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Register a new userGeneralized Bayesian Record Linkage and Regression with Exact Error Propagation
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Added by
Rebecca Steorts
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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Record linkage (de-duplication or entity resolution) is the process of merging noisy databases to remove duplicate entities. While record linkage removes duplicate entities from such databases, the downstream task is any inferential, predictive, or post-linkage task on the linked data. One goal of the downstream task is obtaining a larger reference data set, allowing one to perform more accurate statistical analyses. In addition, there is inherent record linkage uncertainty passed to the downstream task. Motivated by the above, we propose a generalized Bayesian record linkage method and consider multiple regression analysis as the downstream task. Records are linked via a random partition model, which allows for a wide class to be considered. In addition, we jointly model the record linkage and downstream task, which allows one to account for the record linkage uncertainty exactly. Moreover, one is able to generate a feedback propagation mechanism of the information from the proposed Bayesian record linkage model into the downstream task. This feedback effect is essential to eliminate potential biases that can jeopardize resulting downstream task. We apply our methodology to multiple linear regression, and illustrate empirically that the feedback effect is able to improve the performance of record linkage.
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Record linkage (entity resolution or de-deduplication) is the process of merging noisy databases to remove duplicate entities. While record linkage removes duplicate entities from the data, many researchers are interested in performing inference, prediction or post-linkage analysis on the linked data, which we call the downstream task. Depending on the downstream task, one may wish to find the most representative record before performing the post-linkage analysis. Motivated by the downstream task, we propose first performing record linkage using a Bayesian model and then choosing representative records through prototyping. Given the information about the representative records, we then explore two downstream tasks - linear regression and binary classification via logistic regression. In addition, we explore how error propagation occurs in both of these settings. We provide thorough empirical studies for our proposed methodology, and conclude with a discussion of practical insights into our work.
In record linkage (RL), or exact file matching, the goal is to identify the links between entities with information on two or more files. RL is an important activity in areas including counting the population, enhancing survey frames and data, and conducting epidemiological and follow-up studies. RL is challenging when files are very large, no accurate personal identification (ID) number is present on all files for all units, and some information is recorded with error. Without an unique ID number one must rely on comparisons of names, addresses, dates, and other information to find the links. Latent class models can be used to automatically score the value of information for determining match status. Data for fitting models come from comparisons made within groups of units that pass initial file blocking requirements. Data distributions can vary across blocks. This article examines the use of prior information and hierarchical latent class models in the context of RL.
We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how to use a type of model averaging approach to eliminate the nuisance penalty parameters and perform inference through the marginal posterior distribution of the regression coefficients. We establish tail robustness of the resulting estimator as well as conditional and marginal posterior consistency. We develop an efficient component-wise Markov chain Monte Carlo algorithm for sampling. Numerical results show that the method tends to select the optimal penalty and performs well in both variable selection and prediction and is comparable to, and often better than alternative methods. Both simulated and real data examples are provided.
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal assumption is violated. To relax the normal assumption on the error distribution hence reduce the modeling bias, we propose semiparametric mixture of linear regression models with unspecified error distributions. We establish a more general identifiability result under weaker conditions than existing results, construct a class of new estimators, and establish their asymptotic properties. These asymptotic results also apply to many existing semiparametric mixture regression estimators whose asymptotic properties have remained unknown due to the inherent difficulties in obtaining them. Using simulation studies, we demonstrate the superiority of the proposed estimators over the MLE when the normal error assumption is violated and the comparability when the error is normal. Analysis of a newly collected Equine Infectious Anemia Virus data in 2017 is employed to illustrate the usefulness of the new estimator.
Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical expressions composed of some basic functions. However, the search space of all possible expressions grows exponentially with the length of the expression, making it infeasible for enumeration. Genetic programming (GP) has been traditionally and commonly used in SR to search for the optimal solution, but it suffers from several limitations, e.g. the difficulty in incorporating prior knowledge; overly-complicated output expression and reduced interpretability etc. To address these issues, we propose a new method to fit SR under a Bayesian framework. Firstly, Bayesian model can naturally incorporate prior knowledge (e.g., preference of basis functions, operators and raw features) to improve the efficiency of fitting SR. Secondly, to improve interpretability of expressions in SR, we aim to capture concise but informative signals. To this end, we assume the expected signal has an additive structure, i.e., a linear combination of several concise expressions, whose complexity is controlled by a well-designed prior distribution. In our setup, each expression is characterized by a symbolic tree, and the proposed SR model could be solved by sampling symbolic trees from the posterior distribution using an efficient Markov chain Monte Carlo (MCMC) algorithm. Finally, compared with GP, the proposed BSR(Bayesian Symbolic Regression) method saves computer memory with no need to keep an updated genome pool. Numerical experiments show that, compared with GP, the solutions of BSR are closer to the ground truth and the expressions are more concise. Meanwhile we find the solution of BSR is robust to hyper-parameter specifications such as the number of trees.
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