Research map / Learning theory and algorithms / Matrix and tensor methods
Dynamic matrix recovery from incomplete observations under an exact low-rank constraint
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Dynamic temporal weighting (LOWEMS) instead of using only the latest observations | low-rank matrix completion with time-varying V^t · synthetic matrix completion, small perturbation noise | relative recovery error: approximately factor of 4 reduction vs baseline one | Helped |
| Dynamic temporal weighting (LOWEMS) instead of using only the latest observations | low-rank matrix completion sample complexity · synthetic matrix completion, weak perturbation noise | sample complexity (fraction of observed entries p for relative error <= 0.04): reduced approximately by a factor of d compared to baseline one | Helped |
| Dynamic temporal weighting (LOWEMS) with large perturbation noise | low-rank matrix completion sample complexity · synthetic matrix completion, strong perturbation noise | sample complexity | No clear effect |
| Equal weighting across all time steps (baseline two) instead of LOWEMS weights | low-rank matrix completion with large perturbation noise · synthetic matrix completion | relative recovery error | Hurt |
| Dynamic temporal weighting (LOWEMS) instead of using only the latest observations | rank-5 Netflix recommendation with time bins d · truncated Netflix, testing RMSE | testing RMSE | Helped |
| Choice of kappa (perturbation-to-measurement noise ratio) for LOWEMS weights (ablation) | Netflix recommendation validation RMSE · truncated Netflix, validation | validation RMSE | Mixed |
| Dynamic weighting for matrix sensing with Gaussian ensembles | matrix sensing recovery error bound · Gaussian matrix sensing theory | recovery error bound | Helped |
| Matrix sensing: reported simulations for matrix sensing | LOWEMS matrix sensing · synthetic matrix sensing | relative recovery error | Helped |
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