The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

Imagetic and affective measures of memory reverberation diverge at sleep onset in association with theta rhythm

The ‘day residue’ - the presence of waking memories into dreams - is a century-old concept that remains controver- sial in neuroscience. Even at the psychological level, it remains unclear how waking imagery cedes into dreams. Are visual and affective residues enhanced, modified, or erased at sleep onset? Are they linked, or dissociated? What are the neural correlates of these transformations? To address these questions we combined quantitative se- mantics, sleep EEG markers, visual stimulation, and multiple awakenings to investigate visual and affect residues in hypnagogic imagery at sleep onset. Healthy adults were repeatedly stimulated with an affective image, allowed to sleep and awoken seconds to minutes later, during waking (WK), N1 or N2 sleep stages. ‘Image Residue’ was objectively defined as the formal semantic similarity between oral reports describing the last image visualized before closing the eyes (‘ground image’), and oral reports of subsequent visual imagery (‘hypnagogic imagery). Similarly, ‘Affect Residue’ measured the proximity of affective valences between ‘ground image’ and ‘hypnagogic imagery’. We then compared these grounded measures of two distinct aspects of the ‘day residue’, calculated within participants, to randomly generated values calculated across participants. The results show that Image Residue persisted throughout the transition to sleep, increasing during N1 in proportion to the time spent in this stage. In contrast, the Affect Residue was gradually neutralized as sleep progressed, decreasing in proportion to the time spent in N1 and reaching a minimum during N2. EEG power in the theta band (4.5-6.5 Hz) was inversely correlated with the Image Residue during N1. The results show that the visual and affective aspects of the ‘day residue’ in hypnagogic imagery diverge at sleep onset, possibly decoupling visual contents from strong negative emotions, in association with increased theta rhythm.Neuroimag