Personalized recommendation has received a lot of attention as a highly practical research topic. However, existing recommender systems provide the recommendations with a generic statement such as “Customers who bought this item also bought…”. Explainable recommendation, which makes a user aware of why such items are recommended, is in demand. The goal of our research is to make the users feel as if they are receiving recommendations from their friends. To this end, we formulate a new challenging problem called personalized reason generation for explainable recommendation for songs in conversation applications and propose a solution that generates a natural language explanation of the reason for recommending a song to that particular user. For example, if the user is a student, our method can generate an output such as “Campus radio plays this song at noon every day, and I think it sounds wonderful,” which the student may find easy to relate to. In the offline experiments, through manual assessments, the gain of our method is statistically significant on the relevance to songs and personalization to users comparing with baselines. Large-scale online experiments show that our method outperforms manually selected reasons by 8.2% in terms of click-through rate. Evaluation results indicate that our generated reasons are relevant to songs and personalized to users, and they attract users to click the recommendations.
Partial differential equations (PDEs) are essential foundations to model dynamic processes in natural sciences. Discovering the underlying PDEs of complex data collected from real world is key to understanding the dynamic processes of natural laws or behaviors. However, both the collected data and their partial derivatives are often corrupted by noise, especially from sparse outlying entries, due to measurement/process noise in the real-world applications. Our work is motivated by the observation that the underlying data modeled by PDEs are in fact often low rank. We thus develop a robust low-rank discovery framework to recover both the low-rank data and the sparse outlying entries by integrating double low-rank and sparse recoveries with a (group) sparse regression method, which is implemented as a minimization problem using mixed nuclear norms with ℓ1 and ℓ0 norms. We propose a low-rank sequential (grouped) threshold ridge regression algorithm to solve the minimization problem. Results from several experiments on seven canonical models (i.e., four PDEs and three parametric PDEs) verify that our framework outperforms the state-of-art sparse and group sparse regression methods. Code is available at https://github.com/junli2019/Robust-Discovery-of-PDEs
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