Conditional probabilistic graphical models provide a powerful framework for structured regression in spatio-temporal datasets with complex correlation patterns. However, in real-life applications a large fraction of observations is often missing, which can severely limit the representational power of these models. In this paper we propose a Marginalized Gaussian Conditional Random Fields (m-GCRF) structured regression model for dealing with missing labels in partially observed temporal attributed graphs. This method is aimed at learning with both labeled and unlabeled parts and effectively predicting future values in a graph. The method is even capable of learning from nodes for which the response variable is never observed in history, which poses problems for many state-of-the-art models that can handle missing data. The proposed model is characterized for various missingness mechanisms on 500 synthetic graphs. The benefits of the new method are also demonstrated on a challenging application for predicting precipitation based on partial observations of climate variables in a temporal graph that spans the entire continental US. We also show that the method can be useful for optimizing the costs of data collection in climate applications via active reduction of the number of weather stations to consider. In experiments on these real-world and synthetic datasets we show that the proposed model is consistently more accurate than alternative semi-supervised structured models, as well as models that either use imputation to deal with missing values or simply ignore them altogether.
One of the standard ways of handling missing values is imputing values based on some predictive model, and then applying the analysis on a fully observed dataset. To exploit the graph structure, previous studies have proposed imputation of missing values based on the exponential random graph model @cite_11 . The limitation of such an approach is that it is slow, as it requires Gibbs sampling, and so it cannot handle large graphs. Imputation of missing values can also be accomplished using matrix (or tensor) factorization methods. These methods can impute missing values with high accuracy even when large percentages (up to 95 , imputation-based methods use only point estimates of the missing values, effectively ignoring the prediction uncertainty when learning with imputed values. Techniques known as Multiple Imputation (MI) try to correct for this drawback, by sampling from the posterior distribution of missing values. On the other hand, these techniques can be less effective when a larger fraction of data is missing @cite_4 , and can be computationally very demanding.
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Missing values are a common problem in many real world databases. Inadequate handing of missing data can lead to serious problems in data analysis. A common way to cope with this problem is to use imputation methods to fill missing values with plausible values. This paper proposes GPMI, a multiple imputation method that uses genetic programming as a regression method to estimate missing values. Experiments on eight datasets with six levels of missing values compare GPMI with seven other popular and advanced imputation methods on two measures: the prediction accuracy and the classification accuracy. The results show that, in most cases, GPMI not only achieves better prediction accuracy, but also better classification accuracy than the other imputation methods. The predictive analysis of longitudinal social surveys is highly sensitive to the effects of missing data in temporal observations. Such high sensitivity to missing values raises the need for accurate data imputation, because without it a large fraction of collected data could not be used properly. Previous studies focused on the treatment of missing data in longitudinal social networks due to non-respondents and dealt with the problem largely by imputing missing links in isolation or analyzing the imputation effects on network statistics. We propose to account for changing network topology and interdependence between actors' links and attributes to construct a unified approach for imputation of links and attributes in longitudinal social surveys. The new method, based on an exponential random graph model, is evaluated experimentally for five scenarios of missing data models utilizing synthetic and real life datasets with 20 ---60 of nodes missing. The obtained results outperformed all alternatives, four of which were link imputation methods and two node attribute imputation methods. We further discuss the applicability and scalability of our approach to real life problems and compare our model with the latest advancements in the field. Our findings suggest that the proposed method can be used as a viable imputation tool in longitudinal studies. This paper proposes to utilize information within incomplete instances (instances with missing values) when estimating missing values. Accordingly, a simple and efficient nonparametric iterative imputation algorithm, called the NIIA method, is designed for iteratively imputing missing target values. The NIIA method imputes each missing value several times until the algorithm converges. In the first iteration, all the complete instances are used to estimate missing values. The information within incomplete instances is utilized since the second imputation iteration. We conduct some experiments for evaluating the efficiency, and demonstrate: (1) the utilization of information within incomplete instances is of benefit to easily capture the distribution of a dataset; and (2) the NIIA method outperforms the existing methods in accuracy, and this advantage is clearly highlighted when datasets have a high missing ratio. Missing values are a common problem when applying classification algorithms to real-world medical data. This is especially true for trauma patients, where the emergent nature of the cases makes it difficult to collect all of the relevant data for each patient. Standard methods for handling missingness first learn a model to estimate missing data values, and subsequently train and evaluate a classifier using data imputed with this model. Recently, several proposed methods have demonstrated the benefits of jointly estimating the imputation model and classifier parameters. However, these methods make assumptions that limit their utility with many real-world medical datasets. For example, the assumption that data elements are missing at random is often invalid.We address this situation by exploring a novel approach for jointly learning the imputation model and classifier. Unlike previous algorithms, our approach makes no assumptions about the missingness of the data, can be used with arbitrary probabilistic data models and classification loss functions, and can be used when both the training and testing data have missing values. We investigate the utility of this approach on the prediction of several patient outcomes in a large national registry of trauma patients, and find that it significantly outperforms standard sequential methods. Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse.Large-Sample Inference Based on Maximum Likelihood Estimates.Bayes and Multiple Imputation.PART III: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA: APPLICATIONS TO SOME COMMON MODELS.Multivariate Normal Examples, Ignoring the Missing-Data Mechanism.Models for Robust Estimation.Models for Partially Classified Contingency Tables, Ignoring the Missing-Data Mechanism.Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missing-Data Mechanism.Nonignorable Missing-Data Models.References.Author Index.Subject Index. Part 1. A Gentle Introduction to Missing Data. The Concept of Missing Data. The Prevalence of Missing Data. Why Data Might Be Missing. The Impact of Missing Data. What's Missing in the Missing Data Literature? A Cost-Benefit Approach to Missing Data. Missing Data - Not Just for Statisticians Anymore. Part 2. Consequences of Missing Data. Three General Consequences of Missing Data. Consequences of Missing Data on Construct Validity. Consequences of Missing Data on Internal Validity. Consequences on Causal Generalization. Summary. Part 3. Classifying Missing Data. "The Silence That Betokens". The Current Classification System: Mechanisms of Missing Data. Expanding the Classification System. Summary. Part 4. Preventing Missing Data by Design. Overall Study Design. Characteristics of the Target Population and the Sample. Data Collection and Measurement. Treatment Implementation. Data Entry Process. Summary. Part 5. Diagnostic Procedures. Traditional Diagnostics. Dummy Coding Missing Data. Numerical Diagnostic Procedures. Graphical Diagnostic Procedures. Summary. Part 6. The Selection of Data Analytic Procedures. Preliminary Steps. Decision Making. Summary. Part 7. Data Deletion Methods for Handling Missing Data. Data Sets. Complete Case Method. Available Case Method. Available Item Method. Individual Growth Curve Analysis. Multisample Analyses. Summary. Part 8. Data Augmentation Procedures. Model-Based Procedures. Markov Chain Monte Carlo. Adjustment Methods. Summary. Part 9. Single Imputation Procedures. Constant Replacement Methods. Random Value Imputation. Nonrandom Value Imputation: Single Condition. Nonrandom Value Imputation: Multiple Conditions. Summary. Part 10. Multiple Imputation. The MI Process. Summary. Part 11. Reporting Missing Data and Results. APA Task Force Recommendations. Missing Data and Study Stages. TFSI Recommendations and Missing Data. Reporting Format. Summary. Part 12. Epilogue. Missing values widely exist in many real-world datasets, which hinders the performing of advanced data analytics. Properly filling these missing values is crucial but challenging, especially when the missing rate is high. Many approaches have been proposed for missing value imputation (MVI), but they are mostly heuristics-based, lacking a principled foundation and do not perform satisfactorily in practice. In this paper, we propose a probabilistic framework based on deep generative models for MVI. Under this framework, imputing the missing entries amounts to seeking a fixed-point solution between two conditional distributions defined on the missing entries and latent variables respectively. These distributions are parameterized by deep neural networks (DNNs) which possess high approximation power and can capture the nonlinear relationships between missing entries and the observed values. The learning of weight parameters of DNNs is performed by maximizing an approximation of the log-likelihood of observed values. We conducted extensive evaluation on 13 datasets and compared with 11 baselines methods, where our methods largely outperforms the baselines. Data quality is a major concern in Machine Learning and other correlated areas such as Knowledge Discovery from Databases (KDD). As most Machine Learning algorithms induce knowledge strictly from data, the quality of the knowledge extracted is largely determined by the quality of the underlying data. One relevant problem in data quality is the presence of missing data. Despite the frequent occurrence of missing data, many Machine Learning algorithms handle missing data in a rather naive way. Missing data treatment should be carefully thought, otherwise bias might be introduced into the knowledge induced. In this work, we analyse the use of the k-nearest neighbour as an imputation method. Imputation is a term that denotes a procedure that replaces the missing values in a data set by some plausible values. Our analysis indicates that missing data imputation based on the k-nearest neighbour algorithm can outperform the internal methods used by C4.5 and CN2 to treat missing data. Hot deck imputation is a procedure in which missing items are replaced with values from respondents. A model supporting such procedures is the model in which response probabilities are assumed equal within imputation cells. An efficient version of hot deck imputation is described for the cell response model and a computationally efficient variance estimator is given. An approximation to the fully efficient procedure in which a small number of values are imputed for each nonrespondent is described. Variance estimation procedures are illustrated in a Monte Carlo study. Affordable sensors lead to an increasing interest in acquiring and modeling data with multiple modalities. Learning from multiple modalities has shown to significantly improve performance in object recognition. However, in practice it is common that the sensing equipment experiences unforeseeable malfunction or configuration issues, leading to corrupted data with missing modalities. Most existing multi-modal learning algorithms could not handle missing modalities, and would discard either all modalities with missing values or all corrupted data. To leverage the valuable information in the corrupted data, we propose to impute the missing data by leveraging the relatedness among different modalities. Specifically, we propose a novel Cascaded Residual Autoencoder (CRA) to impute missing modalities. By stacking residual autoencoders, CRA grows iteratively to model the residual between the current prediction and original data. Extensive experiments demonstrate the superior performance of CRA on both the data imputation and the object recognition task on imputed data. Handling missing data is a critical step to ensuring good results in data mining. Like most data mining algorithms, existing privacy-preserving data mining algorithms assume data is complete. In order to maintain privacy in the data mining process while cleaning data, privacy-preserving methods of data cleaning will be required. In this paper, we address the problem of privacy-preserving data imputation of missing data. Specifically, we present a privacy-preserving protocol for filling in missing values using a lazy decision tree imputation algorithm for data that is horizontally partitioned between two parties. The participants of the protocol learn only the imputed values; the computed decision tree is not learned by either party. Imputing missing values in high dimensional time-series is a difficult problem. This paper presents a strategy for training energy-based graphical models for imputation directly, bypassing difficulties probabilistic approaches would face. The training strategy is inspired by recent work on optimization-based learning (Domke, 2012) and allows complex neural models with convolutional and recurrent structures to be trained for imputation tasks. In this work, we use this training strategy to derive learning rules for three substantially different neural architectures. Inference in these models is done by either truncated gradient descent or variational mean-field iterations. In our experiments, we found that the training methods outperform the Contrastive Divergence learning algorithm. Moreover, the training methods can easily handle missing values in the training data itself during learning. We demonstrate the performance of this learning scheme and the three models we introduce on one artificial and two real-world data sets. In recent years, multiple imputation has emerged as a convenient and flexible paradigm for analysing data with missing values. Essential features of multiple imputation are reviewed, with answers to frequently asked questions about using the method in practice. We propose a novel method for imputing missing data by adapting the well-known Generative Adversarial Nets (GAN) framework. Accordingly, we call our method Generative Adversarial Imputation Nets (GAIN). The generator (G) observes some components of a real data vector, imputes the missing components conditioned on what is actually observed, and outputs a completed vector. The discriminator (D) then takes a completed vector and attempts to determine which components were actually observed and which were imputed. To ensure that D forces G to learn the desired distribution, we provide D with some additional information in the form of a hint vector. The hint reveals to D partial information about the missingness of the original sample, which is used by D to focus its attention on the imputation quality of particular components. This hint ensures that G does in fact learn to generate according to the true data distribution. We tested our method on various datasets and found that GAIN significantly outperforms state-of-the-art imputation methods. The simplest approach to dealing with missing data is to restrict the analysis to complete cases, i.e. individuals with no missing values. This can induce bias, however. Inverse probability weighting (IPW) is a commonly used method to correct this bias. It is also used to adjust for unequal sampling fractions in sample surveys. This article is a review of the use of IPW in epidemiological research. We describe how the bias in the complete-case analysis arises and how IPW can remove it. IPW is compared with multiple imputation (MI) and we explain why, despite MI generally being more efficient, IPW may sometimes be preferred. We discuss the choice of missingness model and methods such as weight truncation, weight stabilisation and augmented IPW. The use of IPW is illustrated on data from the 1958 British Birth Cohort. A novel algorithm based on random forests with surrogate splits is proposed to address the classification problem of incomplete data without imputation.The algorithm allows each tree to cast a vote even the voting process is interrupted by missing attributes.Experimental results on various acknowledged datasets show that the proposed method is robust and efficient. Random forests (RF) is known as an efficient algorithm in classification, however it depends on the integrity of datasets. Conventional methods in dealing with missing values usually employ estimation and imputation approaches whose efficiency is tied to the assumptions of data features. Recently, algorithm of surrogate decisions in RF was developed and this paper proposes a random forests algorithm with modified surrogate splits (Adjusted Weight Voting Random Forest, AWVRF) which is able to address the incomplete data without imputation.Differing from the present surrogate method, in AWVRF algorithm, when the primary splitting attribute and the surrogate attributes of an internal node are all missing, the undergoing instance is allowed to exit at the current node with a vote. Then the weight of the vote is adjusted by the strength of the involved attributes and the final decision is made by weighted voting. AWVRF does not comprise imputation step, thus it is independent of data features.AWVRF is compared with the methods of mean imputation, LeoFill, knnimpute, BPCAfill and conventional RF with surrogate decisions (surrRF) using 50 times repeated 5-fold cross validation on 10 acknowledged datasets. In a total of 22 experiment settings, the method of AWVRF harvests the highest accuracy in 14 settings and the largest AUC in 7 settings, exhibiting its superiority over other methods. Compared with surrRF, AWVRF is significantly more efficient and remain good discrimination of prediction. Experimental results show that the present AWVRF algorithm can successfully handle the classification task for incomplete data. Missing data analyses have received considerable recent attention in the methodological literature, and two “modern” methods, multiple imputation and maximum likelihood estimation, are recommended. The goals of this article are to (a) provide an overview of missing-data theory, maximum likelihood estimation, and multiple imputation; (b) conduct a methodological review of missing-data reporting practices in 23 applied research journals; and (c) provide a demonstration of multiple imputation and maximum likelihood estimation using the Longitudinal Study of American Youth data. The results indicated that explicit discussions of missing data increased substantially between 1999 and 2003, but the use of maximum likelihood estimation or multiple imputation was rare; the studies relied almost exclusively on listwise and pairwise deletion. Multivariate time series data in practical applications, such as health care, geoscience, and biology, are characterized by a variety of missing values. In time series prediction and other related tasks, it has been noted that missing values and their missing patterns are often correlated with the target labels, a.k.a., informative missingness. There is very limited work on exploiting the missing patterns for effective imputation and improving prediction performance. In this paper, we develop novel deep learning models, namely GRU-D, as one of the early attempts. GRU-D is based on Gated Recurrent Units (GRU), a state-of-the-art recurrent neural network. It takes two representations of missing patterns, i.e., masking and time interval, and effectively incorporates them into a deep model architecture so that it not only captures the long-term temporal dependencies in time series, but also utilizes the missing patterns to achieve better prediction results. Experiments of time series classification tasks on real-world clinical datasets (MIMIC-III, PhysioNet) and synthetic datasets demonstrate that our models achieve state-of-the-art performance and provides useful insights for better understanding and utilization of missing values in time series analysis. Multivariate time series data in practical applications, such as health care, geoscience, and biology, are characterized by a variety of missing values. In time series prediction and other related tasks, it has been noted that missing values and their missing patterns are often correlated with the target labels, a.k.a., informative missingness. There is very limited work on exploiting the missing patterns for effective imputation and improving prediction performance. In this paper, we develop novel deep learning models, namely GRU-D, as one of the early attempts. GRU-D is based on Gated Recurrent Unit (GRU), a state-of-the-art recurrent neural network. It takes two representations of missing patterns, i.e., masking and time interval, and effectively incorporates them into a deep model architecture so that it not only captures the long-term temporal dependencies in time series, but also utilizes the missing patterns to achieve better prediction results. Experiments of time series classification tasks on real-world clinical datasets (MIMIC-III, PhysioNet) and synthetic datasets demonstrate that our models achieve state-of-the-art performance and provides useful insights for better understanding and utilization of missing values in time series analysis. Incomplete information often occur along with many database applications, e.g., in data integration, data cleaning or data exchange. The idea of data imputation is to fill the missing data with the values of its neighbors who share the same information. Such neighbors could either be identified certainly by editing rules or statistically by relational dependency networks. Unfortunately, owing to data sparsity, the number of neighbors (identified w.r.t. value equality) is rather limited, especially in the presence of data values with variances. In this paper, we argue to extensively enrich similarity neighbors by similarity rules with tolerance to small variations. More fillings can thus be acquired that the aforesaid equality neighbors fail to reveal. To fill the missing values more, we study the problem of maximizing the missing data imputation. Our major contributions include (1) the np-hardness analysis on solving and approximating the problem, (2) exact algorithms for tackling the problem, and (3) efficient approximation with performance guarantees. Experiments on real and synthetic data sets demonstrate that the filling accuracy can be improved.