使用機率分布探討量化學習動力的改變

緒論：學習的過程大略可以分成兩類：比例式的學習和新協調型態的學習。在新協調型態的學習方面，動力過程會發生質性轉變，使用常態分布的統計假設來處理這種數據，即以平均數、標準差作為呈現學習前後差異的方法，並不盡完善。探討運動學習的研究，應使用合適的函數，量化學習過程的變化。在具有不同偏態及隨機樣貌的各種分布中，伽馬分布根據參數變化，曲線外型具有多樣性，可能較適於作為初步觀察學習過程中動力質性改變的描述方式。目的：根據不同學習類型的學習過程，找出最適合用來描述不同學習階段狀態的分布模式。方法：將比例式與建立協調型態的學習數據，分別使用常態分布、對數常態分布、均勻分布、指數分布、伽馬分布適配學習過程中不同階段的動作表現，並以重複量數二因子變異數分析比較分布模式在不同學習階段數據分布的決定係數。結果：比例式學習僅有模式間達顯著差異，伽馬分布與常態分布大於對數常態分布、指數分布及均勻分布。在新協調型態學習方面，三階段與兩階段的結果都具有交互作用，伽馬分布在初期優於其他分布，而後期伽馬、對數常態與常態分布優於指數與均勻分布，此外伽馬分布與對數常態分布的決定係數在各階段都較優於其它分布模式。結論：伽馬分布在兩種類型的學習，以及在協調型態的三個階段，適配的決定係數都具有比較優勢的效果。

關鍵字

運動學習；動力系統理論；量化學習；機率密度方程式

並列摘要

The learning process can be classified as a scale learning and learning a new coordination pattern. In coordination learning, qualitative changes of coordination patterns in the dynamic processes may occur. In this case, using the assumption of normality concept of statistic (e.g. mean and standard deviation) to represent dataset may not be appropriate and incomplete. Here we investigated the gamma probability density functions as another candidate approach to qualify and quantify the learning process even though the data distribution deviated from normality. The gamma function with different combinations of the parameters (alpha and beta) may form different shapes to capture qualitative changes of performance outcome through learning process, especially in coordination learning. The purpose of this study was to investigate different distribution models (normal, logarithmic normal, exponential and uniform distributions) to fit the data distribution of scale learning and coordination learning in different learning phases from throwing task (50 trials a day for 3 days) and the rollerball task (50 trials a day for 5 days), respectively. Two factors repeated measure ANOVAs were used to compare the coefficient of determination between distribution models and learning phase. There was a significant difference among distribution models in scale learning, the gamma and lognormal distribution had greater coefficients of determination than the others. In coordination learning, both three and two phase groups had interaction between distribution models and learning phases. The post hoc analyses showed that the coefficient of determination of the gamma and lognormal distribution were both significantly greater than the normal, exponential and uniform distributions at the first and transition phases, the gamma, lognormal and normal distribution were significantly greater than the exponential and uniform distributions at the last phase. In conclusion, the gamma function showed superior descriptive power among the models over the learning phase for both types of learning that have a comparative advantage in the results of curve fitting.