HaiYing Wang

HaiYing Wang, Aonan Zhang, Chong Wang

We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small number of positive instances, which justifies the usage of negative sampling. However, if the negative instances are subsampled to the same level of the positive cases, there is information loss. To maintain more information, we derive the asymptotic distribution of a general inverse probability weighted (IPW) estimator and obtain the optimal sampling probability that minimizes its variance. To further improve the estimation efficiency over the IPW method, we propose a likelihood-based estimator by correcting log odds for the sampled data and prove that the improved estimator has the smallest asymptotic variance among a large class of estimators. It is also more robust to pilot misspecification. We validate our approach on simulated data as well as a real click-through rate dataset with more than 0.3 trillion instances, collected over a period of a month. Both theoretical and empirical results demonstrate the effectiveness of our method.

HaiYing Wang, Jae Kwang Kim

Subsampling is a computationally effective approach to extract information from massive data sets when computing resources are limited. After a subsample is taken from the full data, most available methods use an inverse probability weighted (IPW) objective function to estimate the model parameters. The IPW estimator does not fully utilize the information in the selected subsample. In this paper, we propose to use the maximum sampled conditional likelihood estimator (MSCLE) based on the sampled data. We established the asymptotic normality of the MSCLE and prove that its asymptotic variance covariance matrix is the smallest among a class of asymptotically unbiased estimators, including the IPW estimator. We further discuss the asymptotic results with the L-optimal subsampling probabilities and illustrate the estimation procedure with generalized linear models. Numerical experiments are provided to evaluate the practical performance of the proposed method.

Jun Yu, HaiYing Wang, Mingyao Ai et al.

Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the data volume is so large that nonuniform subsampling probabilities cannot be calculated all at once, then subsampling with replacement is infeasible to implement. This paper solves this problem using Poisson subsampling. We first derive optimal Poisson subsampling probabilities in the context of quasi-likelihood estimation under the A- and L-optimality criteria. For a practically implementable algorithm with approximated optimal subsampling probabilities, we establish the consistency and asymptotic normality of the resultant estimators. To deal with the situation that the full data are stored in different blocks or at multiple locations, we develop a distributed subsampling framework, in which statistics are computed simultaneously on smaller partitions of the full data. Asymptotic properties of the resultant aggregated estimator are investigated. We illustrate and evaluate the proposed strategies through numerical experiments on simulated and real data sets.

Terence Fusco, Yaxin Bi, Haiying Wang et al.

The key issues pertaining to collection of epidemic disease data for our analysis purposes are that it is a labour intensive, time consuming and expensive process resulting in availability of sparse sample data which we use to develop prediction models. To address this sparse data issue, we present novel Incremental Transductive methods to circumvent the data collection process by applying previously acquired data to provide consistent, confidence-based labelling alternatives to field survey research. We investigated various reasoning approaches for semisupervised machine learning including Bayesian models for labelling data. The results show that using the proposed methods, we can label instances of data with a class of vector density at a high level of confidence. By applying the Liberal and Strict Training Approaches, we provide a labelling and classification alternative to standalone algorithms. The methods in this paper are components in the process of reducing the proliferation of the Schistosomiasis disease and its effects.