Missing data is a crucial issue when applying machine learning algorithms to real-world datasets. Starting from the simple assumption that two batches extracted randomly from the same dataset should share the same distribution, we leverage optimal transport distances to quantify that criterion and turn it into a loss function to impute missing data values. We propose practical methods to minimize these losses using end-to-end learning, that can exploit or not parametric assumptions on the underlying distributions of values. We evaluate our methods on datasets from the UCI repository, in MCAR, MAR and MNAR settings. These experiments show that OT-based methods match or out-perform state-of-the-art imputation methods, even for high percentages of missing values.
Missing data are a concern in many real world data sets and imputation methods are often needed to estimate the values of missing data, but data sets with excessive missingness and high dimensionality challenge most approaches to imputation. Here we show that appropriate feature selection can be an effective preprocessing step for imputation, allowing for more accurate imputation and subsequent model predictions. The key feature of this preprocessing is that it incorporates uncertainty: by accounting for uncertainty due to missingness when selecting features we can reduce the degree of missing…
Efficient Imputation for Patch-based Missing Single-cell Data via Cluster-regularized Optimal Transport
Department of Computer Science, Stony Brook University（计算机科学系，石板溪大学）；Department of Computer Science, Emory University（计算机科学系，埃默里大学）；Department of Population Health Sciences, Cornell University（流行病学与公共卫生系，康奈尔大学）；Department of Computer Science and Engineering, Cornell University（计算机科学与工程系，康奈尔大学）；Department of Biomedical Informatics, Stony Brook University（生物医学信息学系，石板溪大学）
Missing data imputation can help improve the performance of prediction models in situations where missing data hide useful information. This paper compares methods for imputing missing categorical data for supervised classification tasks. We experiment on two machine learning benchmark datasets with missing categorical data, comparing classifiers trained on non-imputed (i.e., one-hot encoded) or imputed data with different levels of additional missing-data perturbation. We show imputation methods can increase predictive accuracy in the presence of missing-data perturbation, which can actually …
SimulaMet（西穆拉大都会研究所）；Warsaw University of Technology（华沙理工大学）
Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation techniques. Meanwhile, the data nowadays tends toward high-dimensional. Therefore, in this work, we propose Principal Component Analysis Imputation (PCAI), a simple but versatile framework based on Principal Component Analysis (PCA) to speed up the imputation process and alleviate memory issues of many available imputation techniques, without sacrificing the imputatio…
Missing value imputation is a challenging and well-researched topic in data mining. In this paper, we propose IFGAN, a missing value imputation algorithm based on Feature-specific Generative Adversarial Networks (GAN). Our idea is intuitive yet effective: a feature-specific generator is trained to impute missing values, while a discriminator is expected to distinguish the imputed values from observed ones. The proposed architecture is capable of handling different data types, data distributions, missing mechanisms, and missing rates. It also improves post-imputation analysis by preserving inte…
When sensors collect spatio-temporal data in a large geographical area, the existence of missing data cannot be escaped. Missing data negatively impacts the performance of data analysis and machine learning algorithms. In this paper, we study deep autoencoders for missing data imputation in spatio-temporal problems. We propose a convolution bidirectional-LSTM for capturing spatial and temporal patterns. Moreover, we analyze an autoencoder's latent feature representation in spatio-temporal data and illustrate its performance for missing data imputation. Traffic flow data are used for evaluation…
Institute for Infocomm Research（资讯通信研究院）；Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局（A*STAR））
Real-world clinical time series data sets exhibit a high prevalence of missing values. Hence, there is an increasing interest in missing data imputation. Traditional statistical approaches impose constraints on the data-generating process and decouple imputation from prediction. Recent works propose recurrent neural network based approaches for missing data imputation and prediction with time series data. However, they generate deterministic outputs and neglect the inherent uncertainty. In this work, we introduce a unified Bayesian recurrent framework for simultaneous imputation and prediction…
Intelligent Systems Group（智能系统研究组）；Univ. of the Basque Country（巴斯克大学）；UPV/EHU（巴斯克大学）
Missing data has a ubiquitous presence in real-life applications of machine learning techniques. Imputation methods are algorithms conceived for restoring missing values in the data, based on other entries in the database. The choice of the imputation method has an influence on the performance of the machine learning technique, e.g., it influences the accuracy of the classification algorithm applied to the data. Therefore, selecting and applying the right imputation method is important and usually requires a substantial amount of human intervention. In this paper we propose the use of genetic …
Missing value imputation is crucial for real-world data science workflows. Imputation is harder in the online setting, as it requires the imputation method itself to be able to evolve over time. For practical applications, imputation algorithms should produce imputations that match the true data distribution, handle data of mixed types, including ordinal, boolean, and continuous variables, and scale to large datasets. In this work we develop a new online imputation algorithm for mixed data using the Gaussian copula. The online Gaussian copula model meets all the desiderata: its imputations mat…
National Remote Sensing Centre (ISRO), India（印度国家遥感中心（ISRO））
Decision making from data involves identifying a set of attributes that contribute to effective decision making through computational intelligence. The presence of missing values greatly influences the selection of right set of attributes and this renders degradation in classification accuracies of the classifiers. As missing values are quite common in data collection phase during field experiments or clinical trails appropriate handling would improve the classifier performance. In this paper we present a review of recently developed missing value imputation algorithms and compare their perfor…
The most common strategy of imputing missing values in a table is to study either the column-column relationship or the row-row relationship of the data table, then use the relationship to impute the missing values based on the non-missing values from other columns of the same row, or from the other rows of the same column. This paper introduces a double autoencoder for imputation ($Ae^2I$) that simultaneously and collaboratively uses both row-row relationship and column-column relationship to impute the missing values. Empirical tests on Movielens 1M dataset demonstrated that $Ae^2I$ outperfo…
Dealing with missing data in data analysis is inevitable. Although powerful imputation methods that address this problem exist, there is still much room for improvement. In this study, we examined single imputation based on deep autoencoders, motivated by the apparent success of deep learning to efficiently extract useful dataset features. We have developed a consistent framework for both training and imputation. Moreover, we benchmarked the results against state-of-the-art imputation methods on different data sizes and characteristics. The work was not limited to the one-type variable dataset…
Department of Computing Science Simon Fraser University（西蒙弗雷泽大学计算机科学系）
Missing data is a significant problem impacting all domains. State-of-the-art framework for minimizing missing data bias is multiple imputation, for which the choice of an imputation model remains nontrivial. We propose a multiple imputation model based on overcomplete deep denoising autoencoders. Our proposed model is capable of handling different data types, missingness patterns, missingness proportions and distributions. Evaluation on several real life datasets show our proposed model significantly outperforms current state-of-the-art methods under varying conditions while simultaneously im…
University of Cambridge（剑桥大学）；Microsoft Research Cambridge（微软剑桥研究院）
Real-world datasets often have missing values associated with complex generative processes, where the cause of the missingness may not be fully observed. This is known as missing not at random (MNAR) data. However, many imputation methods do not take into account the missingness mechanism, resulting in biased imputation values when MNAR data is present. Although there are a few methods that have considered the MNAR scenario, their model's identifiability under MNAR is generally not guaranteed. That is, model parameters can not be uniquely determined even with infinite data samples, hence the i…
HDR UK-Turing Wellcome（英国健康数据研究中心-图灵惠康）；University of Edinburgh（爱丁堡大学）；University College London（伦敦大学学院）
Missing data persists as a major barrier to data analysis across numerous applications. Recently, deep generative models have been used for imputation of missing data, motivated by their ability to capture highly non-linear and complex relationships in the data. In this work, we investigate the ability of deep models, namely variational autoencoders (VAEs), to account for uncertainty in missing data through multiple imputation strategies. We find that VAEs provide poor empirical coverage of missing data, with underestimation and overconfident imputations, particularly for more extreme missing …
We propose Conditional Imputation GAN, an extended missing data imputation method based on Generative Adversarial Networks (GANs). The motivating use case is learning-to-rank, the cornerstone of modern search, recommendation system, and information retrieval applications. Empirical ranking datasets do not always follow standard Gaussian distributions or Missing Completely At Random (MCAR) mechanism, which are standard assumptions of classic missing data imputation methods. Our methodology provides a simple solution that offers compatible imputation guarantees while relaxing assumptions for mis…
Datasets with missing values are very common on industry applications, and they can have a negative impact on machine learning models. Recent studies introduced solutions to the problem of imputing missing values based on deep generative models. Previous experiments with Generative Adversarial Networks and Variational Autoencoders showed interesting results in this domain, but it is not clear which method is preferable for different use cases. The goal of this work is twofold: we present a comparison between missing data imputation solutions based on deep generative models, and we propose impr…
Beyond Random Missingness: Clinically Rethinking for Healthcare Time Series Imputation
King’s College London（伦敦国王学院）；PyPOTS Research（PyPOTS研究中心）；University of Oxford（牛津大学）；Hong Kong University of Science and Technology（香港科技大学）；University College London（伦敦大学学院）
This work proposes a non-iterative strategy for missing value imputations which is guided by similarity between observations, but instead of explicitly determining distances or nearest neighbors, it assigns observations to overlapping buckets through recursive semi-random hyperplane cuts, in which weighted averages are determined as imputations for each variable. The quality of these imputations is oftentimes not as good as that of chained equations, but the proposed technique is much faster, non-iterative, can make imputations on new data without re-calculating anything, and scales easily to …
Yantai University（烟台大学）；East China Normal University（华东师范大学）
Datasets with missing values are very common in real world applications. GAIN, a recently proposed deep generative model for missing data imputation, has been proved to outperform many state-of-the-art methods. But GAIN only uses a reconstruction loss in the generator to minimize the imputation error of the non-missing part, ignoring the potential category information which can reflect the relationship between samples. In this paper, we propose a novel unsupervised missing data imputation method named PC-GAIN, which utilizes potential category information to further enhance the imputation powe…
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 betw…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
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 …
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Microsoft Research（微软研究院）；University of Cambridge（剑桥大学）
Variational Autoencoders (VAEs) have recently been highly successful at imputing and acquiring heterogeneous missing data. However, within this specific application domain, existing VAE methods are restricted by using only one layer of latent variables and strictly Gaussian posterior approximations. To address these limitations, we present HH-VAEM, a Hierarchical VAE model for mixed-type incomplete data that uses Hamiltonian Monte Carlo with automatic hyper-parameter tuning for improved approximate inference. Our experiments show that HH-VAEM outperforms existing baselines in the tasks of miss…
Hong Kong University of Science and Technology（香港科技大学）；Zhejiang University（浙江大学）
The real-time crash likelihood prediction has been an important research topic. Various classifiers, such as support vector machine (SVM) and tree-based boosting algorithms, have been proposed in traffic safety studies. However, few research focuses on the missing data imputation in real-time crash likelihood prediction, although missing values are commonly observed due to breakdown of sensors or external interference. Besides, classifying imbalanced data is also a difficult problem in real-time crash likelihood prediction, since it is hard to distinguish crash-prone cases from non-crash cases…
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality of 400--10,000. Experiments suggest that the algorithm converges to a near optimal solution within 4--6 iterations, at runtimes of less than 30 minutes on a medium-grade desktop computer. The imputation of missing data values is applied to collections of damaged images (suffering from data annihilation rates of up to 70\%) which are reconstructed with a surp…
Missing Data Multiple Imputation for Tabular Q-Learning in Online RL
Department of Statistics, Harvard University, Cambridge, United States（哈佛大学统计学系）；Department of Statistics, Stanford University, Stanford, United States（斯坦福大学统计学系）；Department of Computer Science, Harvard University, Cambridge, United States（哈佛大学计算机科学系）
Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data. Our proposed method directly learns the missing values in a bidirec…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST））；Konkuk University Medical Center（建国大学医学中心）
In many applications requiring multiple inputs to obtain a desired output, if any of the input data is missing, it often introduces large amounts of bias. Although many techniques have been developed for imputing missing data, the image imputation is still difficult due to complicated nature of natural images. To address this problem, here we proposed a novel framework for missing image data imputation, called Collaborative Generative Adversarial Network (CollaGAN). CollaGAN converts an image imputation problem to a multi-domain images-to-image translation task so that a single generator and d…
Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism
School of Computer Science, Guangdong University of Technology（广东技术大学计算机科学学院）；Peng Cheng Laboratory（鹏城实验室）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；College of Science, Shantou University（汕头大学理学院）
Missing data is one of the most common preprocessing problems. In this paper, we experimentally research the use of generative and non-generative models for feature reconstruction. Variational Autoencoder with Arbitrary Conditioning (VAEAC) and Generative Adversarial Imputation Network (GAIN) were researched as representatives of generative models, while the denoising autoencoder (DAE) represented non-generative models. Performance of the models is compared to traditional methods k-nearest neighbors (k-NN) and Multiple Imputation by Chained Equations (MICE). Moreover, we introduce WGAIN as the…
Standard methods for anomaly detection assume that all features are observed at both learning time and prediction time. Such methods cannot process data containing missing values. This paper studies five strategies for handling missing values in test queries: (a) mean imputation, (b) MAP imputation, (c) reduction (reduced-dimension anomaly detectors via feature bagging), (d) marginalization (for density estimators only), and (e) proportional distribution (for tree-based methods only). Our analysis suggests that MAP imputation and proportional distribution should give better results than mean i…
Imputation of missing data is a common application in various classification problems where the feature training matrix has missingness. A widely used solution to this imputation problem is based on the lazy learning technique, $k$-nearest neighbor (kNN) approach. However, most of the previous work on missing data does not take into account the presence of the class label in the classification problem. Also, existing kNN imputation methods use variants of Minkowski distance as a measure of distance, which does not work well with heterogeneous data. In this paper, we propose a novel iterative k…
Gary and Mary West Health Institute（加里与玛丽·韦斯特健康研究所）
Although data may be abundant, complete data is less so, due to missing columns or rows. This missingness undermines the performance of downstream data products that either omit incomplete cases or create derived completed data for subsequent processing. Appropriately managing missing data is required in order to fully exploit and correctly use data. We propose a Multiple Imputation model using Denoising Autoencoders to learn the internal representation of data. Furthermore, we use the novel mechanisms of Metamorphic Truth and Imputation Feedback to maintain statistical integrity of attributes…
How to learn a good predictor on data with missing values? Most efforts focus on first imputing as well as possible and second learning on the completed data to predict the outcome. Yet, this widespread practice has no theoretical grounding. Here we show that for almost all imputation functions, an impute-then-regress procedure with a powerful learner is Bayes optimal. This result holds for all missing-values mechanisms, in contrast with the classic statistical results that require missing-at-random settings to use imputation in probabilistic modeling. Moreover, it implies that perfect conditi…
Functional Magnetic Resonance Imaging (fMRI) is a neuroimaging technique with pivotal importance due to its scientific and clinical applications. As with any widely used imaging modality, there is a need to ensure the quality of the same, with missing values being highly frequent due to the presence of artifacts or sub-optimal imaging resolutions. Our work focus on missing values imputation on multivariate signal data. To do so, a new imputation method is proposed consisting on two major steps: spatial-dependent signal imputation and time-dependent regularization of the imputed signal. A novel…
University of Missouri（密苏里大学）；Meta Platforms, Inc.（元平台公司）；Harvard Medical School（哈佛医学院）；Duke University（杜克大学）
Multiple imputation (MI) is a popular approach for dealing with missing data arising from non-response in sample surveys. Multiple imputation by chained equations (MICE) is one of the most widely used MI algorithms for multivariate data, but it lacks theoretical foundation and is computationally intensive. Recently, missing data imputation methods based on deep learning models have been developed with encouraging results in small studies. However, there has been limited research on evaluating their performance in realistic settings compared to MICE, particularly in big surveys. We conduct exte…
Can humans impute missing data with similar proficiency as machines? This is the question we aim to answer in this paper. We present a novel idea of converting observations with missing data in to a survey questionnaire, which is presented to crowdworkers for completion. We replicate a multiple imputation framework by having multiple unique crowdworkers complete our questionnaire. Experimental results demonstrate that using our method, it is possible to generate valid imputations for qualitative and quantitative missing data, with results comparable to imputations generated by complex statisti…
University of California Los Angeles (UCLA)（加州大学洛杉矶分校）
In many machine learning applications, we are faced with incomplete datasets. In the literature, missing data imputation techniques have been mostly concerned with filling missing values. However, the existence of missing values is synonymous with uncertainties not only over the distribution of missing values but also over target class assignments that require careful consideration. In this paper, we propose a simple and effective method for imputing missing features and estimating the distribution of target assignments given incomplete data. In order to make imputations, we train a simple and…
Missing covariates in regression or classification problems can prohibit the direct use of advanced tools for further analysis. Recent research has realized an increasing trend towards the usage of modern Machine Learning algorithms for imputation. It originates from their capability of showing favourable prediction accuracy in different learning problems. In this work, we analyze through simulation the interaction between imputation accuracy and prediction accuracy in regression learning problems with missing covariates when Machine Learning based methods for both, imputation and prediction a…
Harvard University（哈佛大学）；The University of Tokyo（东京大学）；RIKEN Center for Brain Science（理化学研究所脑科学中心）；Iowa State University（爱荷华州立大学）
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. In addition, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction reveal that…
