在数学,统计学和计算机科学中,尤其是在机器学习和逆问题中,正则化是添加信息以解决不适定问题或防止过度拟合的过程。 正则化适用于不适定的优化问题中的目标函数。

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题目: CAST: A Correlation-based Adaptive Spectral Clustering Algorithm on Multi-scale Data

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本文研究了利用光谱聚类方法对多尺度数据进行聚类的问题。传统的光谱聚类技术通过处理一个反映物体接近度的相似矩阵来发现聚类。对于多尺度数据,基于距离的相似度是无效的,因为稀疏聚类的对象可能相距很远,而密集聚类的对象必须足够近。可以通过将物体的“可达相似性”概念与给定的基于距离的相似性相结合,得到物体的系数矩阵,解决了多尺度数据的光谱聚类问题。本文提出了利用轨迹套索对系数矩阵进行正则化的算法CAST。证明了所得到的系数矩阵具有“分组效应”和“稀疏性”。我们表明,这两个特征意味着非常有效的光谱聚类。我们评估CAST和其它10种聚类方法在广泛的数据集w.r.t.各种应用。实验结果表明,该算法在多尺度数据的测试用例中具有良好的鲁棒性。

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Estimation of the value-at-risk (VaR) of a large portfolio of assets is an important task for financial institutions. As the joint log-returns of asset prices can often be projected to a latent space of a much smaller dimension, the use of a variational autoencoder (VAE) for estimating the VaR is a natural suggestion. To ensure the bottleneck structure of autoencoders when learning sequential data, we use a temporal VAE (TempVAE) that avoids an auto-regressive structure for the observation variables. However, the low signal- to-noise ratio of financial data in combination with the auto-pruning property of a VAE typically makes the use of a VAE prone to posterior collapse. Therefore, we propose to use annealing of the regularization to mitigate this effect. As a result, the auto-pruning of the TempVAE works properly which also results in excellent estimation results for the VaR that beats classical GARCH-type and historical simulation approaches when applied to real data.

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Estimation of the value-at-risk (VaR) of a large portfolio of assets is an important task for financial institutions. As the joint log-returns of asset prices can often be projected to a latent space of a much smaller dimension, the use of a variational autoencoder (VAE) for estimating the VaR is a natural suggestion. To ensure the bottleneck structure of autoencoders when learning sequential data, we use a temporal VAE (TempVAE) that avoids an auto-regressive structure for the observation variables. However, the low signal- to-noise ratio of financial data in combination with the auto-pruning property of a VAE typically makes the use of a VAE prone to posterior collapse. Therefore, we propose to use annealing of the regularization to mitigate this effect. As a result, the auto-pruning of the TempVAE works properly which also results in excellent estimation results for the VaR that beats classical GARCH-type and historical simulation approaches when applied to real data.

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