-se bastante agressivo na poda de unidades de entrada (atributos), o que sugere a sua aplicaÃÃo em seleÃÃo de caracterÃsticas. / This thesis proposes a new pruning method which eliminates redundant weights in a multilayer perceptron (MLP). Conventional pruning techniques, like Optimal Brain Surgeon (OBS) and Optimal Brain Damage (OBD), are based on weight sensitivity analysis, which requires the inversion of the error Hessian matrix of the loss function (i.e. mean squared error). This inversion is specially susceptible to numerical problems due to poor conditioning of the Hessian matrix and demands great computational efforts. Another kind of pruning method is based on the regularization of the loss function, but it requires the determination of the regularization parameter by trial and error. The proposed method is based on "Maximum Correlation Errors Principle" (MAXCORE). The idea in this principle is to evaluate the importance of each network connection by calculating the cross correlation among errors in a layer and the back-propagated errors in the preceding layer, starting from the output layer and working through the network until the input layer is reached. The connections which have larger correlations remain and the others are pruned from the network. The evident advantage of this procedure is its simplicity, since matrix inversion or parameter adjustment are not necessary. The performance of the proposed method is evaluated in pattern classification tasks and the results are compared to those achieved by the OBS/OBD techniques and also by regularization-based method. For this purpose, artificial data sets are used to highlight some important characteristics of the proposed methodology. Furthermore, well known benchmarking data sets, such as IRIS, WINE and DERMATOLOGY, are also used for the sake of evaluation. A real-world biomedical data set related to pathologies of the vertebral column is also used. The results obtained show that the proposed method achieves equivalent or superior performance compared to conventional pruning methods, with the additional advantages of low computational cost and simplicity. The proposed method also presents eficient behavior in pruning the input units, which suggests its use as a feature selection method.

本研究的目的是針對退休金的長期負債以資產負債管理的方式提出有效的投資避險策略建議。在過去，傳統精算的資產負債管理大多採用確定投資模型（Deterministic Model），即以過去的經驗設立「精算假設」，但是這樣的假設無法精確的呈現未來的趨勢，所以本文的第一部份，便是根據過去的台灣總體經濟資料，建構一個退休基金的隨機投資模型（Stochastic Investment Model）。首先，我們以ECM（Error Correlation Model）模式建構出第一個投資模型，之後在精簡參數的考量下，建構第二個以因果關係為基礎的Causality投資模型，再以模型配適能力與預測能力比較兩模型，結果顯示Causality投資模型優於ECM投資模型。 　　有了投資模型，我們設定不同的退休金負債形式，如固定成長型負債MF、隨通貨膨脹成長M^R負債及隨max{固定成長比例，通貨膨脹}而成長的退休金負債M^L，以靜態避險的方式去求得各資產的最適配適比例。從模擬的結果中發現隨著到期日的增長，投資在風險性高報酬率佳的投資標的物上的比例也越來越高。另外，隨著負債固定成長比例f的增加，其M^L負債之期初資產配置額便越接近M^F負債之期初資產配置額。整體而言，我們由模擬中可得出，使用投資組合的投資方式優於單一資產投資的結論。 / In this study, we investigate the hedging strategies for pension liabilities by using Asset-Liability Management method. In the past, the traditional actuarial valuation usually does not take account of market value for both assets and liabilities. Most of the traditional actuarial valuation adopted the Deterministic Model, that is, setting the assumptions based on the experiences. However, it can not exactly show the trend in the future. In part one of this study, we build a stochastic investment model for the pension funds based on Taiwan Market data. First, we apply the first model : ECM( Error Correlation Model ). And then, we apply the second model : Causality Model under considering parsimonious parameterization. Finally, we compare the results of ECM with Causality Model on fitting and forecasting efficiency, and we find that Causality Model is better than ECM. With the investment model, we set some formulas of pension liabilities calculated to obtain the best fit proportion of each valuation by the static hedging. This involves finding optimal static hedging strategies to minimize riskiness of the investment portfolio relative to the liability. Overall, from the simulation results, for static hedging in these kinds of liabilities, investing in all three assets is a better strategy than investing in a single asset class. This confirms that the more assets we use, the more effectively we can hedge.