Algorithmic machine teaching has been studied under the linear setting where exact teaching is possible. However, little is known for teaching nonlinear learners. Here, we establish the sample complexity of teaching, aka teaching dimension, for kernelized perceptrons for different families of feature maps. As a warm-up, we show that the teaching complexity is $\Theta(d)$ for the exact teaching of linear perceptrons in $\mathbb{R}^d$, and $\Theta(d^k)$ for kernel perceptron with a polynomial kernel of order $k$. Furthermore, under certain smooth assumptions on the data distribution, we establish a rigorous bound on the complexity for approximately teaching a Gaussian kernel perceptron. We provide numerical examples of the optimal (approximate) teaching set under several canonical settings for linear, polynomial and Gaussian kernel perceptrons.

Syntactic parsing using dependency structures has become a standard technique in natural language processing with many different parsing models, in particular data-driven models that can be trained on syntactically annotated corpora. In this paper, we tackle transition-based dependency parsing using a Perceptron Learner. Our proposed model, which adds more relevant features to the Perceptron Learner, outperforms a baseline arc-standard parser. We beat the UAS of the MALT and LSTM parsers. We also give possible ways to address parsing of non-projective trees.