Xputer: bridging data gaps with NMF, XGBoost, and a streamlined GUI experience

The rapid proliferation of data across diverse fields has accentuated the importance of accurate imputation for missing values. This task is crucial for ensuring data integrity and deriving meaningful insights. In response to this challenge, we present Xputer, a novel imputation tool that adeptly integrates Non-negative Matrix Factorization (NMF) with the predictive strengths of XGBoost. One of Xputer's standout features is its versatility: it supports zero imputation, enables hyperparameter optimization through Optuna, and allows users to define the number of iterations. For enhanced user experience and accessibility, we have equipped Xputer with an intuitive Graphical User Interface (GUI) ensuring ease of handling, even for those less familiar with computational tools. In performance benchmarks, Xputer often outperforms IterativeImputer in terms of imputation accuracy. Furthermore, Xputer autonomously handles a diverse spectrum of data types, including categorical, continuous, and Boolean, eliminating the need for prior preprocessing. Given its blend of performance, flexibility, and user-friendly design, Xputer emerges as a state-of-the-art solution in the realm of data imputation.

Introduction

The task of managing missing data points is an essential component of the preliminary data preparation phase, particularly in the context of data science applications such as machine learning models. A comprehensive dataset with no missing values is a prerequisite for a multitude of algorithms, emphasizing the necessity to address and rectify the absence of certain values. A rudimentary approach to resolve this issue might involve substituting these gaps with zeros or the mean of the column values. However, such methods could be an oversimplification, failing to take into account the inherent structural relationships within the data (Hastie et al., 2016). An advanced and well-accepted technique for managing missing data is the multiple imputation method, which was first proposed by Rubin (1987). This approach recognizes the uncertainty that comes with the imputation of missing values by generating multiple complete datasets. Each of these datasets offers a distinct but statistically plausible replacement for the missing data. The individual analysis results derived from these multiple datasets are then amalgamated to yield a single, more robust result. This process not only provides a method for filling in the missing data but also for estimating the statistical properties for subsequent analysis (Little and Rubin, 2019).

The Multivariate Imputation by Chained Equations (MICE) protocol, also referred to as Fully Conditional Specification (FCS) or Sequential Regression Multiple Imputation (SRMI), is a widely recognized imputation methodology with a process that shares similarities to multiple imputation. This technique is built on the premise of a round-robin approach, whereby every feature in the dataset that contains missing data is modeled as a function of the remaining features, and this process is performed iteratively (Azur et al., 2011; van Buuren and Groothuis-Oudshoorn, 2011). MICE is a flexible method that can handle various types of variables, making it a popular choice for dealing with missing data. Nevertheless, while MICE is a robust and versatile method, it is important to be cognizant of its potential limitations. Specifically, if MICE is implemented using its default settings, it may not fully capture non-linear relationships within the data during the imputation process. The default MICE process employs linear regression models for imputing missing values in continuous variables and logistic regression for binary and ordinal variables, both of which inherently assume a linear relationship between the predictors and the target variable (Raghunathan et al., 2001; Su et al., 2011). Consequently, these models may not be well-suited to data that exhibit non-linear relationships. There are ways to overcome this limitation. For instance, by integrating machine learning algorithms such as decision trees or random forests in the MICE process, non-linear relationships can be taken into account during imputation (Shah et al., 2014). It is, therefore, crucial to understand the characteristics of the dataset at hand and to adjust the imputation strategy accordingly to ensure accurate results.

The application of tree-based models, such as those employing Random Forests or Classification and Regression Trees (CART), for data imputation presents a potentially powerful methodology (Breiman, 2001; Trendowicz and Jeffery, 2013). This is particularly relevant when data exhibit complex non-linear associations that could be otherwise challenging to handle with traditional linear methods. Tree-based models implement a hierarchical decision structure, which allows them to adeptly manage and exploit non-linear relationships embedded within the data. They thus offer an advanced tool for predicting missing data values under complex interaction scenarios. However, the adoption of such methodologies is not without its own set of challenges. Tree-based models, particularly those of a high complexity, can demand substantial computational resources, posing a hindrance for large-scale datasets (Hastie et al., 2016). Additionally, their performance can suffer in situations where a significant proportion of the data is missing. The difficulty of accurately predicting missing values increases as the amount of missing data rises, which may result in less reliable imputations. Furthermore, while tree-based models provide a robust method for capturing complex structures within data, the predictions they provide can be unstable due to their sensitivity to small changes in the training data, which can lead to substantial changes in the tree structure and subsequently in the imputed values. Thus, while tree-based models constitute a versatile tool for imputing missing data in complex scenarios, these limitations need to be carefully considered in the context of the specific dataset and research question at hand.

The process of imputing missing data should not be perceived as a rudimentary or minor phase in data preprocessing. Instead, it should be considered a critical procedure that can profoundly affect downstream analyses and the consequent outcomes. The decision regarding the choice of imputation technique should not be arbitrary or casual; instead, it should be guided by a careful assessment of the unique characteristics of the dataset and the specific requirements of the subsequent analysis (Donders et al., 2006). The impacts that various imputation methods can have on the final results of the data analysis are not trivial and can be substantial. Thus, it is essential to assess the inherent assumptions accompanying each imputation method and to understand how they might influence the findings of the analysis. Notably, an inappropriate choice of an imputation method might introduce bias, distort relationships, or mask patterns in the data, leading to misleading or incorrect conclusions (Sterne et al., 2009). Therefore, understanding the properties and limitations of various imputation methods and their suitability to the specific data context is paramount for a robust and reliable data analysis (van Buuren, 2018).

In this article, we present a unique approach to missing value imputation that leverages the strengths of matrix factorization and the XGBoost algorithm. Our innovative method begins with an initial phase of imputation utilizing matrix factorization, which is a technique primarily aimed at reducing bias associated with the onset of imputation. Matrix factorization techniques help uncover the latent features underlying the interactions of the input data, thus providing a more robust and informed basis for initiating the imputation process. This step effectively minimizes the introduction of potential errors or biases at the very outset, thereby contributing to the overall accuracy and reliability of the imputation process. Following this, our approach utilizes XGBoost, a powerful gradient boosting framework, to predict missing values iteratively. In this phase, overfitting and underfitting—two common challenges in machine learning—are mitigated through automated hyperparameter optimization. The XGBoost model's hyperparameters are fine-tuned in a manner that balances bias and variance, thus preventing the model from becoming too complex (overfitting) or too simple (underfitting). To further enhance the precision of our imputation, we employ a process of iterative refinement of the missing value prediction. In essence, the imputation process is performed iteratively, with each iteration serving to improve the accuracy of the estimated missing values based on the results of the preceding iteration. Finally, in order to promote accessibility and ease of use, we have encapsulated this innovative imputation methodology within a user-friendly graphical user interface (GUI). This allows users, even those with limited programming or technical experience, to conveniently apply our imputation method to their own data. Thus, this powerful imputation tool can be broadly utilized across a range of disciplines and applications where missing data is a challenge.

The architecture of Xputer

To construct the foundation of Xputer, we combined NMF with a supervised learning model. While there is a plethora of supervised learning algorithms suitable for imputation, especially when considering prediction performance and computational efficiency, our choice to pair NMF with XGBoost was informed by a specific aim: addressing potential non-linear relationships in the unseen data. XGBoost is a powerful gradient boosting algorithm that can effectively handle both categorical and continuous data. It stands out for its speed when predicting large datasets and offers a high degree of flexibility in model tuning, which makes it an optimal choice for this integration (Chen and Guestrin, 2016). However, it is worth noting that other gradient boosting frameworks, such as LightGBM, could serve as viable alternatives (Ke et al., 2017). LightGBM also boasts efficient computational and memory usage, and it has shown itself to be an effective tool in predictive modeling scenarios. Thus, our strategy is designed to enhance imputation accuracy by leveraging the strengths of both NMF and XGBoost, thereby accommodating the diverse nature and complexity of data we might encounter.

The structural design of the Xputer is succinctly illustrated in Figure 1. This framework incorporates an array of interconnected modules, each serving a distinct functionality. Beginning with the preprocessing module (Figure 1A), this component undertakes the initial responsibility of data preparation. It executes tasks such as eliminating or correcting missing or erroneous data, standardizing numerical values, and transforming categorical variables into a format suitable for subsequent analyses. The subsequent step in the Xputer framework is the matrix factorization module (Figure 1B). This module leverages linear algebraic techniques to decompose a complex matrix into simpler, interpretable matrix constituents. This operation is pivotal to the simplification of high-dimensional data and the identification of inherent structure and relationships within the data. Next, the architecture encompasses the XGBoost imputation module (Figure 1C), a sophisticated component applying a gradient-boosting framework. This module plays an instrumental role in handling missing data, and extrapolating probable values based on the observed patterns in the existing data. It deploys a set of machine learning models, namely decision trees, which sequentially correct residuals of the preceding model, thereby enhancing the prediction accuracy. Finally, the iterative imputation module (Figure 1D) is incorporated into the Xputer design. This module cyclically estimates missing values, refining its predictions in each iteration. This methodical process ensures that the imputation of missing data is not merely an isolated guess but a robust, data-informed estimation (Dong and Peng, 2013). Together, these modules integrate to form the comprehensive architecture of Xputer, as visually encapsulated in Figure 1. Each module's role and interaction contribute to the efficacy and precision of the overall data analysis and prediction system.

Figure 1

Figure 1. The structure of Xputer. The core structure of Xputer includes (A) data preprocessing unit, (B) adaptive matrix factorization unit, (C) XGBoost hyperparameter search and model implementation unit, and (D) iterative imputation unit.

The preprocessing module

Within this process, Xputer utilizes a Pandas Data Frame where sample identifiers are categorized in the index and feature designators are in the header. It commences by performing a scrutiny for absent or inoperative values, denoted by indicators such as “NaN”, “NAN”, “Nan”, “nan”, “NA”, “#NA”, “N/A”, “NA#”, “#VALUE!”, “#DIV/0!”, etc., and proceeds to substitute any instances of these with the canonical 'np.nan'. In addition, it affords the user the option to convert zeros into 'np.nan' for later imputation. Subsequently, Xputer conducts an individual analysis for each column, distinguishing between continuous and categorical data points. If a specific type of data, say categorical, represents more than 60% of the column's contents, Xputer categorizes the entire column as such and replaces any numerical data with 'np.nan'. This protocol applies reciprocally to columns with over 60% numerical data, which are then considered as columns of continuous values and any non-numerical entries are replaced with 'np.nan'. Categorical data points are subsequently subject to encoding via a label encoder. In case a column fails to meet those criteria, leaves out of imputation. Post-processing, Xputer yields three separate Pandas DataFrames: a cleaned dataset, an encoded dataset, and a pre-imputed encoded dataset. The preprocessing module can function autonomously and be invoked through the “from xputer.utils import preprocessing_df” command.

Adaptive matrix factorization

Our adaptive matrix factorization strategy represents an advanced methodology designed to enhance the quality of pre-imputed data through the deployment of matrix factorization techniques. This process is characterized by its inherent adaptability, altering its computational approach based on the specific characteristics of the data at hand. In circumstances where the data set is devoid of negative values, the strategy deploys iterative sub-grouped non-negative matrix factorization (NMF). NMF is a technique that decomposes the original data into two non-negative matrix factors, providing an efficient and effective tool for representing the data and capturing the underlying structure (Lee and Seung, 1999). As a consequence of NMF's non-negativity constraints, the resulting components are more interpretable and can offer a robust reconstruction of the original data. Conversely, in the presence of negative values within the dataset, the strategy resorts to Singular Value Decomposition (SVD). This method is a general matrix factorization technique that decomposes the data into three distinct matrices (DeSa and Matheson, 2004). SVD is versatile and applicable to any real-valued matrix, providing an elegant solution when the non-negativity condition of NMF is not met. The adaptive matrix factorization strategy operates on both the encoded dataset and the pre-imputed encoded dataset, aiming to produce either a selectively transformed dataset—where only NaN values are replaced—or a fully reconstructed dataset depending on the specific requirements of the analysis. This dynamic approach ensures that the most suitable factorization method is applied, accounting for the unique attributes of the data and optimizing the precision of the imputation process.

XGBoost imputation

Xputer commences the imputation process by processing each column independently. It initiates this operation by selecting a column from the cleansed data, wherein categorical variables have not been encoded, and subsequently identifies the data type. Upon the determination of whether imputation is necessary for the specific column, the column in question is expunged from the pre-imputed or NMF/SVD-transformed data, thereby serving as a training or prediction set. Subsequent to the discernment of the data type, Xputer undertakes the decision as to whether a classifier or regressor is apt for the imputation task. For the optimization of the XGBoost hyperparameters, we have incorporated Optuna, a robust hyperparameter optimization framework (Akiba et al., 2019). However, prior to commencing the hyperparameter search, Xputer evaluates the number of samples, necessitating more than 50, and validates the sample-to-feature ratio, mandating a minimum ratio of 4. Furthermore, it reviews the number of features, with a maximum allowance of 100 columns with missing values. Given these conditions, Xputer determines if the hyperparameter search needs to be executed, or if the deployment of predefined parameters is more pertinent. Regardless of the path chosen, Xputer employs a 70% subsampling strategy. In the event a hyperparameter search is performed, the system is meticulously designed to evade both overfitting and underfitting of the model. Once the hyperparameters are solidified, Xputer executes a minimum of three predictions (with an option to select up to nine) and employs an average value for the imputation. Both the cleansed data and encoded data are consequently updated with the predicted values. Additionally, Xputer accumulates the XGBoost parameters for each column from this phase for potential utilization in iterative imputation procedures in the future.

Iterative imputation

Xputer has been architecturally devised to execute an iterative process of imputation. In this scheme, values that have been previously estimated and subsequently imputed are employed for subsequent predictions, effectively utilizing iterative refinement for the missing data estimation. This mechanism proves particularly efficacious when dealing with datasets afflicted by a substantial proportion of missing values. In such scenarios, every column is sequentially updated with novel predictions, each one informed by the newly imputed values from the previous round. This creates a feedback loop where each iteration enhances the accuracy of imputations in the next, thus leveraging the potential for continuous improvement in the estimation of missing data. As of now, Xputer accommodates a range of iterations from a minimum of one to a maximum of nine, offering flexibility in choosing the depth of refinement according to the specifics of the dataset and the imputation requirements. This iterative imputation process propagates information from observed to unobserved values, making it a powerful method to reconstruct missing data in large datasets.

Results

Supervised learning algorithms hold the superior predictive capacity for missing value imputation

In the initial phase of our study, a comparative analysis was conducted among several supervised and unsupervised machine learning algorithms to evaluate their efficacy in the imputation of missing values. The chosen dataset for this investigation comprised of a heterogeneous collection of gene expression data (Bottomly et al., 2022; Chen et al., 2022), including both microarray and RNAseq data, covering 400 genes (features). To facilitate this comparison, we artificially introduced missing values into the dataset by removing data ranging from 1% up to 25%, thereby generating 25 unique datasets. An initial imputation was then carried out using column mean values, which served as a foundation for the subsequent application of 27 distinct regressors, each tasked with predicting the missing values in every column (Figure 2A). The array of machine learning algorithms under examination comprised unsupervised methods such as autoencoders, non-negative matrix factorization (NMF), and principal component analysis (PCA), which were juxtaposed against their supervised counterparts. The performance of these algorithms was compared based on the log2-transformed mean squared error (MSE) and the log2-transformed computational time in seconds. The majority of supervised algorithms exhibited comparable performances, with the exceptions of RANSAC and the Gaussian process which differed (Figure 2B). In terms of time efficiency, PCA emerged as the most proficient (Figure 2C); however, its performance lagged when evaluated based on the NegLog2RMSL (Nasimian et al., 2024) (Figures 2D, E). The comparative results suggested that supervised algorithms are relatively more efficient in the imputation process than most unsupervised algorithms, with NMF being the exception. However, it should be emphasized that none of the algorithms were optimized for this specific task. Therefore, it is possible that the performance of some algorithms could improve if optimization were to be implemented.

Figure 2

Figure 2. Comparative evaluation of various algorithms' functionality. (A) A composite dataset consisting of RNAseq and microarray data, dimensioned at 1770 X 400, underwent random masking to instigate missing values, ranging from 1% to 25%, thus creating 25 distinct data matrices. In the case of unsupervised learning algorithms, namely autoencoder, NMF, and PCA, the imputation of the entire dataset was accomplished via the column mean through SimpleImputer prior to the execution of the algorithm. For supervised algorithms, an initial identification of columns with NaNs was carried out. An individual column containing NaN was isolated and designated as the label, while the remainder of the data underwent imputation via the column mean with the aid of SimpleImputer. Following the preliminary imputation, the data was segregated into training and predictive datasets corresponding to non-NaN and NaN rows in the label column. (B) Subsequent to imputation with a specific algorithm, imputed values underwent a comparative analysis with their original counterparts, facilitating the determination of the mean squared error. Each box demonstrates 25 measurements employing missing values varying from 1%-25% (in increments of 1%), while the bar represents the minimum to maximum values range. (C) The duration necessitated to carry out imputation utilizing a specific algorithm. (D–E) Six imputed datasets were employed to ascertain the prediction performance of the Trametinib response via the XGBoost algorithm. ^**p < 0.01 and ^***p < 0.001.

Xputer hyperparameters testing

In assessing the performance of Xputer, hyperparameter optimization, though optional, can potentially enhance its efficacy. Six diverse datasets facilitated an exploration of Xputer hyperparameters' impact on imputation. We artificially introduced missing values at varying percentages (10% to 40%) across both categorical and continuous data types within each dataset. Our initial inquiry centered on the influence of pre-imputation on the ultimate imputation outcomes. We employed three distinct strategies: ColumnMean: missing continuous values were substituted with the respective column mean, whereas missing categorical or Boolean entries were replaced by the most frequently occurring value, KNNImputer: utilized the sklearn's KNNImputer to address NaNs across all columns, and MixType: continuous NaNs were supplanted by the column mean, while the remaining were managed using KNNImputer. For the majority of columns across the datasets, there was no discernible preference for any particular strategy. However, certain scenarios evidenced a tilt toward ColumnMean, KNNImputer, or MixType (Figure 3A). By default, Xputer constructs three XGBoost models for imputation, which can be expanded up to nine, leveraging the mean value for imputation. We juxtaposed the efficacy of utilizing 3, 6, or 9 models, maintaining other default parameters. Some attributes benefited from a larger model pool, yet the overall enhancement remained marginal (Figure 3B), implying that three models might suffice for robust imputation. The application of either NMF NaN-transformed or fully transformed data could potentially ameliorate imputation, especially in the presence of outliers (Figure 3C). Though our datasets did not manifest tangible gains from Optuna-driven hyperparameter tuning compared to predefined parameters (Figure 3D), we cannot preclude its potential benefits in other datasets. Notably, a reduced iteration count in Optuna consistently underperformed compared to default parameters. Thus, it's advised to either adhere to default settings or, if using Optuna, opt for a greater number of iterations. Finally, while augmenting the iteration count can confer minor enhancements, the default setting generally sufficed (Figure 3E).

Figure 3

Figure 3. Xputer hyperparameter evaluation. For a comprehensive assessment of Xputer's individual hyperparameters, six distinct datasets were employed, each infused with a diverse spectrum of artificially introduced missing values. These modified datasets were subsequently juxtaposed against their original values. The hyperparameters under examination encompassed (A) pre-imputation strategies, (B) the count of XGBoost models for ensembling, (C) matrix factorization techniques, (D) XGBoost hyperparameter optimization using Optuna, and (E) the total iteration count. The “Bank marketing” data was from archive.ics.uci.edu/dataset/222/bank+marketing, the “Breast cancer” data was collected from archive.ics.uci.edu/dataset/17/breast+cancer+wisconsin+diagnostic, the “NATICUSdroid” data was from archive.ics.uci.edu/dataset/722/naticusdroid+android+permissions+dataset, the “PIMA Indian” data was downloaded from www.kaggle.com/datasets/uciml/pima-indians-diabetes-database, and the “Student's dropout” data was collected from archive.ics.uci.edu/dataset/697/predict+students+dropout+and+academic+success.

Dependency of Xputer's imputation time on feature quantity

The imputation latency experienced with the Xputer system is intricately linked to the quantum of features necessitating imputation. Mechanistically, Xputer operates by scanning for null values within each column, subsequently embarking on a column-wise imputation procedure leveraging the XGBoost algorithm. Specifically, when a column is targeted for imputation, extant values therein are harnessed to construct the XGBoost predictive model, which then projects or fills the absent values. This modus operandi elucidates why columns teeming with null values considerably amplify the temporal demands of the imputation process (Figure 4A). Further analyses revealed a negative logarithmic relationship between the magnitude of missing values and the time commitment per unit of such values (Figure 4B). Intriguingly, while the aggregate sample volume appeared to exert negligible impact on imputation duration (Figure 4C), there was a robust correlation between an escalating feature count and the time invested per feature during imputation (Figure 4D). We conducted a comparative analysis between Xputer and sci-kit learn's IterativeImputer, a multivariate imputation tool that predicts each feature using all other features (Pedregosa et al., 2011). Comparative assessments with the IterativeImputer showed that, under default configurations, IterativeImputer demonstrated superior speed but, when configured with a Random Forest estimator, the IterativeImputer consistently underperformed relative to Xputer, irrespective of the feature quantity (Figure 4E). In aggregate, the empirical evidence posits that Xputer's performance might decelerate as the feature count swells.

Figure 4

Figure 4. Assessment of imputation duration. In this analysis, we utilized data encompassing 7 to 97 features and sample sizes varying from 569 to 29,332. This evaluation covered various metrics: (A) time taken for imputation relative to the number of features, (B) time per unit of missing value, (C) time per individual value, and (D) imputation time for each feature in relation to the total number of features. Additionally, (E) we compared our results with the IterativeImputer's performance. Number of features: Bank Marketing−7, PIMA Indian – 8, Breast Cancer – 30, Students dropout−36, NATICUSdroid−86, Mixed Cancer−97; number of samples: Bank Marketing−4521, PIMA Indian−768, Breast Cancer−569, Students dropou−3630, NATICUSdroid−29332, Mixed Cancer−1770.

Comparing Xputer with IterativeImputer

In this analysis, we juxtaposed the imputation efficacy of Xputer against that of IterativeImputer. Notably, Xputer is intrinsically engineered to seamlessly manage a diverse range of data types, including categorical, bimodal, and continuous datasets. However, to ensure an equitable benchmark, particularly mirroring the primary function of IterativeImputer, our evaluation was confined to continuous data. The rigorousness of our evaluation was upheld through the employment of the Root Mean Square Error (RMSE) metric coupled with detailed density plots. This assessment spanned across scenarios with 10% to 40% missing data values in contrast to the original dataset. Our empirical findings revealed that Xputer demonstrated consistent and robust performance (Figure 5A). Conversely, the IterativeImputer, under its default configuration, occasionally faltered. The augmentation of the IterativeImputer with a Random Forest Regressor enhanced imputation performance in certain instances. This enhancement is substantiated by the density plots, which demonstrate a notable convergence in the distribution between the original dataset, the data imputed by Xputer, and the data imputed through the combined application of the Random Forest Regressor and IterativeImputer (Figure 5B). Our comparative study emphasizes the inherent strengths of Xputer in data imputation.

Figure 5

Figure 5. Comparative analysis of Xputer and Iterativeimputer. Using six continuous-data datasets, we assessed the performance of Xputer against IterativeImputer. Performance comparisons were conducted employing both the RMSE metric (A) and density plots (B) across varying percentages of missing values.

Discussion

Addressing the challenge of missing value imputation is paramount across a range of disciplines (Choi et al., 2023; Mukherjee et al., 2023; Vanderaa and Gatto, 2023). In bioinformatics, dealing with the multifaceted and distinct characteristics of various data types including RNAseq, proteomic and metabolomic data poses unique challenges for missing value imputations (Vanderaa and Gatto, 2023). In the world of marketing, complete datasets are essential to derive accurate consumer insights, optimize advertising strategies, and predict market trends (Anand and Mamidi, 2020). Missing values can lead to misleading segmentation or incomplete customer profiles, which can adversely impact campaign efficacy and return of investment (ROI). Similarly, in the banking and financial sectors, accurate data is the backbone of risk assessments, credit scoring, and investment decisions. Missing or incorrect data can lead to misguided financial strategies, erroneous lending decisions, or misestimation of market risks (Fujimoto et al., 2022). Household surveys, often used for demographic research or to assess consumer behavior, are another domain where imputation plays a pivotal role. Such datasets often contain gaps due to non-responses or incomplete survey returns, and imputation is vital to provide a comprehensive view of the population being studied (Mirzaei et al., 2022). Given the increasing reliance on data across industries, the need for sophisticated and accurate imputation methods becomes ever more crucial. The heterogeneous nature of datasets across sectors underscores the need for robust and tailored imputation methods to ensure data integrity, accurate predictions, and informed decision-making.

Given the complexities highlighted above, we have developed Xputer that combines flexibility, speed, and diversity. However, Xputer may not be suitable for scenarios in which the number of features exceeds the number of samples. In our comprehensive analysis, the role of supervised learning algorithms in enhancing the precision of imputation became distinctly evident (Getz et al., 2023). Through rigorous evaluation using datasets artificially populated with missing values, our findings affirmed the superior predictive capacity of supervised algorithms over their unsupervised counterparts for the imputation of missing values. This advantage held true despite the fact that none of the evaluated algorithms was specifically optimized for the imputation task, suggesting innate strengths within supervised learning paradigms. The only unsupervised exception, NMF, hints at potential niches wherein unsupervised learning could have competitive or even advantageous roles. Furthermore, the detailed hyperparameter testing of Xputer showcased its potential versatility. While it was evident that hyperparameter tuning can yield marginal improvements, for many datasets, the default configurations of Xputer often delivered satisfactory imputation outcomes. Notably, the nature of missing data, whether categorical or continuous, and its percentage appeared to influence the preferred imputation strategy. The relationship between Xputer's imputation time and the volume of features underscores a salient operational aspect of the software. Xputer's meticulous column-wise approach, relying on XGBoost, illuminates the escalating temporal requirements with an increasing proportion of missing values. The observed logarithmic relationship between time and magnitude of missing values points to diminishing returns in efficiency as missing data accrue. Interestingly, this observation is juxtaposed with the rather consistent temporal demands across varying sample sizes, revealing feature count as the more prominent determinant of imputation latency.

The comparative evaluation with IterativeImputer, a similar version of MICE (van Buuren and Groothuis-Oudshoorn, 2011) offered insights into the nuances of these two methodologies. While Xputer's intrinsic design accommodates a diverse gamut of data types, IterativeImputer requires specific configurations, like the inclusion of the Random Forest Regressor, enhanced performance in certain instances. While supervised algorithms, embodied by Xputer, typically excel in these endeavors, the context-specific merits of unsupervised algorithms, or hybrid solutions like IterativeImputer combined with Random Forest, cannot be overlooked. The findings also emphasize the necessity to understand the operational nuances of each tool, ensuring that researchers can harness them effectively, optimizing both imputation accuracy and computational efficiency.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

SY: Formal analysis, Writing – original draft, Writing – review & editing. LR: Funding acquisition, Project administration, Resources, Writing – original draft, Writing – review & editing. JK: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Visualization, Writing – original draft, Writing – review & editing.

Funding

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This research was supported by the Crafoord Foundation (JK # 20230775), the Swedish Cancer Society (JK #19 0004 FE and LR #21 1444 Pj), the Swedish Research Council (LR #2021-03055), the Swedish Childhood Cancer Foundation (JK # PR2022-0106), and SUS Stiftelser och Donationer (LR #95512), and Governmental Funding of Clinical Research within the National Health Service (ALF) (LR # 40609).

Acknowledgments

We thank the Swedish research funding agencies Forte, Formas, Vinnova, and the Swedish Research Council for their generous assistance in covering the costs associated with open access publication.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frai.2024.1345179/full#supplementary-material

References

Akiba, T., Sano, S., Yanase, T., Ohta, T., and Kovama, M. (2019). “Optuna: a next-generation hyperparameter optimization framework,” in Proceedings of the 25th {ACM} {SIGKDD} International Conference on Knowledge Discovery and Data Mining KDD 19, 2623–2631. doi: 10.1145/3292500.3330701

Crossref Full Text | Google Scholar

Anand, V., and Mamidi, V. (2020). “Multiple imputation of missing data in marketing,” in 2020 International Conference on Data Analytics for Business and Industry: Way Towards a Sustainable Economy (ICDABI) (Sakhir), 16. doi: 10.1109/ICDABI51230.2020.9325602

Crossref Full Text | Google Scholar

Azur, M. J., Stuart, E. A., Frangakis, C., and Leaf, P. J. (2011). Multiple imputation by chained equations: what is it and how does it work? Int. J. Methods Psychiatr. Res. 20, 40–49. doi: 10.1002/mpr.329

Crossref Full Text | Google Scholar

Bottomly, D., Long, N., Schultz, A. R., Kurtz, S. E., Tognon, C. E., Johnson, K., et al. (2022). Integrative analysis of drug response and clinical outcome in acute myeloid leukemia. Cancer Cell 40, 850–864.

Google Scholar

Breiman, L. (2001). Random Forests. Machine Learn. 45, 5–32. doi: 10.1023/A:1010933404324

Crossref Full Text | Google Scholar

Chen, J., Wang, X., Ma, A., Wang, Q. E., Liu, B., Li, L., et al. (2022). Deep transfer learning of cancer drug responses by integrating bulk and single-cell RNA-seq data. Nat. Commun. 13, 6494. doi: 10.1038/s41467-022-34277-7

Crossref Full Text | Google Scholar

Chen, T., and Guestrin, C. (2016). “XGBoost: a scalable tree boosting system,” in KDD '16: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794. doi: 10.1145/2939672.2939785

Crossref Full Text | Google Scholar

Choi, J., Lim, K. J., and Ji, B. (2023). Robust imputation method with context-aware voting ensemble model for management of water-quality data. Water Res. 243, 120369. doi: 10.1016/j.watres.2023.120369

Crossref Full Text | Google Scholar

DeSa, R. J., and Matheson, I. B. (2004). A practical approach to interpretation of singular value decomposition results. Methods Enzymol. 384, 1–8. doi: 10.1016/S0076-6879(04)84001-1

Crossref Full Text | Google Scholar

Donders, A. R., van der Heijden, G. J., Stijnen, T., and Moons, K. G. (2006). Review: a gentle introduction to imputation of missing values. J. Clin. Epidemiol. 59, 1087–1091. doi: 10.1016/j.jclinepi.2006.01.014

Crossref Full Text | Google Scholar

Dong, Y., and Peng, C. Y. (2013). Principled missing data methods for researchers. Springerplus 2, 222. doi: 10.1186/2193-1801-2-222

Crossref Full Text | Google Scholar

Fujimoto, S., Mizuno, T., and Ishikawa, A. (2022). Interpolation of non-random missing values in financial statements' big data using CatBoost. J. Computat. Soc. Sci. 5, 1281–1301. doi: 10.1007/s42001-022-00165-9

Crossref Full Text | Google Scholar

Getz, K., Hubbard, R. A., and Linn, K. A. (2023). Performance of multiple imputation using modern machine learning methods in electronic health records data. Epidemiology 34, 206–215. doi: 10.1097/EDE.0000000000001578

Crossref Full Text | Google Scholar

Hastie, T., Tibshirani, R., and Friedman, J. (2016). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Cham: Springer.

Google Scholar

Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., et al. (2017). “LightGBM: a highly efficient gradient boosting decision tree,” in Advances in Neural Information Processing Systems, 3149–3157.

Google Scholar

Lee, D. D., and Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791. doi: 10.1038/44565

Crossref Full Text | Google Scholar

Little, R. J., and Rubin, D. B. (2019). Statistical Analysis with Missing Data. Hoboken, NJ: John Wiley & Sons, Inc. doi: 10.1002/9781119482260

Crossref Full Text | Google Scholar

Mirzaei, A., Carter, S. R., Patanwala, A. E., and Schneider, C. R. (2022). Missing data in surveys: Key concepts, approaches, and applications. Res. Social Administrat. Pharm. 18, 2308–2316. doi: 10.1016/j.sapharm.2021.03.009

Crossref Full Text | Google Scholar

Mukherjee, K., Gunsoy, N. B., Kristy, R. M., Cappelleri, J. C., Roydhouse, J., Stephenson, J. J., et al. (2023). Handling missing data in health economics and outcomes research (HEOR): a systematic review and practical recommendations. Pharmacoeconomics 41, 1589–1601. doi: 10.1007/s40273-023-01297-0

Crossref Full Text | Google Scholar

Nasimian, A., Younus, S., Tatli, Ö., Hammarlund, E. U., Pienta, K. J., Rönnstrand, L., et al. (2024). AlphaML: a clear, legible, explainable, transparent, and elucidative binary classification platform for tabular data. Patterns 5:100897. doi: 10.1016/j.patter.2023.100897

Crossref Full Text | Google Scholar

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., et al. (2011). Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830.

Google Scholar

Raghunathan, T. E., Lepkowski, J. M., Hoewyk, J. V., and Solenberger, P. (2001). A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodol. 27, 85–95.

Google Scholar

Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. Hoboken, NJ: John Wiley & Sons, Inc. doi: 10.1002/9780470316696

Crossref Full Text | Google Scholar

Shah, A. D., Bartlett, J. W., Carpenter, J., Nicholas, O., and Hemingway, H. (2014). Comparison of random forest and parametric imputation models for imputing missing data using MICE: a CALIBER study. Am. J. Epidemiol. 179, 764–774. doi: 10.1093/aje/kwt312

Crossref Full Text | Google Scholar

Sterne, J. A., White, I. R., Carlin, J. B., Spratt, M., Royston, P., Kenward, M. G., et al. (2009). Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls. BMJ 338, b2393. doi: 10.1136/bmj.b2393

Crossref Full Text | Google Scholar

Su, Y. S., Gelman, A., Hill, J., and Yajima, M. (2011). Multiple imputation with diagnostics (mi) in R: opening windows into the black box. J. Statist. Softw. 45, 1–31. doi: 10.18637/jss.v045.i02

Crossref Full Text | Google Scholar

Trendowicz, A., and Jeffery, J. (2013). “Classification and Regression Trees,” in Software Project Effort Estimation. (Cham: Springer), 295–304. doi: 10.1007/978-3-319-03629-8_10

Crossref Full Text | Google Scholar

van Buuren, S. (2018). Flexible Imputation of Missing Data. London: Chapman and Hall/CRC. doi: 10.1201/9780429492259

Crossref Full Text | Google Scholar

van Buuren, S., and Groothuis-Oudshoorn, K. (2011). mice: Multivariate imputation by chained equations in R. J. Statist. Softw. 45, 1–67. doi: 10.18637/jss.v045.i03

Crossref Full Text | Google Scholar

Vanderaa, C., and Gatto, L. (2023). Revisiting the thorny issue of missing values in single-cell proteomics. J Proteome Res. 21, 1418–1427. doi: 10.1021/acs.jproteome.3c00227

Crossref Full Text | Google Scholar