Nested dictionary learning for hierarchical organization of imagery and text

A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is associated with a path through the tree (from root to a leaf), and each of the multiple patches in a given image is associated with one node in that path. Nodes near the tree root are shared between multiple paths, representing image characteristics that are common among different types of images. Moving toward the leaves, nodes become specialized, representing details in image classes. If available, words (text) are also jointly modeled, with a path-dependent probability over words. The tree structure is inferred via a nested Dirichlet process, and a retrospective stick-breaking sampler is used to infer the tree depth and width.

Cross-Domain Multitask Learning with Latent Probit Models

Learning multiple tasks across heterogeneous domains is a challenging problem since the feature space may not be the same for different tasks. We assume the data in multiple tasks are generated from a latent common domain via sparse domain transforms and propose a latent probit model (LPM) to jointly learn the domain transforms, and the shared probit classifier in the common domain. To learn meaningful task relatedness and avoid over-fitting in classification, we introduce sparsity in the domain transforms matrices, as well as in the common classifier. We derive theoretical bounds for the estimation error of the classifier in terms of the sparsity of domain transforms. An expectation-maximization algorithm is derived for learning the LPM. The effectiveness of the approach is demonstrated on several real datasets.

Peer-Informed Learning on Increasing Contraceptive Knowledge Among Women in Rural Haiti

Contraceptive prevalence in Haiti remains low despite extensive foreign aid targeted at improving family planning. [1] Earlier studies have found that peer-informed learning have been successful in promoting sexual and reproductive health. [2-5] This pilot project was implemented as a three-month, community-based, educational intervention to assess the impact of peer education in increasing contraceptive knowledge among women in Fondwa, Haiti. Research investigators conducted contraceptive information trainings to pre-identified female leaders of existing women’s groups in Fondwa, who were recruited as peer educators (n=4). Later, these female leaders shared the knowledge from the training with the test participants in the women’s group (n=23) through an information session. Structured surveys measuring knowledge of contraceptives were conducted with all participants before the intervention began, at the end of the intervention, and four weeks after the intervention. The surveys measured general contraceptive knowledge, knowledge about eight selected types of modern contraceptives and contraceptive preferences and attitudes. Only test participants showed significant improvement in their general contraceptive knowledge score (p<0.001), but both test participants and peer educators showed significant improvement in overall knowledge scores for identifying the types and uses of modern contraceptive methods. Assessment for knowledge retention remained significantly higher four weeks after the intervention than prior to the intervention. Therefore, a one-time, three-hour peer-based educational intervention using existing social structures is effective, and might be valuable in a population with minimal access to education and little to no knowledge about contraceptives.

New Advancements of Scalable Statistical Methods for Learning Latent Structures in Big Data

Constant technology advances have caused data explosion in recent years. Accord- ingly modern statistical and machine learning methods must be adapted to deal with complex and heterogeneous data types. This phenomenon is particularly true for an- alyzing biological data. For example DNA sequence data can be viewed as categorical variables with each nucleotide taking four different categories. The gene expression data, depending on the quantitative technology, could be continuous numbers or counts. With the advancement of high-throughput technology, the abundance of such data becomes unprecedentedly rich. Therefore efficient statistical approaches are crucial in this big data era.

Previous statistical methods for big data often aim to find low dimensional struc- tures in the observed data. For example in a factor analysis model a latent Gaussian distributed multivariate vector is assumed. With this assumption a factor model produces a low rank estimation of the covariance of the observed variables. Another example is the latent Dirichlet allocation model for documents. The mixture pro- portions of topics, represented by a Dirichlet distributed variable, is assumed. This dissertation proposes several novel extensions to the previous statistical methods that are developed to address challenges in big data. Those novel methods are applied in multiple real world applications including construction of condition specific gene co-expression networks, estimating shared topics among newsgroups, analysis of pro- moter sequences, analysis of political-economics risk data and estimating population structure from genotype data.