SWIFT: Scalable Wasserstein Factorization for Sparse Nonnegative Tensors

Existing tensor factorization methods assume that the input tensor follows some specific distribution (i.e. Poisson, Bernoulli, and Gaussian), and solve the factorization by minimizing some empirical loss functions defined based on the corresponding distribution. However, it suffers from several drawbacks: 1) In reality, the underlying distributions are complicated and unknown, making it infeasible to be approximated by a simple distribution. 2) The correlation across dimensions of the input tensor is not well utilized, leading to sub-optimal performance. Although heuristics were proposed to incorporate such correlation as side information under Gaussian distribution, they can not easily be generalized to other distributions. Thus, a more principled way of utilizing the correlation in tensor factorization models is still an open challenge. Without assuming any explicit distribution, we formulate the tensor factorization as an optimal transport problem with Wasserstein distance, which can handle non-negative inputs. We introduce SWIFT, which minimizes the Wasserstein distance that measures the distance between the input tensor and that of the reconstruction. In particular, we define the N-th order tensor Wasserstein loss for the widely used tensor CP factorization and derive the optimization algorithm that minimizes it. By leveraging sparsity structure and different equivalent formulations for optimizing computational efficiency, SWIFT is as scalable as other well-known CP algorithms. Using the factor matrices as features, SWIFT achieves up to 9.65% and 11.31% relative improvement over baselines for downstream prediction tasks. Under the noisy conditions, SWIFT achieves up to 15% and 17% relative improvements over the best competitors for the prediction tasks.Comment: Accepted by AAAI-2

Learning Phenotypes and Dynamic Patient Representations via RNN Regularized Collective Non-Negative Tensor Factorization

Non-negative Tensor Factorization (NTF) has been shown effective to discover clinically relevant and interpretable phenotypes from Electronic Health Records (EHR). Existing NTF based computational phenotyping models aggregate data over the observation window, resulting in the learned phenotypes being mixtures of disease states appearing at different times. We argue that by separating the clinical events happening at different times in the input tensor, the temporal dynamics and the disease progression within the observation window could be modeled and the learned phenotypes will correspond to more specific disease states. Yet how to construct the tensor for data samples with different temporal lengths and properly capture the temporal relationship specific to each individual data sample remains an open challenge. In this paper, we propose a novel Collective Non-negative Tensor Factorization (CNTF) model where each patient is represented by a temporal tensor, and all of the temporal tensors are factorized collectively with the phenotype definitions being shared across all patients. The proposed CNTF model is also flexible to incorporate non-temporal data modality and RNN-based temporal regularization. We validate the proposed model using MIMIC-III dataset, and the empirical results show that the learned phenotypes are clinically interpretable. Moreover, the proposed CNTF model outperforms the state-of-the-art computational phenotyping models for the mortality prediction task