文件模型(Document Model)與語言模型(Language Model)是資訊檢索領域的核心技術，本論文依循近似貝氏推論(Approximate Bayesian Inference)並透過遞迴貝氏(Recursive Bayesian)學習、稀疏貝氏(Sparse Bayesian)學習、變異貝氏(Variational Bayesian)估測、非參數型貝氏(Bayesian Nonparametric)學習及取樣方法(Sampling Method)，發展一系列以潛在狄氏配置(Latent Dirichlet Allocation, LDA)為主之主題模型(Topic Model)並建立文件模型與語言模型，這一系列方法可以廣泛應用在不同資訊系統上包括文件檢索(Document Retrieval)、文件分類(Document Classification)、文件表示(Document Representation)、文件摘要(Document Summarization)及語音辨識(Speech Recognition)。
在資訊檢索的應用方面，一般擷取資訊所用到的查詢關鍵字都不多，我們可以利用關鍵字模型(Query Model)，將關鍵字擴充和延伸，並配合已經訓練好的文件模型(Document Model)進行有效率的相關回饋(Relevance Feedback)。在本論文中，我們提出一種新相關回饋機制，透過最佳事後機率(Maximum a Posteriori)估測法則，結合第一次擷取的相關的文件，擴充並延伸關鍵字相關的Query Model。並利用非監督式學習(Unsupervised Learning)自動調整文件模型的權重，在資訊檢索的實驗評估中，我們提出的貝氏(Bayesian)相關回饋已有效提昇資訊擷取的正確率。
在文件分類方面，我們進一步改良文件模型(Document Model)並透過模型調整(Model Adaptation)將潛在狄氏配置(LDA)模型調整到新的領域(Domain)已提昇新領域之分類正確率，本方法是採用遞迴貝氏(Recursive Bayesian)學習，利用共軛事前機率(Conjugate Prior)分布的特性，收集調整文件(Adaptation Document)並累積事後機率，發展出一套適應性潛在狄氏配置(Adaptive LDA)，除了調整模型適應新領域外，還可透過注入的新文件提昇模型估測的可靠度及分類正確率。
在文件表示法方面，我們關心潛在狄氏配置模型過度訓練(Over-Trained)以及應該要有多少個主題才能適當表示文件資料等問題，在傳統LDA模型中主題的數量(Number of Topics)是必須事先給定的，如何根據收集到的資料自動決定主題數量是非常重要的，設定的主題數量過多，會造成文件模型估測不可靠，設定的主題數量過少，又無法精確的表示文件模型。本論文使用貝氏稀疏學習並建立稀疏性潛在狄氏配置(Sparse LDA)，我們透過尖釘與平板(Spike-and-Slab)模型有效擷取相關性高的主題(Relevant Topic)來表示文件中不同的字詞(Word)，使用特徵過濾(Feature Selection)突顯文件模型的計算效率並節省記憶體需求量，本論文使用變異貝氏(Variational Bayesian Expectation- Maximization, VB-EM)推論法則估測出模型參數，文件表示效能已有效提昇。
在文件摘要方面，我們提出兩套解決方法有效地從海量的文件資料中摘要出精簡資訊或選出具代表性之摘要文句，自動摘要過程是找出文件中重要的主題句，並且依照與文件的相關性進行排序，挑選出前幾名的句子來當摘要文句，文件摘要的效能關鍵在於精確的文句模型(Sentence Model)。因此在第一套方法我們發展出文句式潛在狄氏配置(Sentence LDA)模型，主要的觀念是視文句為文件並將以文件為主(Document-Based)的潛在狄氏配置延伸為以文句為主的模型，模型參數可由VB-EM推論求得。另外第二套方法是提出階層式雙主題模型(Hierarchical Theme and Topic Model, H2TM)，我們透過巢狀式中國餐廳過程(Nested Chinese Restaurant Process, nCRP)進行非參數式貝氏學習並建立文句的階層式模型，雙主題模型結構可自動由收集到的訓練文件自動決定，每個文句會自動配置到其對應的樹節點或主題節點(Theme Node)，每篇文件會選擇多重路徑(Multiple Tree Paths)以表示文件中的文句，在每個節點裡所有的文句及其字詞會透過階層式狄氏過程(Hierarchical Dirichlet Process, HDP)建立起字詞的主題(Topic)，雙主題的個數(Number of Themes and Topics)決定或模型選擇課題可以獲得解決，主題文句可以由此樹狀結構中挑選出來，在這兩套方法中我們使用DUC文件集進行文件摘要評估，已有效改進潛在狄氏配置的摘要效能。
在語音辨識方面，我們發展階層式狄氏及Pitman-Yor語言模型(Hierarchical Dirichlet and Pitman-Yor Language Model)，透過非參數型貝氏學習法則解決語言模型訓練過程中長距離不足及訓練文件過少所產生的問題，這套方法是經由階層式Pitman-Yor過程建立主題相關且平滑化語言模型，將模型Backoff機制融入使訓練文集不足問題獲得解決，另外我們導入階層式狄氏過程(HDP)並結合不同的主題相關語言模型以解決長距離不足的問題，透過新穎的中國餐廳情節(Scenario)及取樣過程(Gibbs Sampling)可以取樣出具韌性之主題式語言模型(Topic-Based Language Model)，在測試文集及語音的實驗結果中驗證了本方法的有效性。

Document model and language model are known as the core technology for building information retrieval systems. This dissertation presents a series of approximate Bayesian inference algorithms including maximum a posteriori, recursive Bayesian, sparse Bayesian, variational Bayesian, nonparametric Bayesian and sampling method and develops different solutions to topic-based document model and language model based on the latent Dirichlet allocation (LDA). These solutions are applied to a wide range of applications including document retrieval, document classification, document representation, document summarization and speech recognition.
The goal of document retrieval basically aims to adopt a few query words to retrieve a set of documents which are relevant to their interests. In this study, we develop a new query model using relevance feedback where the query words are augmented with additional words extracted from the first-pass retrieval. The maximum a posteriori estimation is developed to find the extended query words and conduct the unsupervised reweighting scheme for relevance documents in a query model. This method effectively improves the precision and recall rates in a document retrieval system.
For the application of document classification, we adapt the LDA-based document model to new domain and aim to improve the classification performance in new domain. This thesis proposes a recursive Bayesian learning algorithm to tackle this problem based on the adaptive LDA (ALDA). Using ALDA, we use the adaptation documents to reproduce the posterior distribution by combining the likelihood function from adaptation data and the accumulated conjugate prior from training data. Model robustness to new domain is accordingly improved for document classification.
More generally, we concern model regularization issue in LDA-based document representation. In implementation of topic model, the number of topics is usually too large to properly reflect domain knowledge from training data as well as test data. The reliability of the estimated model is doubtful. However, assigning too few topics shall suffer from the limitation of representation capability. Automatic selection of the number of topics becomes a critical issue in topic model. This thesis presents a sparse Bayesian learning method to deal with the issue of model selection for LDA. We propose the sparse LDA (sLDA) where a spike-and-slab distribution is introduced to autonomously extract the relevant topics to represent individual words. The scheme of feature selection is introduced so that the computation cost and the memory requirement are reduced. This sLDA is inferred according to the variational Bayesian expectation-maximization (VB-EM) algorithm.
In addition, we propose two approaches for document summarization which aims to summarize compact information from a large set of documents or select the thematic sentences from a rank list of representative sentences. The key issue in document summarization is the construction of sentence model. In the first approach, we establish the sentence-based LDA where each sentence is treated as a document or a grouped data in a LDA learning procedure. This model is inferred by using VB-EM algorithm. On the other hand, we improve the sentence-based LDA by relaxing the constraints of the fixed number of topics as well as the independence in the estimated topics. The nonparametric Bayesian learning through a nested Chinese restaurant process (nCRP) compound hierarchical Dirichlet process (HDP) is performed to construct the hierarchical theme and topic model (H2TM). We follow nCRP and represent the sentences from a document collection based on a hierarchical theme model. The structural learning is conducted for flexible modeling with infinite tree nodes, branches and layers. The sentences in a document are represented by the themes allocated in a selected subtree. The words of the sentences in a tree node are then treated as a grouped data. The set of grouped data in different nodes are then represented by a topic model sampled from a HDP. Using this H2TM, two constraints in sentence-based LDA are tackled. The resulting summarization performance is improved in evaluation of DUC corpus.
For the application of speech recognition, we develop the hierarchical Dirichlet and Pitman-Yor language model (HDPY-LM) to resolve the issues of insufficient long distance information and sparse training data in estimation of statistical n-gram model. The HDP compound hierarchical Pitman-Yor (HPY) process is developed to sample the topic-based language model where HDP handles the sampling of latent topics and HPY process draws the smoothed n-gram probabilities from the backoff (n-1)-gram probabilities. Two issues in language model are accordingly resolved through nonparametric Bayesian learning where the backoff scheme and the number of topics are infinitely extensible. We design a new scenario of Chinese restaurant process to perform Gibbs sampling for inference of topic-based language model. This HDPY-LM is evaluated to be effective for speech recognition.

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