Diversified probabilistic graphical models
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Probabilistic graphical models (PGMs) as diverse as Bayesian networks and Markov random fields have provided a fundamental framework to learn and reason using limited and noisy observations. Examples include, but are not limited to, hidden Markov models (HMMs), sequential graphical models, and probabilistic principal component analysis mixture models (PPCA-MM). PGMs have been used in a wide variety of applications such as speech recognition, natural language processing, web searching, and image understanding. However, one potential drawback of using PGMs with traditional learning and inference methods is that the learned parameters or inferred variables are easily trapped within local, clustered optima rather than distributed evenly across the whole space. Taking mixture models as an example, the learned mixing components might overlap. Consequently, the resulting models might show ambiguity when clustering is performed based on these overlapping mixing components. This phenomenon might limit PGM performance. Although efforts have been made to explore a variety of priors to alleviate this potential drawback and to enhance PGM performance, diverse priors have yet to be fully explored and utilized. Diversity is a concept that encourages counterpart model parameters and variables to repel as much as possible and, in doing so, spread out model components and decrease overlapping. However, how to explicitly encode these priors into a PGM and how to solve the resulting diversified PGMs are two critical problems that must be solved. This thesis proposes a unified framework to constrain PGMs with diverse priors. Three different PGMs - HMMs, time-varying determinantal point processes (TV-DPPs), and PCA-MMs - are elaborated to demonstrate the proposed diversified PGM framework. For each PGM, three basic constituent framework elements are examined: which part of the traditional PGM is diversified, how to formulate the diversity, and how to solve the diversified version, e.g., parameter learning and inference. In addition, experiments are conducted using various application scenarios to verify the effectiveness of the proposed diversified PGMs.
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