, If X is (M S , ?)-learnable, then X is (M S , ? )-learnable for all ? ? ?

, If M minimizes K(M) + K(X|M), then X is (M, ?)-learnable for all ?

, If M S is empty (M S = )

, Partant de cette définition informelle, il est clair que les questions levées par l'analogie s'articulent en particulier autour d'une définition formelle de la similarité, et des conditions de validité de cette conjecture. La capacité de produire et de comprendre des analogies est une aptitude fondamentale partagée par les êtres humains, à tel point qu'elle est même utilisée comme une mesure de l'intelligence humaine (avec en particulier les tests de QI qui s'appuient majoritairement sur des analogies), Le terme raisonnement par analogie désigne toute forme de raisonnement établissant des parallèles entre deux domaines distincts et a priori décorrélés. L'idée fondamentale sous-jacente à l'analogie est que, si deux situations sont similaires sous certains aspects, elles doivent être similaires sous d'autres aspects, 1983.

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, Possibilité de collaboration pour les algorithmes de clustering

, Nous nous sommes donc interrogés sur le gain réel apporté par une collaboration. Nous avons exploité deux pistes. La première est celle de la réflexion sur les choix des collaborateurs. Nous avons proposé une modélisation simple du choix de collaborateurs. Dans ce contexte, nous supposons que chaque algorithme de clustering aurait possibilité de donner un poids aux autres algorithmes afin de sélectionner les meilleurs collaborateurs. Nous avons montré théoriquement que, dans ce modèle, un algorithme aurait tendance à privilégier les collaborations avec les algorithmes donnant les solutions les plus semblables. Cette observation peut sembler contre-intuitive : on s'attendrait en effet à ce qu'un algorithme cherche à collaborer avec des méthodes apportant une certaine diversité. Pourtant, ici le choix d'une stabilité est fait. La seconde est celle d'une réflexion sur la stabilité : l'idée est qu'une collaboration devrait augmenter la stabilité globale de la collaboration. Pour mesurer la stabilité, nous nous sommes appuyés sur les travaux de (Ben-David, Von Luxburg, and Pál, 2006) et les avons étendus pour recouvrir le domaine du clustering collaboratif. Nous avons en outre proposé quelques résultats préliminaires. En particulier, nous avons montré qu'une "faible" collaboration d'algorithmes stables restait stable. Cette notion imprécise de faiblesse est formalisée sous le nom de consistance et mesure l'écart entre la collaboration et l'absence de collaboration, La notion de collaboration en clustering est une notion difficile. En apprentissage supervisé, il peut être montré que la collaboration aide à l'apprentissage. Cela est dû en particulier au fait qu'une mesure supervisée est connue par le système apprenant. Le système sait en effet si les résultats sont corrects ou non

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