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Bootstrap Model Aggregation for Distributed Statistical Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add positive probability-ratio weights to the bootstrap M-estimator | KL-Naive · Distributed statistical learning | MSE rate: O(N^{-1}+(dn)^{-1}) -> O(N^{-1}+(dn^2)^{-1}) | Helped |
| Add a linear control-variate correction based on bootstrapped local MLEs | KL-Naive · Distributed statistical learning | MSE rate: O(N^{-1}+(dn)^{-1}) -> O(N^{-1}+(dn^{2})^{-1}) | Helped |
| Use bootstrap samples without variance reduction | KL-Naive · Distributed statistical learning | MSE rate: O(N^{-1}+(dn)^{-1}) | Hurt |
| Use KL-Weighted instead of KL-Naive when local GMM component counts are selected by BIC | GMM with unknown number of components · GMM with unknown number of components | testing log likelihood | Helped |
| Use KL-Weighted and applicable KL-Control rather than the other tested methods | Real-world datasets · SensIT Vehicle, Covertype, and Epsilon | testing log likelihood | Helped |
| Increase bootstrap sample size n | KL-Weighted · Simulated PPCA, mixture of PPCA, and GMM | MSE: O(n^{-2}) | Helped |
| Increase bootstrap sample size n | KL-Naive · Simulated PPCA, mixture of PPCA, and GMM | MSE: O(n^{-1}) | Helped |
| Increase the number of local machines while holding n fixed | KL-Naive and KL-Weighted · Simulated data | MSE: O(d^{-1}) | Helped |
| Increase the number of machines while holding total bootstrap size fixed | KL-Weighted · Simulated data | MSE: O(d n_{\mathrm{tot}}^{-2}) | Hurt |
| Increase the number of machines while holding total bootstrap size fixed | KL-Naive · Simulated data | MSE: O(n_{\mathrm{tot}}^{-1}) | No clear effect |
| Increase α in n = (N/d)^α | KL-Weighted · Simulated data | MSE relative to global MLE | Helped |
| Increase α in n = (N/d)^α | KL-Naive · Simulated data | MSE relative to global MLE | Helped |
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