Les Phases I sont un domaine des essais cliniques dans lequel les statisticiens ont encore beaucoup à apporter. Depuis trente ans, ce secteur bénéficie d'un intérêt croissant et de nombreuses méthodes ont été proposées pour gérer l'allocation séquentielle des doses aux patients intégrés à l'étude. Durant cette Phase, il s'agit d'évaluer la toxicité, et s'adressant à des patients gravement atteints, il s'agit de maximiser les effets curatifs du traitement dont les retours toxiques sont une conséquence. Parmi une gamme de doses, on cherche à déterminer celle dont la probabilité de toxicité est la plus proche d'un seuil souhaité et fixé par les praticiens cliniques. Cette dose est appelée la MTD (maximum tolerated dose). La situation canonique dans laquelle sont introduites la plupart des méthodes consiste en une gamme de doses finie et ordonnée par probabilité de toxicité croissante. Dans cette thèse, on introduit une modélisation très générale du problème, la SPM (semi-parametric methods), qui recouvre une large classe de méthodes. Cela permet d'aborder des questions transversales aux Phases I. Quels sont les différents comportements asymptotiques souhaitables? La MTD peut-elle être localisée? Comment et dans quelles circonstances? Différentes paramétrisations de la SPM sont proposées et testées par simulations. Les performances obtenues sont comparables, voir supérieures à celles des méthodes les plus éprouvées. Les résultats théoriques sont étendus au cas spécifique de l'ordre partiel. La modélisation de la SPM repose sur un traitement hiérarchique inférentiel de modèles satisfaisant des contraintes linéaires de paramètres inconnus. Les aspects théoriques de cette structure sont décrits dans le cas de lois à supports discrets. Dans cette circonstance, de vastes ensembles de lois peuvent aisément être considérés, cela permettant d'éviter les cas de mauvaises spécifications. / Phase I clinical trials is an area in which statisticians have much to contribute. For over 30 years, this field has benefited from increasing interest on the part of statisticians and clinicians alike and several methods have been proposed to manage the sequential inclusion of patients to a study. The main purpose is to evaluate the occurrence of dose limiting toxicities for a selected group of patients with, typically, life threatening disease. The goal is to maximize the potential for therapeutic success in a situation where toxic side effects are inevitable and increase with increasing dose. From a range of given doses, we aim to determine the dose with a rate of toxicity as close as possible to some threshold chosen by the investigators. This dose is called the MTD (maximum tolerated dose). The standard situation is where we have a finite range of doses ordered with respect to the probability of toxicity at each dose. In this thesis we introduce a very general approach to modeling the problem - SPM (semi-parametric methods) - and these include a large class of methods. The viewpoint of SPM allows us to see things in, arguably, more relevant terms and to provide answers to questions such as asymptotic behavior. What kind of behavior should we be aiming for? For instance, can we consistently estimate the MTD? How, and under which conditions? Different parametrizations of SPM are considered and studied theoretically and via simulations. The obtained performances are comparable, and often better, to those of currently established methods. We extend the findings to the case of partial ordering in which more than one drug is under study and we do not necessarily know how all drug pairs are ordered. The SPM model structure leans on a hierarchical set-up whereby certain parameters are linearly constrained. The theoretical aspects of this structure are outlined for the case of distributions with discrete support. In this setting the great majority of laws can be easily considered and this enables us to avoid over restrictive specifications than can results in poor behavior.

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生活於數位時代，巨量的個人生命記憶使得人們難以輕易解讀，必須經過檢索或標籤化才可以進一步瞭解背後的意涵。本研究著力個人記憶裡繁瑣及週期性的廣泛事件，進行於「情節記憶語意化」以及「何以權衡大眾與個人資訊」兩議題之探討。透過生命記憶平台裡影像標籤自動化功能，我們以時空資訊為索引提出持續性概念重構模型，整合共同知識、個人近況以及個人偏好三項因素，模擬人們對每張照片下標籤時的認知歷程，改善其廣泛事件上註釋困難。在實驗設計上，實作大眾資訊模型、個人資訊模型以及本研究持續性概念重構模型，並招收九位受試者來剖析其認知歷程以及註釋效率。實驗結果顯示持續性概念重構模型解決了上述大眾與個人兩模型上的極限，即舊地重遊、季節性活動、非延續性活動性質以及資訊邊界註釋上的問題，因此本研究達成其個人生命記憶在廣泛事件之語意標籤自動化示範。 / In the digital era, labeling and retrieving are ways to understand the meaning behind a huge amount of lifetime archive. Foucusing on tedious and periodic general events, this study will discuss two issues: (1) the semantics of episodic memory (2) the trade-off between common and personal knowledge. Using the automatic image-tagging technique of lifelong digital archiving system, we propose the Coutinuous Reconceptualization Model which models the cognitive processing of examplar categorization based on temporal-spatial information. Integrating the common knowlegde, current personal life and hobby, the Continuous Reconceptualization Model improves the tagging efficiency. In this experiment, we compare the accuracy of cognitive modeling and tagging efficiency of the three distinct models: the common knowledge model, personal knowledge model and Coutinuous Reconceptualization Model. Nine participants were recruited to label the photos. The results show that the Continous Reconceptualization Model overcomes the limitations inherent in other models, including the auto-tagging problems of modeling certain situations, such as re-visiting places, seasonal activities, noncontinuous activities and information boundary. Consequently, the Continuous Reconceptualization Model demonstrated the efficiency of the automatic image-tagging technique used in the semantic labeling of the general event of personal memory.

Hierarchical Bayesian Models and Matrix factorization methods provide an unsupervised way to learn latent components of data from the grouped or sequence data. For example, in document data, latent component corn-responds to topic with each topic as a distribution over a note vocabulary of words. For many applications, there exist sparse relationships between the domain entities and the latent components of the data. Traditional approaches for topic modelling do not take into account these sparsity considerations. Modelling these sparse relationships helps in extracting relevant information leading to improvements in topic accuracy and scalable solution. In our thesis, we explore these sparsity relationships for di errant applications such as text segmentation, topical analysis and entity resolution in dyadic data through the Bayesian and Matrix tri-factorization approaches, propos-in scalable solutions. In our rest work, we address the problem of segmentation of a collection of sequence data such as documents using probabilistic models. Existing state-of-the-art Hierarchical Bayesian Models are connected to the notion of Complete Exchangeability or Markov Exchangeability. Bayesian Nonpareil-metric Models based on the notion of Markov Exchangeability such as HDP-HMM and Sticky HDP-HMM, allow very restricted permutations of latent variables in grouped data (topics in documents), which in turn lead to com-mutational challenges for inference. At the other extreme, models based on Complete Exchangeability such as HDP allow arbitrary permutations within each group or document, and inference is significantly more tractable as a result, but segmentation is not meaningful using such models. To over-come these problems, we explored a new notion of exchangeability called Block Exchangeability that lies between Markov Exchangeability and Com-plate Exchangeability for which segmentation is meaningful, but inference is computationally less expensive than both Markov and Complete Exchange-ability. Parametrically, Block Exchangeability contains sparser number of transition parameters, linear in number of states compared to the quadratic order for Markov Exchangeability that is still less than that for Complete Exchangeability and for which parameters are on the order of the number of documents. For this, we propose a nonparametric Block Exchangeable model (BEM) based on the new notion of Block Exchangeability, which we have shown to be a superclass of Complete Exchangeability and subclass of Markov Exchangeability. We propose a scalable inference algorithm for BEM to infer the topics for words and segment boundaries associated with topics for a document using the collapsed Gibbs Sampling procedure. Empirical results show that BEM outperforms state-of-the-art nonparametric models in terms of scalability and generalization ability and shows nearly the same segmentation quality on News dataset, Product review dataset and on a Synthetic dataset. Interestingly, we can tune the scalability by varying the block size through a parameter in our model for a small trade-o with segmentation quality. In addition to exploring the association between documents and words, we also explore the sparse relationships for dyadic data, where associations between one pair of domain entities such as (documents, words) and as-associations between another pair such as (documents, users) are completely observed. We motivate the analysis of such dyadic data introducing an additional discrete dimension, which we call topics, and explore sparse relation-ships between the domain entities and the topic, such as of user-topic and document-topic respectively. In our second work, for this problem of sparse topical analysis of dyadic data, we propose a formulation using sparse matrix tri-factorization. This formulation requires sparsity constraints, not only on the individual factor matrices, but also on the product of two of the factors. To the best of our knowledge, this problem of sparse matrix tri-factorization has not been stud-ide before. We propose a solution that introduces a surrogate for the product of factors and enforces sparsity on this surrogate as well as on the individual factors through L1-regularization. The resulting optimization problem is e - cogently solvable in an alternating minimization framework over sub-problems involving individual factors using the well-known FISTA algorithm. For the sub-problems that are constrained, we use a projected variant of the FISTA algorithm. We also show that our formulation leads to independent sub-problems towards solving a factor matrix, thereby supporting parallel implementation leading to a scalable solution. We perform experiments over bibliographic and product review data to show that the proposed framework based on sparse tri-factorization formulation results in better generalization ability and factorization accuracy compared to baselines that use sparse bi-factorization. Even though the second work performs sparse topical analysis for dyadic data, ending sparse topical associations for the users, the user references with di errant names could belong to the same entity and those with same names could belong to different entities. The problem of entity resolution is widely studied in the research community, where the goal is to identify real users associated with the user references in the documents. Finally, we focus on the problem of entity resolution in dyadic data, where associations between one pair of domain entities such as documents-words and associations between another pair such as documents-users are ob.-served, an example of which includes bibliographic data. In our nil work, for this problem of entity resolution in bibliographic data, we propose a Bayesian nonparametric `Sparse entity resolution model' (SERM) exploring the sparse relationships between the grouped data involving grouping of the documents, and the topics/author entities in the group. Further, we also exploit the sparseness between an author entity and the associated author aliases. Grouping of the documents is achieved with the stick breaking prior for the Dirichlet processes (DP). To achieve sparseness, we propose a solution that introduces separate Indian Bu et process (IBP) priors over topics and the author entities for the groups and k-NN mechanism for selecting author aliases for the author entities. We propose a scalable inference for SERM by appropriately combining partially collapsed Gibbs sampling scheme in Focussed topic model (FTM), the inference scheme used for parametric IBP prior and the k-NN mechanism. We perform experiments over bibliographic datasets, Cite seer and Rexa, to show that the proposed SERM model imp-proves the accuracy of entity resolution by ending relevant author entities through modelling sparse relationships and is scalable, when compared to the state-of-the-art baseline

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現今市場競爭愈來愈激烈，迫使廠商紛紛至海外尋求產品消費市場，在跨國銷售的背景之下，需要有更多可以確定國家選擇、預測銷售及估計需求的方法。而其中可以滿足這些需求的方法之中，就是研究產品跨國擴散型態，藉以瞭解後進國家與領先國家中新產品如何擴散且會如何互相影響 (Douglas and Craig, 1992)。 在眾多的跨國產品中，本研究選擇好萊塢電影做為實證分析的對象。 經由集群分析，本研究發現（一）台灣高首週票房且口碑佳的電影，會遇到假日人潮、有很高的美國總票房、以及很高的美國首週票房；（二）美國影片在美國及台灣映演的每週票房趨勢有差異存在；（三）片商沒有做好影片在台灣映演的檔期歸劃；（四）三群電影中，在影片類型沒有明顯地區別。 經由十二個新產品銷售預測模型的建立：對數線性迴歸模式（LN-Regression Model）（不考慮新產品領先國擴散經驗）（以OLS估計）、卜瓦松迴歸模式(Poisson Regression Model) （不考慮新產品領先國擴散經驗）（以MLE估計）、負二項分配迴歸模式(Negative Binomial Distribution Regression Model) （不考慮新產品領先國擴散經驗）（以MLE估計）、Exponential Decay模式（以OLS估計）＋迴歸方程式體系（不考慮新產品領先國擴散經驗）（以SUR估計）、Exponential Decay模式（以OLS估計）＋迴歸方程式體系（考慮新產品領先國擴散經驗）（以SUR估計）、Exponential Decay模式＋層級貝氏迴歸模式（考慮新產品領先國擴散經驗）、Bass連續型擴散模式（以NLS估計）＋迴歸方程式體系（不考慮新產品領先國擴散經驗（以SUR估計）、Bass連續型擴散模式（以NLS估計）＋迴歸方程式體系（考慮新產品領先國擴散經驗（以SUR估計）、Bass離散型擴散模式（以OLS估計）＋迴歸方程式體系（不考慮新產品領先國擴散經驗）（以SUR估計）、Bass離散型擴散模式（以OLS估計）＋迴歸方程式體系（考慮新產品領先國擴散經驗）（以SUR估計）、層級貝氏BASS離散型擴散模式＋迴歸方程式體系（不考慮新產品領先國擴散經驗）（以SUR估計）、層級貝氏BASS離散型擴散模式＋迴歸方程式體系（考慮新產品領先國擴散經驗）（以SUR估計）。本研究發現：（一）在考慮影響後進國的新產品擴散速度時，領先國的擴散經驗為絕對必要的考慮因子；（二）必須使用Bass連續型擴散模式做為建構新產品銷售預測模型的基礎；（三）必須使用Bass連續型擴散模式的NLS估計法估計Bass模型的創新係數p、模仿係數q及市場潛量m。