Semantic Information G Theory and Logical Bayesian Inference for Machine Learning

An important problem with machine learning is that when label number n\u3e2, 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. MultilabelMultilabel 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 are 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-Maxmization (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

Semantic Information Measure with Two Types of Probability for Falsification and Confirmation

Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional LP function). The Semantic Information Measure (SIM) proposed is compatible with Shannon’s information theory and Fisher’s likelihood method. It can ensure that the less the LP of a predicate is and the larger the true value of the proposition is, the more information there is. So the SIM can be used as Popper's information criterion for falsification or test. The SIM also allows us to optimize the true-value of counterexamples or degrees of disbelief in a hypothesis to get the optimized degree of belief, i. e. Degree of Confirmation (DOC). To explain confirmation, this paper 1) provides the calculation method of the DOC of universal hypotheses; 2) discusses how to resolve Raven Paradox with new DOC and its increment; 3) derives the DOC of rapid HIV tests: DOC of “+” =1-(1-specificity)/sensitivity, which is similar to Likelihood Ratio (=sensitivity/(1-specificity)) but has the upper limit 1; 4) discusses negative DOC for excessive affirmations, wrong hypotheses, or lies; and 5) discusses the DOC of general hypotheses with GPS as example

Scheduling uncertain orders in the customer–subcontractor context

Within the customer–subcontractor negotiation process, the first problem of the subcontractor is to provide the customer with a reliable order lead-time although his workload is partially uncertain. Actually, a part of the subcontractor workload is composed of orders under negotiation which can be either confirmed or cancelled. Fuzzy logic and possibility theory have widely been used in scheduling in order to represent the uncertainty or imprecision of processing times, but the existence of the manufacturing orders is not usually set into question. We suggest a method allowing to take into account the uncertainty of subcontracted orders. This method is consistent with list scheduling: as a consequence, it can be used in many classical schedulers. Its implementation in a scheduler prototype called TAPAS is described. In this article, we focus on the performance of validation tests which show the interest of the method

Children’s ability to recall unique aspects of one occurrence of a repeated event

Preschool and school-age children’s memory and source monitoring were investigated by questioning them about one occurrence of a repeated lab event (n = 39). Each of the four occurrences had the same structure, but with varying alternatives for the specific activities and items presented. Variable details had a different alternative each time; hi/lo details presented the identical alternative three times and changed once. New details were present in one occurrence only and thus had no alternatives. Children more often confused variable, lo, and new details across occurrences than hi details. The 4- to 5-year-oldchildren were less accurate than 7- to 8-year-old children at attributing details to the correct occurrence when specifically asked. Younger children rarely recalled new details spontaneously, whereas 50% of the older children did and were above chance at attributing them to their correct occurrence. Results are discussed with reference to script theory, fuzzy-trace theory and the source-monitoring framework