Reasoning with Co-variations

Case-based prediction – A survey

“…such as adaptation rules [7, 27, 73, 90], co-variations [5], or dependencies between analogical proportions [9,17]. Some case-based adaptation approaches implement this strategy, as well as analogical proportion-based classifiers.…”

“…these rules can be written (σ S = α) → (σ R = β) and can be expressed in various forms, such as adaptation rules [7,27,73,90], dependencies between problem and solution features [42], co-variations [5] or fuzzy rules [16] to name a few. The prediction strategy consists in triggering the rules on pairs of cases involving 405 the new case using a kind of similarity-based inference, as detailed below, in order to derive potential outcomes for the new case.…”

“…Several works [11,17,28,91] have emphasized the idea that the rules ( σ S = α) → ( σ R = β) that are reasoned upon should be functional dependencies, i.e., have a confidence value of 1 on any two pairs of cases of the case base. From this observation, [5] defined a variation as any function that associates a value to a pair of situations, and a co-variation as a functional dependency between variations. For example, the variation nb rooms ≤ : S × S → {0, 1} maps a pair of apartments to 1 if the number of rooms increases, and to 0 otherwise, and the co-variation (nb rooms ≤ = 1) → (price ≤ = 1) expresses that if the number of rooms of an apartment increases, then the price also increases.…”

“…Learning such co-variations from data corresponds to the task called gradual pattern mining, for which various meanings and approaches have been proposed [5,14,29,63,78].…”

On the Role of Similarity in Analogical Transfer

“…If each " υi is the identity relation, then a co-variation is a functional dependency [1] between the two values " υ i pabq and k " υ j pabq, and the co-variation υ i ab ñ υ j can be written pυ i : q ab ñ pυ j : kq. For example, the co-variation…”