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We consider a regression problem, where the correspondence between the input and output data is not available. Such shuffled data are commonly observed in many real world problems. Take flow cytometry as an example: the measuring instruments are unable to preserve the correspondence between the samples and the measurements. Due to the combinatorial nature of the problem, most of the existing methods are only applicable when the sample size is small, and are limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework --- ROBOT --- for the shuffled regression problem, which is applicable to large data and complex models. Specifically, we propose to formulate regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we propose to develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression model, and therefore it allows us to find a better descent direction for the model parameters by differentiating through the data correspondence. ROBOT is quite general, and can be further extended to an inexact correspondence setting, where the input and output datamore »are not necessarily exactly aligned. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking.« less

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often ex- hibit complicated short-term and long-term temporal dependencies. However, most of the ex- isting recurrent neural network-based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long- term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorpo- rate additional structural knowledge. We provide a concrete example, where THP achieves im- proved prediction performance for learning multiple point processes when incorporating their relational information.