دانلود مقاله ISI انگلیسی شماره 28786
عنوان فارسی مقاله

# بعد VC و فضای ضرب داخلی ناشی از شبکه های بیزی

کد مقاله سال انتشار مقاله انگلیسی ترجمه فارسی تعداد کلمات
28786 2009 10 صفحه PDF سفارش دهید 7334 کلمه
خرید مقاله
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عنوان انگلیسی
VC dimension and inner product space induced by Bayesian networks
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : International Journal of Approximate Reasoning, Volume 50, Issue 7, July 2009, Pages 1036–1045

کلمات کلیدی
شبکه های بیزی - بعد - فضای ضرب داخلی - کلاس مفهوم -
کلمات کلیدی انگلیسی
Bayesian networks, VC dimension, Inner product space, Concept classes,
پیش نمایش مقاله

#### چکیده انگلیسی

Bayesian networks are graphical tools used to represent a high-dimensional probability distribution. They are used frequently in machine learning and many applications such as medical science. This paper studies whether the concept classes induced by a Bayesian network can be embedded into a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. For full Bayesian networks and almost full Bayesian networks with n variables, we show that VC dimension and the minimum dimension of the inner product space induced by them are 2n-12n-1. Also, for each Bayesian network NN we show that VCdim(N)=Edim(N)=2n-1+2iVCdim(N)=Edim(N)=2n-1+2i if the network N′N′ constructed from NN by removing XnXn satisfies either (i) N′N′ is a full Bayesian network with n-1n-1 variables, i is the number of parents of XnXn, and i<n-1i<n-1 or (ii) N′N′ is an almost full Bayesian network, the set of all parents of XnXnPAn={X1,X2,Xn3,…,Xni}PAn={X1,X2,Xn3,…,Xni} and 2⩽i<n-12⩽i<n-1. Our results in the paper are useful in evaluating the VC dimension and the minimum dimension of the inner product space of concept classes induced by other Bayesian networks.

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