Graduation date: 1995

Thesis (Ph.D.) -- McMaster University, 1999. / Includes bibliographical references (leaves 76-79). Also available via World Wide Web.

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Thesis (Ph. D.)--University of Hong Kong, 1990.

Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. Exponential family embeddings extend the idea of word embeddings to other types of high-dimensional data. Exponential family embeddings have three ingredients; embeddings as latent variables, a predefined conditioning set for each observation called the context and a conditional likelihood from the exponential family. The embeddings are inferred with a scalable algorithm. This thesis highlights three advantages of the exponential family embeddings model class: (A) The approximations used for existing methods such as word2vec can be understood as a biased stochastic gradients procedure on a specific type of exponential family embedding model --- the Bernoulli embedding. (B) By choosing different likelihoods from the exponential family we can generalize the task of learning distributed representations to different application domains. For example, we can learn embeddings of grocery items from shopping data, embeddings of movies from click data, or embeddings of neurons from recordings of zebrafish brains. On all three applications, we find exponential family embedding models to be more effective than other types of dimensionality reduction. They better reconstruct held-out data and find interesting qualitative structure. (C) Finally, the probabilistic modeling perspective allows us to incorporate structure and domain knowledge in the embedding space. We develop models for studying how language varies over time, differs between related groups of data, and how word usage differs between languages. Key to the success of these methods is that the embeddings share statistical information through hierarchical priors or neural networks. We demonstrate the benefits of this approach in empirical studies of Senate speeches, scientific abstracts, and shopping baskets.

Wong, Tat Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 53-55). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Problem Formulation --- p.5 / Chapter 2.1 --- Phase-type distribution --- p.5 / Chapter 2.1.1 --- A generalization of the exponential distribution --- p.5 / Chapter 2.1.2 --- Properties of the phase-type distribution --- p.6 / Chapter 2.2 --- Phase-type jump diffusion model --- p.8 / Chapter 2.2.1 --- Jump diffusion model --- p.8 / Chapter 2.2.2 --- The stock price model --- p.9 / Chapter 2.3 --- Stock Loans --- p.10 / Chapter 3 --- General Properties of Stock Loans --- p.12 / Chapter 3.1 --- Preliminary results --- p.12 / Chapter 3.2 --- Characterization of the function V(x) --- p.15 / Chapter 4 --- Valuation / Chapter 4.1 --- Hyperexponential jumps --- p.25 / Chapter 4.1.1 --- Solution of the linear system --- p.29 / Chapter 4.1.2 --- Solution of the optimal exercise boundary --- p.30 / Chapter 4.2 --- Phase-type jumps --- p.33 / Chapter 4.3 --- The case for G'(1)≥ 0 --- p.36 / Chapter 5 --- Future Research Direction --- p.38 / Chapter 5.1 --- The fast mean-reverting stochastic volatility model --- p.38 / Chapter 5.2 --- Asymptotic expansion of stock loan --- p.39 / Chapter 5.2.1 --- The zeroth order term --- p.41 / Chapter 5.2.2 --- The first order term --- p.43 / Chapter 6 --- Conclusion --- p.52 / Bibliography --- p.53

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 105-108). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 105-108). Also available on the Internet.

Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica. / Department of Mathematical Sciences