In recent times, a considerable number of research studies have been carried out to address the issue of Missing Value Imputation (MVI). MVI aims to provide a primary solution for datasets that have one or more missing attribute values. The advancements in Artificial Intelligence (AI) drive the development of new and improved machine learning (ML) algorithms and methods. The advancements in ML have opened up significant opportunities for effectively imputing these missing values. The main objective of this article is to conduct a comprehensive and rigorous review, as well as analysis, of the state-of-the-art ML applications in MVI methods. This analysis seeks to enhance researchers' understanding of the subject and facilitate the development of robust and impactful interventions in data preprocessing for Data Analytics. The review is performed following the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) technique. More than 100 articles published between 2014 and 2023 are critically reviewed, considering the methods and findings. Furthermore, the latest literature is examined to scrutinize the trends in MVI methods and their evaluation. The accomplishments and limitations of the existing literature are discussed in detail. The survey concludes by identifying the current gaps in research and providing suggestions for future research directions and emerging trends in related fields of interest.
Machine learning (ML) has become a ubiquitous tool across various domains of data mining and big data analysis. The efficacy of ML models depends heavily on high-quality datasets, which are often complicated by the presence of missing values. Consequently, the performance and generalization of ML models are at risk in the face of such datasets. This paper aims to examine the nuanced impact of missing values on ML workflows, including their types, causes, and consequences. Our analysis focuses on the challenges posed by missing values, including biased inferences, reduced predictive power, and increased computational burdens. The paper further explores strategies for handling missing values, including imputation techniques and removal strategies, and investigates how missing values affect model evaluation metrics and introduces complexities in cross-validation and model selection. The study employs case studies and real-world examples to illustrate the practical implications of addressing missing values. Finally, the discussion extends to future research directions, emphasizing the need for handling missing values ethically and transparently. The primary goal of this paper is to provide insights into the pervasive impact of missing values on ML models and guide practitioners toward effective strategies for achieving robust and reliable model outcomes.
Missing values are a common problem that poses significant challenges to data analysis and machine learning. This problem necessitates the development of an effective imputation method to fill in the missing values accurately, thereby enhancing the overall quality and utility of the datasets. Existing imputation methods, however, fall short of explicitly considering the `missingness' information in the data during the embedding initialization stage and modeling the entangled feature and sample correlations during the learning process, thus leading to inferior performance. We propose M$^3$-Impute, which aims to explicitly leverage the missingness information and such correlations with novel masking schemes. M$^3$-Impute first models the data as a bipartite graph and uses a graph neural network to learn node embeddings, where the refined embedding initialization process directly incorporates the missingness information. They are then optimized through M$^3$-Impute's novel feature correlation unit (FRU) and sample correlation unit (SRU) that effectively captures feature and sample correlations for imputation. Experiment results on 25 benchmark datasets under three different missingness settings show the effectiveness of M$^3$-Impute by achieving 20 best and 4 second-best MAE scores on average.
The problem of imputing multivariate time series spans a wide range of fields, from clinical healthcare to multi-sensor systems. Initially, Recurrent Neural Networks (RNNs) were employed for this task; however, their error accumulation issues led to the adoption of Transformers, leveraging attention mechanisms to mitigate these problems. Concurrently, the promising results of diffusion models in capturing original distributions have positioned them at the forefront of current research, often in conjunction with Transformers. In this paper, we propose replacing time-oriented Transformers with State-Space Models (SSM), which are better suited for temporal data modeling. Specifically, we utilize the latest SSM variant, S6, which incorporates attention-like mechanisms. By embedding S6 within Mamba blocks, we develop a model that integrates SSM, Graph Neural Networks, and node-oriented Transformers to achieve enhanced spatiotemporal representations. Implementing these architectural modifications, previously unexplored in this field, we present Time series Imputation with Bi-directional mamba blocks and diffusion models (TIMBA). TIMBA achieves superior performance in almost all benchmark scenarios and performs comparably in others across a diverse range of missing value situations and three real-world datasets. We also evaluate how the performance of our model varies with different amounts of missing values and analyse its performance on downstream tasks. In addition, we provide the original code to replicate the results.
The exoplanet archive is an incredible resource of information on the properties of discovered extrasolar planets, but statistical analysis has been limited by the number of missing values. One of the most informative bulk properties is planet mass, which is particularly challenging to measure with more than 70\% of discovered planets with no measured value. We compare the capabilities of five different machine learning algorithms that can utilize multidimensional incomplete datasets to estimate missing properties for imputing planet mass. The results are compared when using a partial subset of the archive with a complete set of six planet properties, and where all planet discoveries are leveraged in an incomplete set of six and eight planet properties. We find that imputation results improve with more data even when the additional data is incomplete, and allows a mass prediction for any planet regardless of which properties are known. Our favored algorithm is the newly developed $k$NN$\times$KDE, which can return a probability distribution for the imputed properties. The shape of this distribution can indicate the algorithm's level of confidence, and also inform on the underlying demographics of the exoplanet population. We demonstrate how the distributions can be interpreted with a series of examples for planets where the discovery was made with either the transit method, or radial velocity method. Finally, we test the generative capability of the $k$NN$\times$KDE to create a large synthetic population of planets based on the archive, and identify potential categories of planets from groups of properties in the multidimensional space. All codes are Open Source.
Time series analysis is widely used in many fields such as power energy, economics, and transportation, including different tasks such as forecasting, anomaly detection, classification, etc. Missing values are widely observed in these tasks, and often leading to unpredictable negative effects on existing methods, hindering their further application. In response to this situation, existing time series imputation methods mainly focus on restoring sequences based on their data characteristics, while ignoring the performance of the restored sequences in downstream tasks. Considering different requirements of downstream tasks (e.g., forecasting), this paper proposes an efficient downstream task-oriented time series imputation evaluation approach. By combining time series imputation with neural network models used for downstream tasks, the gain of different imputation strategies on downstream tasks is estimated without retraining, and the most favorable imputation value for downstream tasks is given by combining different imputation strategies according to the estimated gain.
Medical time series datasets feature missing values that need data imputation methods, however, conventional machine learning models fall short due to a lack of uncertainty quantification in predictions. Among these models, the CATSI (Context-Aware Time Series Imputation) stands out for its effectiveness by incorporating a context vector into the imputation process, capturing the global dependencies of each patient. In this paper, we propose a Bayesian Context-Aware Time Series Imputation (Bayes-CATSI) framework which leverages uncertainty quantification offered by variational inference. We consider the time series derived from electroencephalography (EEG), electrooculography (EOG), electromyography (EMG), electrocardiology (EKG). Variational Inference assumes the shape of the posterior distribution and through minimization of the Kullback-Leibler(KL) divergence it finds variational densities that are closest to the true posterior distribution. Thus , we integrate the variational Bayesian deep learning layers into the CATSI model. Our results show that Bayes-CATSI not only provides uncertainty quantification but also achieves superior imputation performance compared to the CATSI model. Specifically, an instance of Bayes-CATSI outperforms CATSI by 9.57 %. We provide an open-source code implementation for applying Bayes-CATSI to other medical data imputation problems.
Language typology databases enhance multi-lingual Natural Language Processing (NLP) by improving model adaptability to diverse linguistic structures. The widely-used lang2vec toolkit integrates several such databases, but its coverage remains limited at 28.9\%. Previous work on automatically increasing coverage predicts missing values based on features from other languages or focuses on single features, we propose to use textual data for better-informed feature prediction. To this end, we introduce a multi-lingual Part-of-Speech (POS) tagger, achieving over 70\% accuracy across 1,749 languages, and experiment with external statistical features and a variety of machine learning algorithms. We also introduce a more realistic evaluation setup, focusing on likely to be missing typology features, and show that our approach outperforms previous work in both setups.
Learning performance data describe correct and incorrect answers or problem-solving attempts in adaptive learning, such as in intelligent tutoring systems (ITSs). Learning performance data tend to be highly sparse (80\%\(\sim\)90\% missing observations) in most real-world applications due to adaptive item selection. This data sparsity presents challenges to using learner models to effectively predict future performance explore new hypotheses about learning. This article proposes a systematic framework for augmenting learner data to address data sparsity in learning performance data. First, learning performance is represented as a three-dimensional tensor of learners' questions, answers, and attempts, capturing longitudinal knowledge states during learning. Second, a tensor factorization method is used to impute missing values in sparse tensors of collected learner data, thereby grounding the imputation on knowledge tracing tasks that predict missing performance values based on real observations. Third, a module for generating patterns of learning is used. This study contrasts two forms of generative Artificial Intelligence (AI), including Generative Adversarial Networks (GANs) and Generate Pre-Trained Transformers (GPT) to generate data associated with different clusters of learner data. We tested this approach on an adult literacy dataset from AutoTutor lessons developed for Adult Reading Comprehension (ARC). We found that: (1) tensor factorization improved the performance in tracing and predicting knowledge mastery compared with other knowledge tracing techniques without data augmentation, showing higher relative fidelity for this imputation method, and (2) the GAN-based simulation showed greater overall stability and less statistical bias based on a divergence evaluation with varying simulation sample sizes compared to GPT.
Multivariate time series data suffer from the problem of missing values, which hinders the application of many analytical methods. To achieve the accurate imputation of these missing values, exploiting inter-correlation by employing the relationships between sequences (i.e., a network) is as important as the use of temporal dependency, since a sequence normally correlates with other sequences. Moreover, exploiting an adequate network depending on time is also necessary since the network varies over time. However, in real-world scenarios, we normally know neither the network structure nor when the network changes beforehand. Here, we propose a missing value imputation method for multivariate time series, namely MissNet, that is designed to exploit temporal dependency with a state-space model and inter-correlation by switching sparse networks. The network encodes conditional independence between features, which helps us understand the important relationships for imputation visually. Our algorithm, which scales linearly with reference to the length of the data, alternatively infers networks and fills in missing values using the networks while discovering the switching of the networks. Extensive experiments demonstrate that MissNet outperforms the state-of-the-art algorithms for multivariate time series imputation and provides interpretable results.
In the era of big data, ensuring the quality of datasets has become increasingly crucial across various domains. We propose a comprehensive framework designed to automatically assess and rectify data quality issues in any given dataset, regardless of its specific content, focusing on both textual and numerical data. Our primary objective is to address three fundamental types of defects: absence, redundancy, and incoherence. At the heart of our approach lies a rigorous demand for both explainability and interpretability, ensuring that the rationale behind the identification and correction of data anomalies is transparent and understandable. To achieve this, we adopt a hybrid approach that integrates statistical methods with machine learning algorithms. Indeed, by leveraging statistical techniques alongside machine learning, we strike a balance between accuracy and explainability, enabling users to trust and comprehend the assessment process. Acknowledging the challenges associated with automating the data quality assessment process, particularly in terms of time efficiency and accuracy, we adopt a pragmatic strategy, employing resource-intensive algorithms only when necessary, while favoring simpler, more efficient solutions whenever possible. Through a practical analysis conducted on a publicly provided dataset, we illustrate the challenges that arise when trying to enhance data quality while keeping explainability. We demonstrate the effectiveness of our approach in detecting and rectifying missing values, duplicates and typographical errors as well as the challenges remaining to be addressed to achieve similar accuracy on statistical outliers and logic errors under the constraints set in our work.
Data pre-processing is a significant step in machine learning to improve the performance of the model and decreases the running time. This might include dealing with missing values, outliers detection and removing, data augmentation, dimensionality reduction, data normalization and handling the impact of confounding variables. Although it is found the steps improve the accuracy of the model, but they might hinder the explainability of the model if they are not carefully considered especially in medicine. They might block new findings when missing values and outliers removal are implemented inappropriately. In addition, they might make the model unfair against all the groups in the model when making the decision. Moreover, they turn the features into unitless and clinically meaningless and consequently not explainable. This paper discusses the common steps of the data preprocessing in machine learning and their impacts on the explainability and interpretability of the model. Finally, the paper discusses some possible solutions that improve the performance of the model while not decreasing its explainability.
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific structure tuned to a given algorithm. There is still a gap in our understanding when it comes to arbitrary sampling patterns. Given an arbitrary sampling pattern, we introduce a matrix completion algorithm based on network flows in the bipartite graph induced by the observation pattern. For additive matrices, the particular flow we used is the electrical flow and we establish error upper bounds customized to each entry as a function of the observation set, along with matching minimax lower bounds. Our results show that the minimax squared error for recovery of a particular entry in the matrix is proportional to the effective resistance of the corresponding edge in the graph. Furthermore, we show that our estimator is equivalent to the least squares estimator. We apply our estimator to the two-way fixed effects model and show that it enables us to accurately infer individual causal effects and the unit-specific and time-specific confounders. For rank-$1$ matrices, we use edge-disjoint paths to form an estimator that achieves minimax optimal estimation when the sampling is sufficiently dense. Our discovery introduces a new family of estimators parametrized by network flows, which provide a fine-grained and intuitive understanding of the impact of the given sampling pattern on the relative difficulty of estimation at an entry-specific level. This graph-based approach allows us to quantify the inherent complexity of matrix completion for individual entries, rather than relying solely on global measures of performance.
Motion prediction plays an essential role in autonomous driving systems, enabling autonomous vehicles to achieve more accurate local-path planning and driving decisions based on predictions of the surrounding vehicles. However, existing methods neglect the potential missing values caused by object occlusion, perception failures, etc., which inevitably degrades the trajectory prediction performance in real traffic scenarios. To address this limitation, we propose a novel end-to-end framework for incomplete vehicle trajectory prediction, named Multi-scale Temporal Fusion Transformer (MTFT), which consists of the Multi-scale Attention Head (MAH) and the Continuity Representation-guided Multi-scale Fusion (CRMF) module. Specifically, the MAH leverages the multi-head attention mechanism to parallelly capture multi-scale motion representation of trajectory from different temporal granularities, thus mitigating the adverse effect of missing values on prediction. Furthermore, the multi-scale motion representation is input into the CRMF module for multi-scale fusion to obtain the robust temporal feature of the vehicle. During the fusion process, the continuity representation of vehicle motion is first extracted across time steps to guide the fusion, ensuring that the resulting temporal feature incorporates both detailed information and the overall trend of vehicle motion, which facilitates the accurate decoding of future trajectory that is consistent with the vehicle's motion trend. We evaluate the proposed model on four datasets derived from highway and urban traffic scenarios. The experimental results demonstrate its superior performance in the incomplete vehicle trajectory prediction task compared with state-of-the-art models, e.g., a comprehensive performance improvement of more than 39% on the HighD dataset.
With recent advances in building foundation models for texts and video data, there is a surge of interest in foundation models for time series. A family of models have been developed, utilizing a temporal auto-regressive generative Transformer architecture, whose effectiveness has been proven in Large Language Models. While the empirical results are promising, almost all existing time series foundation models have only been tested on well-curated ``benchmark'' datasets very similar to texts. However, real-world time series exhibit unique challenges, such as variable channel sizes across domains, missing values, and varying signal sampling intervals due to the multi-resolution nature of real-world data. Additionally, the uni-directional nature of temporally auto-regressive decoding limits the incorporation of domain knowledge, such as physical laws expressed as partial differential equations (PDEs). To address these challenges, we introduce the Time Diffusion Transformer (TimeDiT), a general foundation model for time series that employs a denoising diffusion paradigm instead of temporal auto-regressive generation. TimeDiT leverages the Transformer architecture to capture temporal dependencies and employs diffusion processes to generate high-quality candidate samples without imposing stringent assumptions on the target distribution via novel masking schemes and a channel alignment strategy. Furthermore, we propose a finetuning-free model editing strategy that allows the seamless integration of external knowledge during the sampling process without updating any model parameters. Extensive experiments conducted on a varity of tasks such as forecasting, imputation, and anomaly detection, demonstrate the effectiveness of TimeDiT.
Multi-agent trajectory data collected from domains such as team sports often suffer from missing values due to various factors. While many imputation methods have been proposed for spatiotemporal data, they are not well-suited for multi-agent sports scenarios where player movements are highly dynamic and inter-agent interactions continuously evolve. To address these challenges, we propose MIDAS (Multi-agent Imputer with Derivative-Accumulating Self-ensemble), a framework that imputes multi-agent trajectories with high accuracy and physical plausibility. It jointly predicts positions, velocities, and accelerations through a Set Transformer-based neural network and generates alternative estimates by recursively accumulating predicted velocity and acceleration values. These predictions are then combined using a learnable weighted ensemble to produce final imputed trajectories. Experiments on three sports datasets demonstrate that MIDAS significantly outperforms existing baselines in both positional accuracy and physical plausibility. Lastly, we showcase use cases of MIDAS, such as approximating total distance and pass success probability, to highlight its applicability to practical downstream tasks that require complete tracking data.
Emerging evidence indicates that human cancers are intricately linked to human microbiomes, forming an inseparable connection. However, due to limited sample sizes and significant data loss during collection for various reasons, some machine learning methods have been proposed to address the issue of missing data. These methods have not fully utilized the known clinical information of patients to enhance the accuracy of data imputation. Therefore, we introduce mbVDiT, a novel pre-trained conditional diffusion model for microbiome data imputation and denoising, which uses the unmasked data and patient metadata as conditional guidance for imputating missing values. It is also uses VAE to integrate the the other public microbiome datasets to enhance model performance. The results on the microbiome datasets from three different cancer types demonstrate the performance of our methods in comparison with existing methods.
Time series classification with missing data is a prevalent issue in time series analysis, as temporal data often contain missing values in practical applications. The traditional two-stage approach, which handles imputation and classification separately, can result in sub-optimal performance as label information is not utilized in the imputation process. On the other hand, a one-stage approach can learn features under missing information, but feature representation is limited as imputed errors are propagated in the classification process. To overcome these challenges, this study proposes an end-to-end neural network that unifies data imputation and representation learning within a single framework, allowing the imputation process to take advantage of label information. Differing from previous methods, our approach places less emphasis on the accuracy of imputation data and instead prioritizes classification performance. A specifically designed multi-scale feature learning module is implemented to extract useful information from the noise-imputation data. The proposed model is evaluated on 68 univariate time series datasets from the UCR archive, as well as a multivariate time series dataset with various missing data ratios and 4 real-world datasets with missing information. The results indicate that the proposed model outperforms state-of-the-art approaches for incomplete time series classification, particularly in scenarios with high levels of missing data.
Missing values are prevalent in multivariate time series, compromising the integrity of analyses and degrading the performance of downstream tasks. Consequently, research has focused on multivariate time series imputation, aiming to accurately impute the missing values based on available observations. A key research question is how to ensure imputation consistency, i.e., intra-consistency between observed and imputed values, and inter-consistency between adjacent windows after imputation. However, previous methods rely solely on the inductive bias of the imputation targets to guide the learning process, ignoring imputation consistency and ultimately resulting in poor performance. Diffusion models, known for their powerful generative abilities, prefer to generate consistent results based on available observations. Therefore, we propose a conditional diffusion model for Multivariate Time Series Consistent Imputation (MTSCI). Specifically, MTSCI employs a contrastive complementary mask to generate dual views during the forward noising process. Then, the intra contrastive loss is calculated to ensure intra-consistency between the imputed and observed values. Meanwhile, MTSCI utilizes a mixup mechanism to incorporate conditional information from adjacent windows during the denoising process, facilitating the inter-consistency between imputed samples. Extensive experiments on multiple real-world datasets demonstrate that our method achieves the state-of-the-art performance on multivariate time series imputation task under different missing scenarios. Code is available at https://github.com/JeremyChou28/MTSCI.
Missing values are prevalent across various fields, posing challenges for training and deploying predictive models. In this context, imputation is a common practice, driven by the hope that accurate imputations will enhance predictions. However, recent theoretical and empirical studies indicate that simple constant imputation can be consistent and competitive. This empirical study aims at clarifying if and when investing in advanced imputation methods yields significantly better predictions. Relating imputation and predictive accuracies across combinations of imputation and predictive models on 20 datasets, we show that imputation accuracy matters less i) when using expressive models, ii) when incorporating missingness indicators as complementary inputs, iii) matters much more for generated linear outcomes than for real-data outcomes. Interestingly, we also show that the use of the missingness indicator is beneficial to the prediction performance, even in MCAR scenarios. Overall, on real-data with powerful models, improving imputation only has a minor effect on prediction performance. Thus, investing in better imputations for improved predictions often offers limited benefits.