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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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Bayes Theorem and the cMPE-Method: Differences, Complementarities and the Importance of Discerning between Weight-bearing and Extensional Evidence
R. Gottlob · 2004-06-07 · via math.ST updates on arXiv.org

Both, Bayes Theorem and the cMPE-Method serve for establishing relations between systems of probabilities. By the cMPE-Method non-conditional probabilities are added, by the DPE-Method, they are subtracted, however, in both versions allowing for the non-linearity of non-disjunctive probabilities. Semantic independence is prerequisite. As compared with the results of semantically homogeneous series of observations, the variety of evidence permits arrival at higher probabilities. The advantage of the Bayesian method lies in allowing for evidence extraneous to the domain covered by the hypothesis. We must differentiate between extensional and weight-bearing evidence. Operations based on purely weight-bearing evidence (cMPE-Method) neglect the extensional evidence and some operations according to Bayes Theorem may neglect weight-bearing evidence at least partially. These and some other shortcomings may be remedied by operations, combining both of the approaches.

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