This paper introduces a randomized variation of the alternating least squares (ALS) algorithm for rank reduction of canonical tensor formats. The aim is to address the potential numerical ill-conditioning of least squares matrices at each ALS iteration. The proposed algorithm, dubbed randomized ALS, mitigates large condition numbers via projections onto random tensors, a technique inspired by well-established randomized projection methods for solving overdetermined least squares problems in a matrix setting. A probabilistic bound on the condition numbers of the randomized ALS matrices is provided, demonstrating reductions relative to their standard counterparts. Additionally, results are provided that guarantee comparable accuracy of the randomized ALS solution at each iteration. The performance of the randomized algorithm is studied with three examples, including manufactured tensors and an elliptic PDE with random inputs. In particular, for the latter, tests illustrate not only improvements in condition numbers, but also improved accuracy of the iterative solver for the PDE solution represented in a canonical tensor format.
Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantification applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high-and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data is then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.
Background: Patients with acute myeloid leukemia (AML) face an abrupt life-threatening illness and experience immense physical and psychological symptoms. However, no data describe how patients with AML cope longitudinally with their illness or the relationship between longitudinal coping and outcomes. Methods: We conducted a secondary analysis of longitudinal data from 160 patients with high-risk AML enrolled in a supportive care intervention trial to describe coping strategies longitudinally across the illness course. We used the Brief COPE questionnaire, the Hospital Anxiety and Depression Scale, the Post-Traumatic Stress Disorder (PTSD) Checklist-Civilian Version, and the Functional Assessment of Cancer Therapy-Leukemia to measure coping strategies, psychological distress, and quality of life (QoL) at baseline and at weeks 2, 4, 12, and 24 after diagnosis. Electronic health records were used to assess healthcare utilization and end-of-life (EoL) outcomes, and multivariate analyses were used to assess the relationship between coping and outcomes. Results: Longitudinal utilization of approach-oriented coping strategies was significantly associated with less distress (anxiety: β, –0.18; P<.001; depression symptoms: β, –0.42; P<.001; PTSD symptoms: β, –0.60; P<.001) and better QoL (β, 2.00; P<.001). Longitudinal utilization of avoidant coping strategies was significantly associated with greater distress (anxiety: β, 0.64; depression symptoms: β, 0.54; PTSD symptoms: β, 2.13; P<.001 for all) and worse QoL (β, –4.27; P<.001). Although the use of approach-oriented and avoidant coping strategies was not significantly associated with hospitalization, chemotherapy administration, or hospice use in the last 30 days of life, approach-oriented coping was associated with lower odds of ICU admissions (odds ratio, 0.92; P=.049). Conclusions: Longitudinal use of approach-oriented coping strategies was associated with less psychological distress, better QoL, and a lower likelihood of ICU admission, suggesting a possible target for supportive oncology interventions. Coping strategies did not impact EoL outcomes, and further research is needed to elucidate which patient factors impact EoL decision-making.
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