Researchers have been persistently working to address the issue of missing values in time series data. Numerous models have been proposed, striving to estimate the distribution of the data. The Radial Basis Functions Neural Network (RBFNN) has recently exhibited exceptional performance in estimating data distribution. In this paper, we propose a time series imputation model based on RBFNN. Our imputation model learns local information from timestamps to create a continuous function. Additionally, we incorporate time gaps to facilitate learning information considering the missing terms of missing values. We name this model the Missing Imputation Multivariate RBFNN (MIM-RBFNN). However, MIM-RBFNN relies on a local information-based learning approach, which presents difficulties in utilizing temporal information. Therefore, we propose an extension called the Missing Value Imputation Recurrent Neural Network with Continuous Function (MIRNN-CF) using the continuous function generated by MIM-RBFNN. We evaluate the performance using two real-world datasets with non-random missing and random missing patterns, and conduct an ablation study comparing MIM-RBFNN and MIRNN-CF.
Sepsis is the leading cause of in-hospital mortality in the USA. Early sepsis onset prediction and diagnosis could significantly improve the survival of sepsis patients. Existing predictive models are usually trained on high-quality data with few missing information, while missing values widely exist in real-world clinical scenarios (especially in the first hours of admissions to the hospital), which causes a significant decrease in accuracy and an increase in uncertainty for the predictive models. The common method to handle missing values is imputation, which replaces the unavailable variables with estimates from the observed data. The uncertainty of imputation results can be propagated to the sepsis prediction outputs, which have not been studied in existing works on either sepsis prediction or uncertainty quantification. In this study, we first define such propagated uncertainty as the variance of prediction output and then introduce uncertainty propagation methods to quantify the propagated uncertainty. Moreover, for the potential high-risk patients with low confidence due to limited observations, we propose a robust active sensing algorithm to increase confidence by actively recommending clinicians to observe the most informative variables. We validate the proposed models in both publicly available data (i.e., MIMIC-III and AmsterdamUMCdb) and proprietary data in The Ohio State University Wexner Medical Center (OSUWMC). The experimental results show that the propagated uncertainty is dominant at the beginning of admissions to hospitals and the proposed algorithm outperforms state-of-the-art active sensing methods. Finally, we implement a SepsisLab system for early sepsis prediction and active sensing based on our pre-trained models. Clinicians and potential sepsis patients can benefit from the system in early prediction and diagnosis of sepsis.
Understanding causal relationships between machines is crucial for fault diagnosis and optimization in manufacturing processes. Real-world datasets frequently exhibit up to 90% missing data and high dimensionality from hundreds of sensors. These datasets also include domain-specific expert knowledge and chronological order information, reflecting the recording order across different machines, which is pivotal for discerning causal relationships within the manufacturing data. However, previous methods for handling missing data in scenarios akin to real-world conditions have not been able to effectively utilize expert knowledge. Conversely, prior methods that can incorporate expert knowledge struggle with datasets that exhibit missing values. Therefore, we propose COKE to construct causal graphs in manufacturing datasets by leveraging expert knowledge and chronological order among sensors without imputing missing data. Utilizing the characteristics of the recipe, we maximize the use of samples with missing values, derive embeddings from intersections with an initial graph that incorporates expert knowledge and chronological order, and create a sensor ordering graph. The graph-generating process has been optimized by an actor-critic architecture to obtain a final graph that has a maximum reward. Experimental evaluations in diverse settings of sensor quantities and missing proportions demonstrate that our approach compared with the benchmark methods shows an average improvement of 39.9% in the F1-score. Moreover, the F1-score improvement can reach 62.6% when considering the configuration similar to real-world datasets, and 85.0% in real-world semiconductor datasets. The source code is available at https://github.com/OuTingYun/COKE.
Missing values are a major challenge in most data science projects working on real data. To avoid losing valuable information, imputation methods are used to fill in missing values with estimates, allowing the preservation of samples or variables that would otherwise be discarded. However, if the process is not well controlled, imputation can generate spurious values that introduce uncertainty and bias into the learning process. The abundance of univariate and multivariate imputation techniques, along with the complex trade-off between data reliability and preservation, makes it difficult to determine the best course of action to tackle missing values. In this work, we present ITI-IQA (Imputation Quality Assessment), a set of utilities designed to assess the reliability of various imputation methods, select the best imputer for any feature or group of features, and filter out features that do not meet quality criteria. Statistical tests are conducted to evaluate the suitability of every tested imputer, ensuring that no new biases are introduced during the imputation phase. The result is a trainable pipeline of filters and imputation methods that streamlines the process of dealing with missing data, supporting different data types: continuous, discrete, binary, and categorical. The toolbox also includes a suite of diagnosing methods and graphical tools to check measurements and results during and after handling missing data.
Handling missing values in tabular datasets presents a significant challenge in training and testing artificial intelligence models, an issue usually addressed using imputation techniques. Here we introduce "Not Another Imputation Method" (NAIM), a novel transformer-based model specifically designed to address this issue without the need for traditional imputation techniques. NAIM's ability to avoid the necessity of imputing missing values and to effectively learn from available data relies on two main techniques: the use of feature-specific embeddings to encode both categorical and numerical features also handling missing inputs; the modification of the masked self-attention mechanism to completely mask out the contributions of missing data. Additionally, a novel regularization technique is introduced to enhance the model's generalization capability from incomplete data. We extensively evaluated NAIM on 5 publicly available tabular datasets, demonstrating its superior performance over 6 state-of-the-art machine learning models and 5 deep learning models, each paired with 3 different imputation techniques when necessary. The results highlight the efficacy of NAIM in improving predictive performance and resilience in the presence of missing data. To facilitate further research and practical application in handling missing data without traditional imputation methods, we made the code for NAIM available at https://github.com/cosbidev/NAIM.
Motion forecasting plays a pivotal role in autonomous driving systems, enabling vehicles to execute collision warnings and rational local-path planning based on predictions of the surrounding vehicles. However, prevalent methods often assume complete observed trajectories, neglecting the potential impact of missing values induced by object occlusion, scope limitation, and sensor failures. Such oversights inevitably compromise the accuracy of trajectory predictions. To tackle this challenge, we propose an end-to-end framework, termed Multiscale Transformer (MSTF), meticulously crafted for incomplete trajectory prediction. MSTF integrates a Multiscale Attention Head (MAH) and an Information Increment-based Pattern Adaptive (IIPA) module. Specifically, the MAH component concurrently captures multiscale motion representation of trajectory sequence from various temporal granularities, utilizing a multi-head attention mechanism. This approach facilitates the modeling of global dependencies in motion across different scales, thereby mitigating the adverse effects of missing values. Additionally, the IIPA module adaptively extracts continuity representation of motion across time steps by analyzing missing patterns in the data. The continuity representation delineates motion trend at a higher level, guiding MSTF to generate predictions consistent with motion continuity. We evaluate our proposed MSTF model using two large-scale real-world datasets. Experimental results demonstrate that MSTF surpasses state-of-the-art (SOTA) models in the task of incomplete trajectory prediction, showcasing its efficacy in addressing the challenges posed by missing values in motion forecasting for autonomous driving systems.
Time series generation is a crucial research topic in the area of decision-making systems, which can be particularly important in domains like autonomous driving, healthcare, and, notably, robotics. Recent approaches focus on learning in the data space to model time series information. However, the data space often contains limited observations and noisy features. In this paper, we propose TimeLDM, a novel latent diffusion model for high-quality time series generation. TimeLDM is composed of a variational autoencoder that encodes time series into an informative and smoothed latent content and a latent diffusion model operating in the latent space to generate latent information. We evaluate the ability of our method to generate synthetic time series with simulated and real-world datasets and benchmark the performance against existing state-of-the-art methods. Qualitatively and quantitatively, we find that the proposed TimeLDM persistently delivers high-quality generated time series. For example, TimeLDM achieves new state-of-the-art results on the simulated benchmarks and an average improvement of 55% in Discriminative score with all benchmarks. Further studies demonstrate that our method yields more robust outcomes across various lengths of time series data generation. Especially, for the Context-FID score and Discriminative score, TimeLDM realizes significant improvements of 80% and 50%, respectively. The code will be released after publication.
As the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear Discriminant Analysis (LDA) remains a popular choice for classification due to its interpretable nature, derived from its capacity to model class distributions and enhance class separation through linear combinations of features. However, real-world datasets often suffer from incomplete data, posing substantial challenges for both classification accuracy and model interpretability. In this paper, we introduce a novel and robust classification method, termed Weighted missing Linear Discriminant Analysis (WLDA), which extends LDA to handle datasets with missing values without the need for imputation. Our approach innovatively incorporates a weight matrix that penalizes missing entries, thereby refining parameter estimation directly on incomplete data. This methodology not only preserves the interpretability of LDA but also significantly enhances classification performance in scenarios plagued by missing data. We conduct an in-depth theoretical analysis to establish the properties of WLDA and thoroughly evaluate its explainability. Experimental results across various datasets demonstrate that WLDA consistently outperforms traditional methods, especially in challenging environments where missing values are prevalent in both training and test datasets. This advancement provides a critical tool for improving classification accuracy and maintaining model transparency in the face of incomplete data.
Missing data is a prevalent issue that can significantly impair model performance and explainability. This paper briefly summarizes the development of the field of missing data with respect to Explainable Artificial Intelligence and experimentally investigates the effects of various imputation methods on SHAP (SHapley Additive exPlanations), a popular technique for explaining the output of complex machine learning models. Next, we compare different imputation strategies and assess their impact on feature importance and interaction as determined by Shapley values. Moreover, we also theoretically analyze the effects of missing values on Shapley values. Importantly, our findings reveal that the choice of imputation method can introduce biases that could lead to changes in the Shapley values, thereby affecting the explainability of the model. Moreover, we also show that a lower test prediction MSE (Mean Square Error) does not necessarily imply a lower MSE in Shapley values and vice versa. Also, while XGBoost (eXtreme Gradient Boosting) is a method that could handle missing data directly, using XGBoost directly on missing data can seriously affect explainability compared to imputing the data before training XGBoost. This study provides a comprehensive evaluation of imputation methods in the context of model explanations, offering practical guidance for selecting appropriate techniques based on dataset characteristics and analysis objectives. The results underscore the importance of considering imputation effects to ensure robust and reliable insights from machine learning models.
Time series forecasting (TSF) is crucial in fields like economic forecasting, weather prediction, traffic flow analysis, and public health surveillance. Real-world time series data often include noise, outliers, and missing values, making accurate forecasting challenging. Traditional methods model point-to-point relationships, which limits their ability to capture complex temporal patterns and increases their susceptibility to noise.To address these issues, we introduce the WindowMixer model, built on an all-MLP framework. WindowMixer leverages the continuous nature of time series by examining temporal variations from a window-based perspective. It decomposes time series into trend and seasonal components, handling them individually. For trends, a fully connected (FC) layer makes predictions. For seasonal components, time windows are projected to produce window tokens, processed by Intra-Window-Mixer and Inter-Window-Mixer modules. The Intra-Window-Mixer models relationships within each window, while the Inter-Window-Mixer models relationships between windows. This approach captures intricate patterns and long-range dependencies in the data.Experiments show WindowMixer consistently outperforms existing methods in both long-term and short-term forecasting tasks.
Remote sensing images often suffer from substantial data loss due to factors such as thick cloud cover and sensor limitations. Existing methods for imputing missing values in remote sensing images fail to fully exploit spatiotemporal auxiliary information, which restricts the accuracy of their reconstructions. To address this issue, this paper proposes a novel deep learning-based approach called MS2TAN (Multi-Scale Masked Spatial-Temporal Attention Network) for reconstructing time-series remote sensing images. First, we introduce an efficient spatiotemporal feature extractor based on Masked Spatial-Temporal Attention (MSTA) to capture high-quality representations of spatiotemporal neighborhood features surrounding missing regions while significantly reducing the computational complexity of the attention mechanism. Second, a Multi-Scale Restoration Network composed of MSTA-based Feature Extractors is designed to progressively refine missing values by exploring spatiotemporal neighborhood features at different scales. Third, we propose a "Pixel-Structure-Perception" Multi-Objective Joint Optimization method to enhance the visual quality of the reconstructed results from multiple perspectives and to preserve more texture structures. Finally, quantitative experimental results under multi-temporal inputs on two public datasets demonstrate that the proposed method outperforms competitive approaches, achieving a 9.76%/9.30% reduction in Mean Absolute Error (MAE) and a 0.56 dB/0.62 dB increase in Peak Signal-to-Noise Ratio (PSNR), along with stronger texture and structural consistency. Ablation experiments further validate the contribution of the core innovations to imputation accuracy.
This project intends to study a cardiovascular disease risk early warning model based on one-dimensional convolutional neural networks. First, the missing values of 13 physiological and symptom indicators such as patient age, blood glucose, cholesterol, and chest pain were filled and Z-score was standardized. The convolutional neural network is converted into a 2D matrix, the convolution function of 1,3, and 5 is used for the first-order convolution operation, and the Max Pooling algorithm is adopted for dimension reduction. Set the learning rate and output rate. It is optimized by the Adam algorithm. The result of classification is output by a soft classifier. This study was conducted based on Statlog in the UCI database and heart disease database respectively. The empirical data indicate that the forecasting precision of this technique has been enhanced by 11.2%, relative to conventional approaches, while there is a significant improvement in the logarithmic curve fitting. The efficacy and applicability of the novel approach are corroborated through the examination employing a one-dimensional convolutional neural network.
Current clinical decision support systems (DSS) are trained and validated on observational data from the target clinic. This is problematic for treatments validated in a randomized clinical trial (RCT), but not yet introduced in any clinic. In this work, we report on a method for training and validating the DSS using the RCT data. The key challenges we address are of missingness -- missing rationale for treatment assignment (the assignment is at random), and missing verification evidence, since the effectiveness of a treatment for a patient can only be verified (ground truth) for treatments what were actually assigned to a patient. We use data from a multi-armed RCT that investigated the effectiveness of single- and combination- treatments for 240+ tinnitus patients recruited and treated in 5 clinical centers. To deal with the 'missing rationale' challenge, we re-model the target variable (outcome) in order to suppress the effect of the randomly-assigned treatment, and control on the effect of treatment in general. Our methods are also robust to missing values in features and with a small number of patients per RCT arm. We deal with 'missing verification evidence' by using counterfactual treatment verification, which compares the effectiveness of the DSS recommendations to the effectiveness of the RCT assignments when they are aligned v/s not aligned. We demonstrate that our approach leverages the RCT data for learning and verification, by showing that the DSS suggests treatments that improve the outcome. The results are limited through the small number of patients per treatment; while our ensemble is designed to mitigate this effect, the predictive performance of the methods is affected by the smallness of the data. We provide a basis for the establishment of decision supporting routines on treatments that have been tested in RCTs but have not yet been deployed clinically.
Accurate time series forecasts are crucial for various applications, such as traffic management, electricity consumption, and healthcare. However, limitations in models and data quality can significantly impact forecasts accuracy. One common issue with data quality is the absence of data points, referred to as missing data. It is often caused by sensor malfunctions, equipment failures, or human errors. This paper proposes Hinge-FM2I, a novel method for handling missing data values in univariate time series data. Hinge-FM2I builds upon the strengths of the Forecasting Method by Image Inpainting (FM2I). FM2I has proven effective, but selecting the most accurate forecasts remain a challenge. To overcome this issue, we proposed a selection algorithm. Inspired by door hinges, Hinge-FM2I drops a data point either before or after the gap (left/right-hinge), then use FM2I for imputation, and then select the imputed gap based on the lowest error of the dropped data point. Hinge-FM2I was evaluated on a comprehensive sample composed of 1356 time series, extracted from the M3 competition benchmark dataset, with missing value rates ranging from 3.57\% to 28.57\%. Experimental results demonstrate that Hinge-FM2I significantly outperforms established methods such as, linear/spline interpolation, K-Nearest Neighbors (K-NN), and ARIMA. Notably, Hinge-FM2I achieves an average Symmetric Mean Absolute Percentage Error (sMAPE) score of 5.6\% for small gaps, and up to 10\% for larger ones. These findings highlight the effectiveness of Hinge-FM2I as a promising new method for addressing missing values in univariate time series data.
Probabilistic forecasting models for joint distributions of targets in irregular time series with missing values are a heavily under-researched area in machine learning, with, to the best of our knowledge, only two Models have been researched so far: The Gaussian Process Regression model, and ProFITi. While ProFITi, thanks to using multivariate normalizing flows, is very expressive, leading to better predictive performance, it suffers from marginalization inconsistency: It does not guarantee that the marginal distributions of a subset of variables in its predictive distributions coincide with the directly predicted distributions of these variables. When asked to directly predict marginal distributions, they are often vastly inaccurate. We propose MOSES (Marginalization Consistent Mixture of Separable Flows), a model that parametrizes a stochastic process through a mixture of several latent multivariate Gaussian Processes combined with separable univariate Normalizing Flows. In particular, MOSES can be analytically marginalized, allowing it to directly answer a wider range of probabilistic queries than most competitors. Experiments on four datasets show that MOSES achieves both accurate joint and marginal predictions, surpassing all other marginalization consistent baselines, while only trailing slightly behind ProFITi in joint prediction, but vastly superior when predicting marginal distributions.
The evolution of industry has enabled the integration of physical and digital systems, facilitating the collection of extensive data on manufacturing processes. This integration provides a reliable solution for improving process quality and managing equipment health. However, data collected from real manufacturing processes often exhibit challenging properties, such as severe class imbalance, high rates of missing values, and noisy features, which hinder effective machine learning implementation. In this study, a rare class prediction approach is developed for in situ data collected from a smart semiconductor manufacturing process. The primary objective is to build a model that addresses issues of noise and class imbalance, enhancing class separation. The developed approach demonstrated promising results compared to existing literature, which would allow the prediction of new observations that could give insights into future maintenance plans and production quality. The model was evaluated using various performance metrics, with ROC curves showing an AUC of 0.95, a precision of 0.66, and a recall of 0.96
Due to detector malfunctions and communication failures, missing data is ubiquitous during the collection of traffic data. Therefore, it is of vital importance to impute the missing values to facilitate data analysis and decision-making for Intelligent Transportation System (ITS). However, existing imputation methods generally perform zero pre-filling techniques to initialize missing values, introducing inevitable noises. Moreover, we observe prevalent over-smoothing interpolations, falling short in revealing the intrinsic spatio-temporal correlations of incomplete traffic data. To this end, we propose Mask-Aware Graph imputation Network: MagiNet. Our method designs an adaptive mask spatio-temporal encoder to learn the latent representations of incomplete data, eliminating the reliance on pre-filling missing values. Furthermore, we devise a spatio-temporal decoder that stacks multiple blocks to capture the inherent spatial and temporal dependencies within incomplete traffic data, alleviating over-smoothing imputation. Extensive experiments demonstrate that our method outperforms state-of-the-art imputation methods on five real-world traffic datasets, yielding an average improvement of 4.31% in RMSE and 3.72% in MAPE.
Data Mining is a promising field and is applied in multiple domains for its predictive capabilities. Data in the real world cannot be readily used for data mining as it suffers from the problems of multidimensionality, unbalance and missing values. It is difficult to use its predictive capabilities by novice users. It is difficult for a beginner to find the relevant set of attributes from a large pool of data available. The paper presents a Robust Prediction Model that finds a relevant set of attributes; resolves the problems of unbalanced and multidimensional real-life datasets and helps in finding patterns for informed decision making. Model is tested upon five different datasets in the domain of Health Sector, Education, Business and Fraud Detection. The results showcase the robust behaviour of the model and its applicability in various domains.
In this paper, our goal is to generate synthetic data for heterogeneous (mixed-type) tabular datasets with high machine learning utility (MLu). Since the MLu performance depends on accurately approximating the conditional distributions, we focus on devising a synthetic data generation method based on conditional distribution estimation. We introduce MaCoDE by redefining the consecutive multi-class classification task of Masked Language Modeling (MLM) as histogram-based non-parametric conditional density estimation. Our approach enables the estimation of conditional densities across arbitrary combinations of target and conditional variables. We bridge the theoretical gap between distributional learning and MLM by demonstrating that minimizing the orderless multi-class classification loss leads to minimizing the total variation distance between conditional distributions. To validate our proposed model, we evaluate its performance in synthetic data generation across 10 real-world datasets, demonstrating its ability to adjust data privacy levels easily without re-training. Additionally, since masked input tokens in MLM are analogous to missing data, we further assess its effectiveness in handling training datasets with missing values, including multiple imputations of the missing entries.
In an era of rapidly advancing data-driven applications, there is a growing demand for data in both research and practice. Synthetic data have emerged as an alternative when no real data is available (e.g., due to privacy regulations). Synthesizing tabular data presents unique and complex challenges, especially handling (i) missing values, (ii) dataset imbalance, (iii) diverse column types, and (iv) complex data distributions, as well as preserving (i) column correlations, (ii) temporal dependencies, and (iii) integrity constraints (e.g., functional dependencies) present in the original dataset. While substantial progress has been made recently in the context of generational models, there is no one-size-fits-all solution for tabular data today, and choosing the right tool for a given task is therefore no trivial task. In this paper, we survey the state of the art in Tabular Data Synthesis (TDS), examine the needs of users by defining a set of functional and non-functional requirements, and compile the challenges associated with meeting those needs. In addition, we evaluate the reported performance of 36 popular research TDS tools about these requirements and develop a decision guide to help users find suitable TDS tools for their applications. The resulting decision guide also identifies significant research gaps.