Lambert Matrix Factorization

Background Patient representation learning aims to learn features, also called representations, from input sources automatically, often in an unsupervised manner, for use in predictive models. This obviates the need for cumbersome, time- and resource-intensive manual feature engineering, especially from unstructured data such as text, images, or graphs. Most previous techniques have used neural network–based autoencoders to learn patient representations, primarily from clinical notes in electronic medical records (EMRs). Knowledge graphs (KGs), with clinical entities as nodes and their relations as edges, can be extracted automatically from biomedical literature and provide complementary information to EMR data that have been found to provide valuable predictive signals. Objective This study aims to evaluate the efficacy of collective matrix factorization (CMF), both the classical variant and a recent neural architecture called deep CMF (DCMF), in integrating heterogeneous data sources from EMR and KG to obtain patient representations for clinical decision support tasks. Methods Using a recent formulation for obtaining graph representations through matrix factorization within the context of CMF, we infused auxiliary information during patient representation learning. We also extended the DCMF architecture to create a task-specific end-to-end model that learns to simultaneously find effective patient representations and predictions. We compared the efficacy of such a model to that of first learning unsupervised representations and then independently learning a predictive model. We evaluated patient representation learning using CMF-based methods and autoencoders for 2 clinical decision support tasks on a large EMR data set. Results Our experiments show that DCMF provides a seamless way for integrating multiple sources of data to obtain patient representations, both in unsupervised and supervised settings. Its performance in single-source settings is comparable with that of previous autoencoder-based representation learning methods. When DCMF is used to obtain representations from a combination of EMR and KG, where most previous autoencoder-based methods cannot be used directly, its performance is superior to that of previous nonneural methods for CMF. Infusing information from KGs into patient representations using DCMF was found to improve downstream predictive performance. Conclusions Our experiments indicate that DCMF is a versatile model that can be used to obtain representations from single and multiple data sources and combine information from EMR data and KGs. Furthermore, DCMF can be used to learn representations in both supervised and unsupervised settings. Thus, DCMF offers an effective way of integrating heterogeneous data sources and infusing auxiliary knowledge into patient representations.

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“…The network was trained using the Adam [ 52 ]. The R package for CMF [ 53 ] was used with default parameters.…”

Section: Methodsmentioning

confidence: 99%

Patient Representation Learning From Heterogeneous Data Sources and Knowledge Graphs Using Deep Collective Matrix Factorization: Evaluation Study

Kumar¹,

Shi²,

Mariappan³

et al. 2022

JMIR Med Inform

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“…In [12], the Lambert W approach was applied to normalize a vector regardless of its actual distribution. The use of the Lambert W distribution in matrix factorization with an implementation in probabilistic programming was presented in [13]. The Lambert W function has been used to derive the exact distribution of the likelihood ratio test statistic and to solve related problems in [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Lambert W Random Variables and Their Applications in Loss Modelling

Käärik,

Selart,

Puhkim

et al. 2023

Symmetry

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Several distributions and families of distributions are proposed to model skewed data, e.g., with skew-normal and related distributions. Lambert W random variables offer an alternative approach in which, instead of constructing a new distribution, a certain transformation is proposed. Such an approach allows the construction of a Lambert W skewed version from any distribution. Here, we choose the Lambert W normal distribution as a natural starting point and include the Lambert W exponential distribution due to the simplicity and shape of the exponential distribution, which, after skewing, may produce a reasonably heavy tail for loss models. In the theoretical part, we focus on the mathematical properties of obtained distributions, including the range of skewness. In the practical part, the suitability of the corresponding Lambert W transformed distributions is evaluated on real insurance data. Finally, the results are compared with those obtained using common loss distributions.

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Lambert Matrix Factorization

Cited by 2 publications

References 13 publications

Patient Representation Learning From Heterogeneous Data Sources and Knowledge Graphs Using Deep Collective Matrix Factorization: Evaluation Study

Patient Representation Learning From Heterogeneous Data Sources and Knowledge Graphs Using Deep Collective Matrix Factorization: Evaluation Study

Lambert W Random Variables and Their Applications in Loss Modelling

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