This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which the learner operates, that is exploited by the learning algorithm together with the information available in the supervised examples. In particular, we consider a multi-task learning scheme, where multiple unary predicates on the feature space are to be learned by kernel machines and a higher level abstract representation consists of logic clauses on these predicates, known to hold for any input. A general approach is presented to convert the logic clauses into a continuous implementation, that processes the outputs computed by the kernel-based predicates. The learning task is formulated as a primal optimization problem of a loss function that combines a term measuring the fitting of the supervised examples, a regularization term, and a penalty term that enforces the constraints on both supervised and unsupervised examples. The proposed semi-supervised learning framework is particularly suited for learning in high dimensionality feature spaces, where the supervised training examples tend to be sparse and generalization difficult. Unlike for standard kernel machines, the cost function to optimize is not generally guaranteed to be convex. However, the experimental results show that it is still possible to find good solutions using a two stage learning schema, in which first the supervised examples are learned until convergence and then the logic constraints are forced. Some promising experimental results on artificial multi-task learning tasks are reported, showing how the classification accuracy can be effectively improved by exploiting the a priori rules and the unsupervised examples.

As far back as 3,500 years ago ancient Egyptian doctors were performing invasive surgeries. Even though our tools and knowledge have improved drastically over time, until very recently surgery was still a manual task for human hands. "We're on the verge of what we might call the second wave in surgical robotics," said Catherine Mohr, vice president of strategy at Intuitive Surgical, while speaking at Singularity University's Exponential Medicine conference this week. IBM Watson: Watson is an expert-system type of AI. Watson can store more medical information than any single human can store and and give responses to natural language queries from surgeons. Watson (or AI like it) will become an intelligent surgical assistant.