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1. GP-VAE: Deep Probabilistic Time Series Imputation

   Fortuin, V. (June 2020, International Conference on Artificial Intelligence and Statistics)

   Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical data imputation methods in this domain. However, naïve applications of deep learning fall short in giving reliable confidence estimates and lack interpretability. We propose a new deep sequential latent variable model for dimensionality reduction and data imputation. Our modeling assumption is simple and interpretable: the high dimensional time series has a lower-dimensional representation which evolves smoothly in time according to a Gaussian process. The nonlinear dimensionality reduction in the presence of missing data is achieved using a VAE approach with a novel structured variational approximation. We demonstrate that our approach outperforms several classical and deep learning-based data imputation methods on high-dimensional data from the domains of computer vision and healthcare, while additionally improving the smoothness of the imputations and providing interpretable uncertainty estimates. 

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2. Sparse Convolutional Denoising Autoencoders for Genotype Imputation

   https://doi.org/10.3390/genes10090652  

   Chen, Junjie; Shi, Xinghua (September 2019, Genes)

   Genotype imputation, where missing genotypes can be computationally imputed, is an essential tool in genomic analysis ranging from genome wide associations to phenotype prediction. Traditional genotype imputation methods are typically based on haplotype-clustering algorithms, hidden Markov models (HMMs), and statistical inference. Deep learning-based methods have been recently reported to suitably address the missing data problems in various fields. To explore the performance of deep learning for genotype imputation, in this study, we propose a deep model called a sparse convolutional denoising autoencoder (SCDA) to impute missing genotypes. We constructed the SCDA model using a convolutional layer that can extract various correlation or linkage patterns in the genotype data and applying a sparse weight matrix resulted from the L1 regularization to handle high dimensional data. We comprehensively evaluated the performance of the SCDA model in different scenarios for genotype imputation on the yeast and human genotype data, respectively. Our results showed that SCDA has strong robustness and significantly outperforms popular reference-free imputation methods. This study thus points to another novel application of deep learning models for missing data imputation in genomic studies. 

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3. Unsupervised Imputation of Non-Ignorably Missing Data Using Importance-Weighted Autoencoders

   https://doi.org/10.1080/19466315.2024.2368787  

   Lim, David K; Rashid, Naim U; Oliva, Junier B; Ibrahim, Joseph G (July 2024, Statistics in Biopharmaceutical Research)

   Deep Learning (DL) methods have dramatically increased in popularity in recent years. While its initial success was demonstrated in the classification and manipulation of image data, there has been significant growth in the application of DL methods to problems in the biomedical sciences. However, the greater prevalence and complexity of missing data in biomedical datasets present significant challenges for DL methods. Here, we provide a formal treatment of missing data in the context of Variational Autoencoders (VAEs), a popular unsupervised DL architecture commonly used for dimension reduction, imputation, and learning latent representations of complex data. We propose a new VAE architecture, NIMIWAE, that is one of the first to flexibly account for both ignorable and non-ignorable patterns of missingness in input features at training time. Following training, samples can be drawn from the approximate posterior distribution of the missing data can be used for multiple imputation, facilitating downstream analyses on high dimensional incomplete datasets. We demonstrate through statistical simulation that our method outperforms existing approaches for unsupervised learning tasks and imputation accuracy. We conclude with a case study of an EHR dataset pertaining to 12,000 ICU patients containing a large number of diagnostic measurements and clinical outcomes, where many features are only partially observed. 

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4. Self-Supervised Transformer for Sparse and Irregularly Sampled Multivariate Clinical Time-Series

   https://doi.org/10.1145/3516367  

   Tipirneni, Sindhu; Reddy, Chandan_K (July 2022, ACM Transactions on Knowledge Discovery from Data)

   Multivariate time-series data are frequently observed in critical care settings and are typically characterized by sparsity (missing information) and irregular time intervals. Existing approaches for learning representations in this domain handle these challenges by either aggregation or imputation of values, which in-turn suppresses the fine-grained information and adds undesirable noise/overhead into the machine learning model. To tackle this problem, we propose aSelf-supervisedTransformer forTime-Series (STraTS) model, which overcomes these pitfalls by treating time-series as a set of observation triplets instead of using the standard dense matrix representation. It employs a novel Continuous Value Embedding technique to encode continuous time and variable values without the need for discretization. It is composed of a Transformer component with multi-head attention layers, which enable it to learn contextual triplet embeddings while avoiding the problems of recurrence and vanishing gradients that occur in recurrent architectures. In addition, to tackle the problem of limited availability of labeled data (which is typically observed in many healthcare applications), STraTS utilizes self-supervision by leveraging unlabeled data to learn better representations by using time-series forecasting as an auxiliary proxy task. Experiments on real-world multivariate clinical time-series benchmark datasets demonstrate that STraTS has better prediction performance than state-of-the-art methods for mortality prediction, especially when labeled data is limited. Finally, we also present an interpretable version of STraTS, which can identify important measurements in the time-series data. Our data preprocessing and model implementation codes are available athttps://github.com/sindhura97/STraTS. 

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5. HyperTools: A Python toolbox for visualizing and manipulating high-dimensional data

   Heusser, Andrew C; Ziman, Kirsten; Owen, Lucy LW; Manning, Jeremy R (January 2017, arXiv.org)

   Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable over time as (x,y) coordinates on a graph), it is not always obvious how to visualize high-dimensional datasets in a similarly intuitive way. Here we present HypeTools, a Python toolbox for visualizing and manipulating large, high-dimensional datasets. Our primary approach is to use dimensionality reduction techniques (Pearson, 1901; Tipping & Bishop, 1999) to embed high-dimensional datasets in a lower-dimensional space, and plot the data using a simple (yet powerful) API with many options for data manipulation [e.g. hyperalignment (Haxby et al., 2011), clustering, normalizing, etc.] and plot styling. The toolbox is designed around the notion of data trajectories and point clouds. Just as the position of an object moving through space can be visualized as a 3D trajectory, HyperTools uses dimensionality reduction algorithms to create similar 2D and 3D trajectories for time series of high-dimensional observations. The trajectories may be plotted as interactive static plots or visualized as animations. These same dimensionality reduction and alignment algorithms can also reveal structure in static datasets (e.g. collections of observations or attributes). We present several examples showcasing how using our toolbox to explore data through trajectories and low-dimensional embeddings can reveal deep insights into datasets across a wide variety of domains. 

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