یادگیری پارامترهای شبکه بیزی از داده حاوی مقادیر گم‌شده
محورهای موضوعی : مهندسی برق و کامپیوترکبری اطمینانی 1 , محمود نقیب‌زاده 2 , مهدی عمادی 3 , امیررضا رضوی 4
1 - دانشگاه فردوسی مشهد
2 - دانشگاه فردوسی مشهد
3 - دانشگاه فردوسی مشهد
4 - دانشگاه علوم پزشکی مشهد
کلید واژه: پارامترهای شبکه بیزی راست‌نمایی شبکه بیزی مقدار گم‌شده,
چکیده مقاله :
یادگیری ساختار شبکه بیزی از داده، در سال‌های اخیر توجه بسیاری از محققین را به خود جلب نموده است. از طرفی، یافتن شبکه بهینه از داده کامل، خود یک مسأله غیر چندجمله‌ای سخت می‌باشد و پیچیدگی مسأله، زمانی که داده ناقص است، بیشتر می‌شود. به طور کلی دو حالت یادگیری شبکه بیزی از داده ناقص وجود دارد: زمانی که ساختار مشخص است و زمانی که ساختار نیز نامشخص است. در این مقاله سعی بر آن است تا پارامترهای بهینه را برای یک شبکه بیزی با ساختار مشخص از داده حاوی مقادیر گم‌شده بیابیم. برای این منظور مفهوم "پارامتر مؤثر" را معرفی نمودیم، به طوری که درست‌نمایی ساختار شبکه به شرط داده کامل‌شده، بیشینه گردد. این روش می‌تواند به هر الگوریتمی همچون بیشینه‌سازی امید ساختاری که به پارامترهای بهینه برای یافتن ساختار شبکه بیزی نیاز دارند، متصل شود. در این مقاله ثابت کردیم که روش پیشنهادی از دیدگاه تابع درست‌نمایی به پارامترهای بهینه شبکه دست می‌یابد. نتایج اعمال روش پیشنهادی به چندین شبکه بیزی استاندارد، نشان‌دهنده سرعت روش در مقایسه با روش‌های شناخته‌شده قبلی است و نیز این که به پارامترهای بهتری نسبت به آنها دست می‌یابد.
Learning Bayesian network structure from data has attracted a great deal of research in recent years. It is shown that finding the optimal network is an NP-hard problem when data is complete. This problem gets worse when data is incomplete i.e. contains missing values and/or hidden variables. Generally, there are two cases of learning Bayesian networks from incomplete data: in a known structure, and unknown structure. In this paper, we try to find the best parameters for a known structure by introducing the “effective parameter”, in a way that the likelihood of the network structure given the completed data being maximized. This approach can be attached to any algorithm such as SEM (structural expectation maximization) that needs the best parameters to be known to reach the optimal Bayesian network structure. We prove that the proposed method gains the optimal parameters with respect to the likelihood function. Results of applying the proposed method to some known Bayesian networks show the speed of the proposed method compared to the well-known methods.
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