This paper studies the problem of learning under both large datasets and large-dimensional feature space scenarios. The feature information is assumed to be spread across agents in a network, where each agent observes some of the features. Through local cooperation, the agents are supposed to interact with each other to solve an inference problem and converge towards the global minimizer of an empirical risk. We study this problem exclusively in the primal domain, and propose new and effective distributed solutions with guaranteed convergence to the minimizer with linear rate under strong convexity. This is achieved by combining a dynamic diffusion construction, a pipeline strategy, and variance-reduced techniques. Simulation results illustrate the conclusions.