Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM.
Identifying influential nodes is an important topic in many diverse applications, such as accelerating information propagation, controlling rumors and diseases. Many methods have been put forward to identify influential nodes in complex networks, ranging from node centrality to diffusion-based processes. However, most of the previous studies do not take into account overlapping communities in networks. In this paper, we propose an effective method based on network representation learning. The method considers not only the overlapping communities in networks, but also the network structure. Experiments on real-world networks show that the proposed method outperforms many benchmark algorithms and can be used in large-scale networks.
Area Under the ROC Curve (AUC) is a widely used metric for measuring classification performance. It has important theoretical and academic values to develop AUC maximization algorithms. Traditional methods often apply batch learning algorithm to maximize AUC which is inefficient and unscalable for large-scale applications. Recently some online learning algorithms have been introduced to maximize AUC by going through the data only once. However, these methods sometimes fail to converge to an optimal solution due to the fixed or rapid decay of learning rates. To tackle this problem, we propose an algorithm AdmOAM, Adaptive Moment estimation method for Online AUC Maximization. It applies the estimation of moments of gradients to accelerate the convergence and mitigates the rapid decay of the learning rates. We establish the regret bound of the proposed algorithm and implement extensive experiments to demonstrate its effectiveness and efficiency.
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