Research map / Learning theory and algorithms / Matrix and tensor methods
Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimality
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use data-driven plug-in variance estimates from residuals and the estimated tensor factors | Nonconvex tensor completion · Synthetic tensor completion, tensor-factor entries | 95% confidence-interval coverage: 0.9481; 0.9477; 0.9478; 0.9450; 0.9472; 0.9462 | No clear effect |
| Use data-driven plug-in variance estimates from residuals and the estimated tensor factors | Nonconvex tensor completion · Synthetic tensor completion, tensor entries | 95% confidence-interval coverage: 0.9494; 0.9513; 0.9475; 0.9434; 0.9494; 0.9494 | No clear effect |
| Use nonconvex completion with the proposed estimator | Tensor factors and completed tensor · Noisy tensor completion under i.i.d. Gaussian noise | ℓ2 estimation risk: 2+o(1); 6+o(1) | Helped |
| Adapt confidence intervals to local noise levels using residual-based variance estimates | Nonconvex tensor completion · Heteroscedastic tensor completion | confidence-interval validity | Helped |
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