臺灣博碩士論文加值系統

許多新的稀少資料的應用領域，給機器學習帶來了新的挑戰。例如，我們會希望有個模型能事先預測本地的恐佈事件。這類事件不常發生，但是當它們發生時，會帶來很大的衝擊。同時，事件發生的前兆可能是未知、沒有觀察到、或是每次都不大相同。因此，從少量的資料學習正確的模型是困難的，但是也很重要。使用機率模型是處理這類問題的一個方法。機率的理論可以處理不確定性和稀少的資料。我們使用貝氏網路作為機率的模型。貝氏網路對於專家而言，含意容易了解，而且網路的結構可以由專家所知的因果關連來決定。然而，決定貝氏網路的參數對專家而言，是件煩鎖的工作。這一方面，我們可以從訓練資料中學得參數。
本論文提出以搜尋為基礎的方法，來從稀少資料學習貝氏網路的參數。我們的方法包含了新的評分函式和搜尋法。評分函式方面，我們對於最常使用的最大近似值估計法加以分析，發現它常常高估/低估多項隨機變數常出現/不常出現的狀態的機率值。因此，我們提出"熵修正函式"來修正這部份的偏移。在搜尋法方面，我們提出了固定點期望值最大化演算法。這個方法的好處，是在最大化步驟時，可以直接求出解，而不必像傳統的方法，使用數值方法來求解。
實驗顯示，我們的方法優於以往的參數學習法。首先，我們的方法找到的參數，和真正模型之間差異較低的；其次，我們的方法使用的時間相當的短，大約是以往方法的一半甚至更少。

Many newly-emerging applications with small and incomplete
(sparse for abbreviation) data sets present new challenges
to machine learning. For example, we would like to have a model
that can accurately predict the possibility of domestic terrorist
incidents and attack terrorism in advance. Such incidents are
rare, but always bring severe impact once they really happen. In
addition, the relevant symptoms may be unknown, unobserved, and
different case by case. Therefore, learning accurate models from
this kind of sparse data is difficult, but very meaningful and
important. One way to deal with such situations is to learn
probabilistic models from sparse data sets. Probability theory is
well-founded for domains with uncertainty and for data sets with
missing values. We use the Bayesian network as the modeling tool
because of its clear semantics for human experts. The network
structure can be determined by the domain experts, showing the
causal relations between features. Then, the parameters can be
learned from data sets, which is more tedious for human experts.
This thesis proposes a search-based approach to the parameter
learning problem in Bayesian networks from sparse training sets. A
search-based solution consists of the metric and the search
algorithm. The most frequently used solution is to search on the
data likelihood metric based on Maximum-Likelihood estimation (ML)
with the Expectation-Maximization (EM) algorithm or the gradient
ascent algorithm. However, our analysis shows that the ML
learning for sparse data tends to over/underestimate the
probabilities for low/high-frequency states of multinomial random
variables. Therefore, we propose Entropic Rectification
Function (ERF) to rectify the deviation without prior
information about the application domain. The general EM-based
framework for penalized data likelihood function, Penalized EM
(PEM) algorithm, can search on ERF, but time-consuming numerical
methods are required in the M-step. To accelerate the
computation, we propose Fixed-Point PEM (FPEM) algorithm,
in which there is a closed-form solution for the M-step based on
the framework of the fixed-point iteration method.
We show that ERF outperforms the data likelihood metric by leading
the search algorithms to stop at the estimates with smaller KL
divergences to the true distribution, and FPEM outperforms PEM by
searching out local maxima faster. In addition, ERF can also be
used to learn other probabilistic models with multinomial
distributions, like Hidden Markov model. FPEM can search on other
penalized data likelihood metrics as well.

1.Introduction
1.1 Motivation
1.2 Related Work
1.3 Contributions
1.4 Outline of the Thesis
2.Background
2.1 Bayesian Networks
2.2 Bayesian Network Learning Problem
2.3 Parameter Learning in Bayesian Networks
3.Entropic Rectification Function
3.1 Analysis of Parameter Learning from Sparse Data Set
3.2 Entropic Rectification Function
3.3 Entropic Prior
4.Search Algorithms for ERF
4.1 Gradient Ascent Algorithm
4.2 Fixed-Point Penalized EM Algorithm
5.Empirical Evalluation of ERF
5.1 Gradient Ascent and FPEM for Bayesian Networks
5.2 FPEM for Hidden Markov Model
6.Conclusion and Future Work

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}
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}
#################################
books
#################################
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#######################################
inbook
#########################################
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location = {}
}
##########################
Technical Reports
##########################
@techreport { Cowell99Principle,
author = {Cowell, Robert G.},
title = {Parameter Learning from Incomplete Data Using Maximum Entropy I: Principles},
institution = {},
year = {1999},
citation = {\cite{Cowell99Principle}}
}
################################
incollection
################################
@incollection { EM_free_energy,
author = {Neal, Radford M. and Hinton, Geoffrey E.},
title = {A View of the {EM} Algorithm that Justifies Incremental, Sparse, and Other Variants},
booktitle = {Learning in Graphical Models},
year = {1998},
publisher = {Kluwer Academic Publishers},
editor = {Jordan, Michael I.},
volume = {},
number = {},
series = {},
type = {},
chapter = {},
pages = {355--368},
address = {},
month = {},
note = {},
citation = {\cite{EM_free_energy}},
location = {}
}
@incollection {BN_Introduction,
author = {Heckerman, David},
title = {A Tutorial on Learning with {B}ayesian Networks},
booktitle = {Learning in Graphical Models},
year = {1998},
publisher = {Kluwer Academic Publishers},
editor = {Jordan, Michael I.},
volume = {},
number = {},
series = {},
type = {},
chapter = {},
pages = {301--354},
address = {},
month = {},
note = {},
citation = {\cite{BN_Introduction}},
location = {}
}
######################################################
technique report
######################################################
@techreport{ david94characterization,
author = "Heckerman, Dan Geiger David",
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number = "MSR-TR-94-16",
month = "November",
year = "1994",
#url = "citeseer.nj.nec.com/article/geiger96characterization.html"
}
@techreport{ david94learning,
author = "Chickering, David M. and Geiger, Dan and Heckerman, David",
title = "{L}earning {B}ayesian {N}etworks is {NP}-{H}ard",
number = "MSR-TR-94-17",
month = "November",
year = "1994",
institution = "Microsoft Research",
#url = "citeseer.nj.nec.com/chickering94learning.html"
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year = 2002,
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##################################
workshop
##################################
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year = "2001"
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MONTH = {October},
PUBLISHER = {Springer-Verlag},
#URL = {http://www.sdl.sri.com/papers/adaptbn/},
COPYRIGHT = {Springer-Verlag, Berlin Heidelberg 2000},
KEYWORDS = {Intrusion detection, Innovative approaches, {IDS}
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year = {2002},
author = {Murphy, Kevin},
title = {Dynamic {B}ayesian Networks: Representation, Inference and Learning},
school = {University of California, Berkeley}
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