LATENT VARIABLE MODELS GIVEN INCOMPLETELY OBSERVED SURROGATE OUTCOMES AND COVARIATES

Latent variable models (LVMs) are commonly used in the scenario where the outcome of the main interest is an unobservable measure, associated with multiple observed surrogate outcomes, and affected by potential risk factors. This thesis develops an approach of efficient handling missing surrogate outcomes and covariates in two- and three-level latent variable models. However, corresponding statistical methodologies and computational software are lacking efficiently analyzing the LVMs given surrogate outcomes and covariates subject to missingness in the LVMs. We analyze the two-level LVMs for longitudinal data from the National Growth of Health Study where surrogate outcomes and covariates are subject to missingness at any of the levels. A conventional method for efficient handling of missing data is to reexpress the desired model as a joint distribution of variables, including the surrogate outcomes that are subject to missingness conditional on all of the covariates that are completely observable, and estimate the joint model by maximum likelihood, which is then transformed to the desired model. The joint model, however, identifies more parameters than desired, in general. The over-identified joint model produces biased estimates of LVMs so that it is most necessary to describe how to impose constraints on the joint model so that it has a one-to-one correspondence with the desired model for unbiased estimation. The constrained joint model handles missing data efficiently under the assumption of ignorable missing data and is estimated by a modified application of the expectation-maximization (EM) algorithm

Unbiased Comparative Evaluation of Ranking Functions

Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling has shown intriguing promise since it enables the design of estimators that are provably unbiased even when reusing data with missing judgments. In this paper, we first unify and extend these sampling approaches by viewing the evaluation problem as a Monte Carlo estimation task that applies to a large number of common IR metrics. Drawing on the theoretical clarity that this view offers, we tackle three practical evaluation scenarios: comparing two systems, comparing $k$ systems against a baseline, and ranking $k$ systems. For each scenario, we derive an estimator and a variance-optimizing sampling distribution while retaining the strengths of sampling-based evaluation, including unbiasedness, reusability despite missing data, and ease of use in practice. In addition to the theoretical contribution, we empirically evaluate our methods against previously used sampling heuristics and find that they generally cut the number of required relevance judgments at least in half.Comment: Under review; 10 page

A Deep Embedding Model for Co-occurrence Learning

Co-occurrence Data is a common and important information source in many areas, such as the word co-occurrence in the sentences, friends co-occurrence in social networks and products co-occurrence in commercial transaction data, etc, which contains rich correlation and clustering information about the items. In this paper, we study co-occurrence data using a general energy-based probabilistic model, and we analyze three different categories of energy-based model, namely, the $L_1$, $L_2$ and $L_k$ models, which are able to capture different levels of dependency in the co-occurrence data. We also discuss how several typical existing models are related to these three types of energy models, including the Fully Visible Boltzmann Machine (FVBM) ($L_2$), Matrix Factorization ($L_2$), Log-BiLinear (LBL) models ($L_2$), and the Restricted Boltzmann Machine (RBM) model ($L_k$). Then, we propose a Deep Embedding Model (DEM) (an $L_k$ model) from the energy model in a \emph{principled} manner. Furthermore, motivated by the observation that the partition function in the energy model is intractable and the fact that the major objective of modeling the co-occurrence data is to predict using the conditional probability, we apply the \emph{maximum pseudo-likelihood} method to learn DEM. In consequence, the developed model and its learning method naturally avoid the above difficulties and can be easily used to compute the conditional probability in prediction. Interestingly, our method is equivalent to learning a special structured deep neural network using back-propagation and a special sampling strategy, which makes it scalable on large-scale datasets. Finally, in the experiments, we show that the DEM can achieve comparable or better results than state-of-the-art methods on datasets across several application domains

Linear filtering reveals false negatives in species interaction data

Species interaction datasets, often represented as sparse matrices, are usually collected through observation studies targeted at identifying species interactions. Due to the extensive required sampling effort, species interaction datasets usually contain many false negatives, often leading to bias in derived descriptors. We show that a simple linear filter can be used to detect false negatives by scoring interactions based on the structure of the interaction matrices. On 180 different datasets of various sizes, sparsities and ecological interaction types, we found that on average in about 75% of the cases, a false negative interaction got a higher score than a true negative interaction. Furthermore, we show that this filter is very robust, even when the interaction matrix contains a very large number of false negatives. Our results demonstrate that unobserved interactions can be detected in species interaction datasets, even without resorting to information about the species involved