Many real-world data represent sequences of interdependent events unfolding over time. They can be modeled naturally as realizations of a point process. Despite many potential applications, existing point process models are limited in their ability to capture complex patterns of interaction. Hawkes processes admit many efficient inference algorithms, but are limited to mutually excitatory effects. Nonlinear Hawkes processes allow for more complex influence patterns, but for their estimation it is typically necessary to resort to discrete-time approximations that may yield poor generative models. In this paper, we introduce the first general class of Bayesian point process models extended with a nonlinear component that allows both excitatory and inhibitory relationships in continuous time. We derive a fully Bayesian inference algorithm for these processes using Pólya-Gamma augmentation and Poisson thinning. We evaluate the proposed model on single and multi-neuronal spike train recordings. Results demonstrate that the proposed model, unlike existing point process models, can generate biologically-plausible spike trains, while still achieving competitive predictive likelihoods.

We study the problem of interactively learning a binary classifier using noisy labeling and pairwise comparison oracles, where the comparison oracle answers which one in the given two instances is more likely to be positive. Learning from such oracles has multiple applications where obtaining direct labels is harder but pairwise comparisons are easier, and the algorithm can leverage both types of oracles. In this paper, we attempt to characterize how the access to an easier comparison oracle helps in improving the label and total query complexity. We show that the comparison oracle reduces the learning problem to that of learning a threshold function. We then present an algorithm that interactively queries the label and comparison oracles and we characterize its query complexity under Tsybakov and adversarial noise conditions for the comparison and labeling oracles. Our lower bounds show that our label and total query complexity is almost optimal.

Neural Information Processing Systems http://nips.cc/

Many real-world data represent sequences of interdependent events unfolding over time. They can be modeled naturally as realizations of a point process. Despite many potential applications, existing point process models are limited in their ability to capture complex patterns of interaction. Hawkes processes admit many efficient inference algorithms, but are limited to mutually excitatory effects. Nonlinear Hawkes processes allow for more complex influence patterns, but for their estimation it is typically necessary to resort to discrete-time approximations that may yield poor generative models. In this paper, we introduce the first general class of Bayesian point process models extended with a nonlinear component that allows both excitatory and inhibitory relationships in continuous time. We derive a fully Bayesian inference algorithm for these processes using Pólya-Gamma augmentation and Poisson thinning. We evaluate the proposed model on single and multi-neuronal spike train recordings. Results demonstrate that the proposed model, unlike existing point process models, can generate biologically-plausible spike trains, while still achieving competitive predictive likelihoods.