Atsushi Suzuki

Takayuki Katsuki, Kohei Miyaguchi, Akira Koseki et al.

We address the problem of predicting when a disease will develop, i.e., medical event time (MET), from a patient's electronic health record (EHR). The MET of non-communicable diseases like diabetes is highly correlated to cumulative health conditions, more specifically, how much time the patient spent with specific health conditions in the past. The common time-series representation is indirect in extracting such information from EHR because it focuses on detailed dependencies between values in successive observations, not cumulative information. We propose a novel data representation for EHR called cumulative stay-time representation (CTR), which directly models such cumulative health conditions. We derive a trainable construction of CTR based on neural networks that has the flexibility to fit the target data and scalability to handle high-dimensional EHR. Numerical experiments using synthetic and real-world datasets demonstrate that CTR alone achieves a high prediction performance, and it enhances the performance of existing models when combined with them.

Atsushi Suzuki, Atsushi Nitanda, Taiji Suzuki et al.

Recent studies have experimentally shown that we can achieve in non-Euclidean metric space effective and efficient graph embedding, which aims to obtain the vertices' representations reflecting the graph's structure in the metric space. Specifically, graph embedding in hyperbolic space has experimentally succeeded in embedding graphs with hierarchical-tree structure, e.g., data in natural languages, social networks, and knowledge bases. However, recent theoretical analyses have shown a much higher upper bound on non-Euclidean graph embedding's generalization error than Euclidean one's, where a high generalization error indicates that the incompleteness and noise in the data can significantly damage learning performance. It implies that the existing bound cannot guarantee the success of graph embedding in non-Euclidean metric space in a practical training data size, which can prevent non-Euclidean graph embedding's application in real problems. This paper provides a novel upper bound of graph embedding's generalization error by evaluating the local Rademacher complexity of the model as a function set of the distances of representation couples. Our bound clarifies that the performance of graph embedding in non-Euclidean metric space, including hyperbolic space, is better than the existing upper bounds suggest. Specifically, our new upper bound is polynomial in the metric space's geometric radius $R$ and can be $O(\frac{1}{S})$ at the fastest, where $S$ is the training data size. Our bound is significantly tighter and faster than the existing one, which can be exponential to $R$ and $O(\frac{1}{\sqrt{S}})$ at the fastest. Specific calculations on example cases show that graph embedding in non-Euclidean metric space can outperform that in Euclidean space with much smaller training data than the existing bound has suggested.