Guaranteed Sampling Flexibility for Low-tubal-rank Tensor Completion

While Bernoulli sampling is extensively studied in tensor completion, t-CUR sampling approximates low-tubal-rank tensors via lateral and horizontal subtensors. However, both methods lack sufficient flexibility for diverse practical applications. To address this, we introduce Tensor Cross-Concentrated Sampling (t-CCS), a novel and straightforward sampling model that advances the matrix cross-concentrated sampling concept within a tensor framework. t-CCS effectively bridges the gap between Bernoulli and t-CUR sampling, offering additional flexibility that can lead to computational savings in various contexts. A key aspect of our work is the comprehensive theoretical analysis provided. We establish a sufficient condition for the successful recovery of a low-rank tensor from its t-CCS samples. In support of this, we also develop a theoretical framework validating the feasibility of t-CUR via uniform random sampling and conduct a detailed theoretical sampling complexity analysis for tensor completion problems utilizing the general Bernoulli sampling model. Moreover, we introduce an efficient non-convex algorithm, the Iterative t-CUR Tensor Completion (ITCURTC) algorithm, specifically designed to tackle the t-CCS-based tensor completion. We have intensively tested and validated the effectiveness of the t-CCS model and the ITCURTC algorithm across both synthetic and real-world datasets.

On the Robustness of Cross-Concentrated Sampling for Matrix Completion

Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has caught much attention. However, the robustness of the CCS model against sparse outliers remains unclear in the existing studies. In this paper, we aim to answer this question by exploring a novel Robust CCS Completion problem. A highly efficient non-convex iterative algorithm, dubbed Robust CUR Completion (RCURC), is proposed. The empirical performance of the proposed algorithm, in terms of both efficiency and robustness, is verified in synthetic and real datasets.

Efficient estimation of weighted cumulative treatment effects by double/debiased machine learning

In empirical studies with time-to-event outcomes, investigators often leverage observational data to conduct causal inference on the effect of exposure when randomized controlled trial data is unavailable. Model misspecification and lack of overlap are common issues in observational studies, and they often lead to inconsistent and inefficient estimators of the average treatment effect. Estimators targeting overlap weighted effects have been proposed to address the challenge of poor overlap, and methods enabling flexible machine learning for nuisance models address model misspecification. However, the approaches that allow machine learning for nuisance models have not been extended to the setting of weighted average treatment effects for time-to-event outcomes when there is poor overlap. In this work, we propose a class of one-step cross-fitted double/debiased machine learning estimators for the weighted cumulative causal effect as a function of restriction time. We prove that the proposed estimators are consistent, asymptotically linear, and reach semiparametric efficiency bounds under regularity conditions. Our simulations show that the proposed estimators using nonparametric machine learning nuisance models perform as well as established methods that require correctly-specified parametric nuisance models, illustrating that our estimators mitigate the need for oracle parametric nuisance models. We apply the proposed methods to real-world observational data from a UK primary care database to compare the effects of anti-diabetic drugs on cancer clinical outcomes.