Browsing by Subject "Bayesian Models"
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Item Bayesian Semiparametric Models for Heterogeneous Cross-platform Differential Gene Expression(2012-02-14) Dhavala, Soma SekharWe are concerned with testing for differential expression and consider three different aspects of such testing procedures. First, we develop an exact ANOVA type model for discrete gene expression data, produced by technologies such as a Massively Parallel Signature Sequencing (MPSS), Serial Analysis of Gene Expression (SAGE) or other next generation sequencing technologies. We adopt two Bayesian hierarchical models?one parametric and the other semiparametric with a Dirichlet process prior that has the ability to borrow strength across related signatures, where a signature is a specific arrangement of the nucleotides. We utilize the discreteness of the Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using non-parametric approaches, while controlling the false discovery rate. Next, we consider ways to combine expression data from different studies, possibly produced by different technologies resulting in mixed type responses, such as Microarrays and MPSS. Depending on the technology, the expression data can be continuous or discrete and can have different technology dependent noise characteristics. Adding to the difficulty, genes can have an arbitrary correlation structure both within and across studies. Performing several hypothesis tests for differential expression could also lead to false discoveries. We propose to address all the above challenges using a Hierarchical Dirichlet process with a spike-and-slab base prior on the random effects, while smoothing splines model the unknown link functions that map different technology dependent manifestations to latent processes upon which inference is based. Finally, we propose an algorithm for controlling different error measures in a Bayesian multiple testing under generic loss functions, including the widely used uniform loss function. We do not make any specific assumptions about the underlying probability model but require that indicator variables for the individual hypotheses are available as a component of the inference. Given this information, we recast multiple hypothesis testing as a combinatorial optimization problem and in particular, the 0-1 knapsack problem which can be solved efficiently using a variety of algorithms, both approximate and exact in nature.Item Factorial Hidden Markov Models for full and weakly supervised supertagging(2009-08) Ramanujam, Srivatsan; Mooney, Raymond J. (Raymond Joseph); Baldridge, JasonFor many sequence prediction tasks in Natural Language Processing, modeling dependencies between individual predictions can be used to improve prediction accuracy of the sequence as a whole. Supertagging, involves assigning lexical entries to words based on lexicalized grammatical theory such as Combinatory Categorial Grammar (CCG). Previous work has used Bayesian HMMs to learn taggers for both POS tagging and supertagging separately. Modeling them jointly has the potential to produce more robust and accurate supertaggers trained with less supervision and thereby potentially help in the creation of useful models for new languages and domains. Factorial Hidden Markov Models (FHMM) support joint inference for multiple sequence prediction tasks. Here, I use them to jointly predict part-of-speech tag and supertag sequences with varying levels of supervision. I show that supervised training of FHMM models improves performance compared to standard HMMs, especially when labeled training material is scarce. Secondly, FHMMs trained from tag dictionaries rather than labeled examples also perform better than a standard HMM. Finally, I show that an FHMM and a maximum entropy Markov model can complement each other in a single step co-training setup that improves the performance of both models when there is limited labeled training material available.