  An important problem with machine learning is that when label number n>2, it
is very difficult to construct and optimize a group of learning functions, and
we wish that optimized learning functions are still useful when prior
distribution P(x) (where x is an instance) is changed. To resolve this problem,
the semantic information G theory, Logical Bayesian Inference (LBI), and a
group of Channel Matching (CM) algorithms together form a systematic solution.
A semantic channel in the G theory consists of a group of truth functions or
membership functions. In comparison with likelihood functions, Bayesian
posteriors, and Logistic functions used by popular methods, membership
functions can be more conveniently used as learning functions without the above
problem. In Logical Bayesian Inference (LBI), every label's learning is
independent. For Multilabel learning, we can directly obtain a group of
optimized membership functions from a big enough sample with labels, without
preparing different samples for different labels. A group of Channel Matching
(CM) algorithms is developed for machine learning. For the Maximum Mutual
Information (MMI) classification of three classes with Gaussian distributions
on a two-dimensional feature space, 2-3 iterations can make mutual information
between three classes and three labels surpass 99% of the MMI for most initial
partitions. For mixture models, the Expectation-Maximization (EM) algorithm is
improved and becomes the CM-EM algorithm, which can outperform the EM algorithm
when mixture ratios are imbalanced, or local convergence exists. The CM
iteration algorithm needs to combine neural networks for MMI classifications on
high-dimensional feature spaces. LBI needs further studies for the unification
of statistics and logic.
