In this study, we introduce a sophisticated generative conditional strategy designed to impute missing values within datasets, an area of considerable importance in statistical analysis. Specifically, we initially elucidate the theoretical underpinnings of the Generative Conditional Missing Imputation Networks (GCMI), demonstrating its robust properties in the context of the Missing Completely at Random (MCAR) and the Missing at Random (MAR) mechanisms. Subsequently, we enhance the robustness and accuracy of GCMI by integrating a multiple imputation framework using a chained equations approach. This innovation serves to bolster model stability and improve imputation performance significantly. Finally, through a series of meticulous simulations and empirical assessments utilizing benchmark datasets, we establish the superior efficacy of our proposed methods when juxtaposed with other leading imputation techniques currently available. This comprehensive evaluation not only underscores the practicality of GCMI but also affirms its potential as a leading-edge tool in the field of statistical data analysis.

Anomaly detection methods typically require fully observed data for model training and inference and cannot handle incomplete data, while the missing data problem is pervasive in science and engineering, leading to challenges in many important applications such as abnormal user detection in recommendation systems and novel or anomalous cell detection in bioinformatics, where the missing rates can be higher than 30\% or even 80\%. In this work, first, we construct and evaluate a straightforward strategy, ''impute-then-detect'', via combining state-of-the-art imputation methods with unsupervised anomaly detection methods, where the training data are composed of normal samples only. We observe that such two-stage methods frequently yield imputation bias from normal data, namely, the imputation methods are inclined to make incomplete samples ''normal, where the fundamental reason is that the imputation models learned only on normal data and cannot generalize well to abnormal data in the inference stage. To address this challenge, we propose an end-to-end method that integrates data imputation with anomaly detection into a unified optimization problem. The proposed model learns to generate well-designed pseudo-abnormal samples to mitigate the imputation bias and ensure the discrimination ability of both the imputation and detection processes. Furthermore, we provide theoretical guarantees for the effectiveness of the proposed method, proving that the proposed method can correctly detect anomalies with high probability. Experimental results on datasets with manually constructed missing values and inherent missing values demonstrate that our proposed method effectively mitigates the imputation bias and surpasses the baseline methods significantly.

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing counterparts including autoregressive models in many tasks such as image generation and audio synthesis, and would be promising for time series imputation. In this paper, we propose Conditional Score-based Diffusion model (CSDI), a novel time series imputation method that utilizes score-based diffusion models conditioned on observed data. Unlike existing score-based approaches, the conditional diffusion model is explicitly trained for imputation and can exploit correlations between observed values. On healthcare and environmental data, CSDI improves by 40-65% over existing probabilistic imputation methods on popular performance metrics. In addition, deterministic imputation by CSDI reduces the error by 5-20% compared to the state-of-the-art deterministic imputation methods. Furthermore, CSDI can also be applied to time series interpolation and probabilistic forecasting, and is competitive with existing baselines.

Missing data is an important problem in machine learning practice. Starting from the premise that imputation methods should preserve the causal structure of the data, we develop a regularization scheme that encourages any baseline imputation method to be causally consistent with the underlying data generating mechanism. Our proposal is a causally-aware imputation algorithm (MIRACLE). MIRACLE iteratively refines the imputation of a baseline by simultaneously modeling the missingness generating mechanism, encouraging imputation to be consistent with the causal structure of the data. We conduct extensive experiments on synthetic and a variety of publicly available datasets to show that MIRACLE is able to consistently improve imputation over a variety of benchmark methods across all three missingness scenarios: at random, completely at random, and not at random.

In real data, missing values occur frequently, which affects the interpretation with interpretable machine learning (IML) methods. Recent work considers bias and shows that model explanations may differ between imputation methods, while ignoring additional imputation uncertainty and its influence on variance and confidence intervals. We therefore compare the effects of different imputation methods on the confidence interval coverage probabilities of the IML methods permutation feature importance, partial dependence plots and Shapley values. We show that single imputation leads to underestimation of variance and that, in most cases, only multiple imputation is close to nominal coverage.

A modified Gate Recurrent Unit is employed in GAN to model the temporal irregularity of the incomplete time series.

Specifically, we summarize our contributions into the following points.

Neural Information Processing Systems http://nips.cc/

Medical imaging and multi-modal clinical settings often face the challange of missing modality in their diagnostic pipelines. Existing imputation methods either lack representational capacity or are computationally expensive. We propose PI-NAIM, a novel dual-path architecture that dynamically routes samples to optimized imputation approaches based on missingness complexity. Our framework integrates: (1) intelligent path routing that directs low missingness samples to efficient statistical imputation (MICE) and complex patterns to powerful neural networks (GAIN with temporal analysis); (2) cross-path attention fusion that leverages missingness-aware embeddings to intelligently combine both branches; and (3) end-to-end joint optimization of imputation accuracy and downstream task performance. Extensive experiments on MIMIC-III and multimodal benchmarks demonstrate state-of-the-art performance, achieving RMSE of 0.108 (vs. baselines' 0.119-0.152) and substantial gains in downstream tasks with an AUROC of 0.812 for mortality prediction. PI-NAIM's modular design enables seamless integration into vision pipelines handling incomplete sensor measurements, missing modalities, or corrupted inputs, providing a unified solution for real-world scenario. The code is publicly available at https://github.com/AfifaKhaled/PI-NAIM-Path-Integrated-Neural-Adaptive-Imputation-Model