Meta-Neighborhoods

Making an adaptive prediction based on one's input is an important ability for general artificial intelligence. In this work, we step forward in this direction and propose a semi-parametric method, Meta-Neighborhoods, where predictions are made adaptively to the neighborhood of the input. We show that Meta-Neighborhoods is a generalization of $k$-nearest-neighbors. Due to the simpler manifold structure around a local neighborhood, Meta-Neighborhoods represent the predictive distribution $p(y \mid x)$ more accurately. To reduce memory and computation overhead, we propose induced neighborhoods that summarize the training data into a much smaller dictionary. A meta-learning based training mechanism is then exploited to jointly learn the induced neighborhoods and the model. Extensive studies demonstrate the superiority of our method.