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تسجيل مستخدم جديدالنهج العام لنمذجة الإحصائية لقوانين الفيزياء: انحدار غير معلم
A general approach to statistical modeling of physical laws: nonparametric regression
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تأليف
I. Grabec
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تستخدم التحليل الإحصائي لقوانين الفيزياء التجريبية على دالة توزيع الاحتمالات للمتغيرات المقياسة. ويتم تعبيرها عن طريق تقدير النواة بواسطة البيانات التجريبية. ويتم تحديد النواة بشكل عادل بواسطة تشويش البيانات أثناء تعيين الإعداد التجريبي. وتتم استخراج قانون فيزيائي يربط المتغيرات المقياسة بشكل أفضل من البيانات التجريبية بواسطة محدد المتوسط الشرطي. ويتم توليده مباشرة من محدد النواة ويتوافق مع الانحدار غير المعياري. ويتم إظهار الطريقة المقترحة بواسطة تحليل خريطة العودة للبيانات الكائجة الضوئية. في هذا المثال يتم استخدام الانحدار غير المعياري لتنبؤ قيمة المستقبل للسلسلة الزمنية الكائجة من الحالية. ويتم استخدام خطأ المنبؤ في تعريف جودة المنبؤ ، في حين أن التكرار يتم تعبيره بواسطة المسافة المربعة المتوسطة بين نقاط البيانات. ويتم استخدام كلا من الإحصاءات في تعريف دالة تكلفة المنبؤ الجديدة. من الحد الأدنى لدالة تكلفة المنبؤ ، يتم تقدير عدد البيانات الصحيح في النموذج.
Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of data during calibration of experimental setup. A physical law, which relates measured variables, is optimally extracted from experimental data by the conditional average estimator. It is derived directly from the kernel estimator and corresponds to a general nonparametric regression. The proposed method is demonstrated by the modeling of a return map of noisy chaotic data. In this example, the nonparametric regression is used to predict a future value of chaotic time series from the present one. The mean predictor error is used in the definition of predictor quality, while the redundancy is expressed by the mean square distance between data points. Both statistics are used in a new definition of predictor cost function. From the minimum of the predictor cost function, a proper number of data in the model is estimated.
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