This letter proposes a one-shot algorithm for feature-distributed kernel PCA. Our algorithm is inspired by the dual relationship between sample-distributed and feature-distributed scenarios. This interesting relations...
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This letter proposes a one-shot algorithm for feature-distributed kernel PCA. Our algorithm is inspired by the dual relationship between sample-distributed and feature-distributed scenarios. This interesting relationship makes it possible to establish distributed kernel PCA for feature-distributed cases from ideas of distributed PCA in the sample-distributed scenario. In the theoretical part, we analyze the approximation error for both linear and RBF kernels. The result suggests that when eigenvalues decay fast, the proposed algorithm gives high-quality results with low communication cost. This result is also verified by numerical experiments, showing the effectiveness of our algorithm in practice.
To estimate accurately the parameters of a regression model, the sample size must be large enough relative to the number of possible predictors for the model. In practice, sufficient data is often lacking, which can l...
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To estimate accurately the parameters of a regression model, the sample size must be large enough relative to the number of possible predictors for the model. In practice, sufficient data is often lacking, which can lead to overfitting of the model and, as a consequence, unreliable predictions of the outcome of new patients. Pooling data from different data sets collected in different (medical) centers would alleviate this problem, but is often not feasible due to privacy regulation or logistic problems. An alternative route would be to analyze the local data in the centers separately and combine the statistical inference results with the Bayesian Federated Inference (BFI) methodology. The aim of this approach is to compute from the inference results in separate centers what would have been found if the statistical analysis was performed on the combined data. We explain the methodology under homogeneity and heterogeneity across the populations in the separate centers, and give real life examples for better understanding. Excellent performance of the proposed methodology is shown. An R-package to do all the calculations has been developed and is illustrated in this article. The mathematical details are given in the Appendix.
For original paper, see D.P. Palomar et al., ibid., vol. 35, no. 13, pp. 1058-9 (1999). Palomar et al. addressed the question of LPC filter re-optimisation and proposed a recursive algorithm that they considered promi...
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For original paper, see D.P. Palomar et al., ibid., vol. 35, no. 13, pp. 1058-9 (1999). Palomar et al. addressed the question of LPC filter re-optimisation and proposed a recursive algorithm that they considered promising. The present commentator shows that the iterative algorithm employed by Palomar is unnecessarily complex because of poor initialisation. The algorithm that uses available speech data at the very first step is shown to perform well. The results of the one-shot algorithm can be used to initiate Paolmar's method to significantly reduce the number of iterations
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