A path-based framework for analyzing large markov models

Reliability and dependability modeling can be employed during many stages of analysis of a computing system to gain insights into its critical behaviors. To provide useful results, realistic models of systems are often necessarily large and complex. Numerical analysis of these models presents a formidable challenge because the sizes of their state-space descriptions grow exponentially in proportion to the sizes of the models. On the other hand, simulation of the models requires analysis of many trajectories in order to compute statistically correct solutions. This dissertation presents a novel framework for performing both numerical analysis and simulation. The new numerical approach computes bounds on the solutions of transient measures in large continuous-time Markov chains (CTMCs). It extends existing path-based and uniformization-based methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship makes it possible for the approach to explore multiple paths at the same time,· thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow it to analyze very large models using a very small amount of storage. Often, path-based techniques must compute many paths to obtain tight bounds. In addition to presenting the basic path-based approach, we also present algorithms for computing more paths and tighter bounds quickly. One resulting approach is based on the concept of path composition whereby precomputed subpaths are composed to compute the whole paths efficiently. Another approach is based on selecting important paths (among a set of many paths) for evaluation. Many path-based techniques suffer from having to evaluate many (unimportant) paths. Evaluating the important ones helps to compute tight bounds efficiently and quickly.

Contextual text mining

With the dramatic growth of text information, there is an increasing need for powerful text mining systems that can automatically discover useful knowledge from text. Text is generally associated with all kinds of contextual information. Those contexts can be explicit, such as the time and the location where a blog article is written, and the author(s) of a biomedical publication, or implicit, such as the positive or negative sentiment that an author had when she wrote a product review; there may also be complex context such as the social network of the authors. Many applications require analysis of topic patterns over different contexts. For instance, analysis of search logs in the context of the user can reveal how we can improve the quality of a search engine by optimizing the search results according to particular users; analysis of customer reviews in the context of positive and negative sentiments can help the user summarize public opinions about a product; analysis of blogs or scientific publications in the context of a social network can facilitate discovery of more meaningful topical communities. Since context information significantly affects the choices of topics and language made by authors, in general, it is very important to incorporate it into analyzing and mining text data. In general, modeling the context in text, discovering contextual patterns of language units and topics from text, a general task which we refer to as Contextual Text Mining, has widespread applications in text mining. In this thesis, we provide a novel and systematic study of contextual text mining, which is a new paradigm of text mining treating context information as the ``first-class citizen.'' We formally define the problem of contextual text mining and its basic tasks, and propose a general framework for contextual text mining based on generative modeling of text. This conceptual framework provides general guidance on text mining problems with context information and can be instantiated into many real tasks, including the general problem of contextual topic analysis. We formally present a functional framework for contextual topic analysis, with a general contextual topic model and its various versions, which can effectively solve the text mining problems in a lot of real world applications. We further introduce general components of contextual topic analysis, by adding priors to contextual topic models to incorporate prior knowledge, regularizing contextual topic models with dependency structure of context, and postprocessing contextual patterns to extract refined patterns. The refinements on the general contextual topic model naturally lead to a variety of probabilistic models which incorporate different types of context and various assumptions and constraints. These special versions of the contextual topic model are proved effective in a variety of real applications involving topics and explicit contexts, implicit contexts, and complex contexts. We then introduce a postprocessing procedure for contextual patterns, by generating meaningful labels for multinomial context models. This method provides a general way to interpret text mining results for real users. By applying contextual text mining in the ``context'' of other text information management tasks, including ad hoc text retrieval and web search, we further prove the effectiveness of contextual text mining techniques in a quantitative way with large scale datasets. The framework of contextual text mining not only unifies many explorations of text analysis with context information, but also opens up many new possibilities for future research directions in text mining.