Hawkes processes are a class of auto-regressive point processes that are commonly used in modeling data in which events tend to cluster and influence the likelihood of future events. Because of their ability to model and explain how events or processes can influence each other, Hawkes processes (and their multivariate extensions) have been applied in a variety of practical applications such as analyzing financial time series, communication networks, and biological networks, to name just a few. In practice, the dynamics of such systems often depend on external factors that may change over time and that may drive different kinds of behavior. In this paper, we consider a switched Hawkes process which can be used to model systems in which the parameters of the process dynamically change depending on some (known) external state. We propose a simple maximum likelihood estimation approach which we validate using synthetic simulations. We then apply our model to a real-world traffic sensor dataset to study traffic patterns during different configurations of the traffic lights at an intersection.

Active learning is commonly used to train label-efficient models by adaptively selecting the most informative queries. However, most active learning strategies are designed to either learn a representation of the data (e.g., embedding or metric learning) or perform well on a task (e.g., classification) on the data. However, many machine learning tasks involve a combination of both representation learning and a task-specific goal. Motivated by this, we propose a novel unified query framework that can be applied to any problem in which a key component is learning a representation of the data that reflects similarity. Our approach builds on similarity or nearest neighbor (NN) queries which seek to select samples that result in improved embeddings. The queries consist of a reference and a set of objects, with an oracle selecting the object most similar (i.e., nearest) to the reference. In order to reduce the number of solicited queries, they are chosen adaptively according to an information theoretic criterion. We demonstrate the effectiveness of the proposed strategy on two tasks -active metric learning and active classificationusing a variety of synthetic and real world datasets. In particular, we demonstrate that actively selected NN queries outperform recently developed active triplet selection methods in a deep metric learning setting. Further, we show that in classification, actively selecting class labels can be reformulated as a process of selecting the most informative NN query, allowing direct application of our method.

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