4 个月前

基于高斯过程和签名协方差的贝叶斯序贯数据学习

摘要

我们开发了一种基于高斯过程（Gaussian Processes, GPs）的贝叶斯方法，通过使用所谓的签名核作为协方差函数来从序列数据中学习。这使得不同长度的序列可以进行比较，并且可以依赖随机分析中的强大理论结果。签名通过张量捕捉序列结构，但这些张量在序列长度和状态空间维度上可能会不利地扩展。为了解决这一问题，我们引入了一种带有诱导张量的稀疏变分方法。然后，我们将得到的高斯过程与长短期记忆网络（LSTMs）和门控循环单元（GRUs）相结合，构建更大的模型，以充分利用每种方法的优势，并在多变量时间序列（Time Series, TS）分类数据集上对这些高斯过程进行了基准测试。代码可在 https://github.com/tgcsaba/GPSig 获取。

代码仓库

tgcsaba/GPSig

官方

GitHub 中提及

基准测试

基准	方法	指标
time-series-classification-on	GP-Sig-LSTM	Accuracy: 0.991 NLL: 0.031
time-series-classification-on	GP-LSTM	Accuracy: 0.233 NLL: 2.506
time-series-classification-on	GP-KConv1D	Accuracy: 0.941 NLL: 0.409
time-series-classification-on	GP-Sig	Accuracy: 0.979 NLL: 0.108
time-series-classification-on	GP-Sig-GRU	Accuracy: 0.925 NLL: 0.258
time-series-classification-on	GP-GRU	Accuracy: 0.114 NLL: 3.523
time-series-classification-on-arabicdigits	GP-KConv1D	Accuracy: 0.984 NLL: 0.050
time-series-classification-on-arabicdigits	GP-LSTM	Accuracy: 0.985 NLL: 0.082
time-series-classification-on-arabicdigits	GP-Sig-GRU	Accuracy: 0.994 NLL: 0.023
time-series-classification-on-arabicdigits	GP-GRU	Accuracy: 0.986 NLL: 0.066
time-series-classification-on-arabicdigits	GP-Sig	Accuracy: 0.979 NLL: 0.071
time-series-classification-on-arabicdigits	GP-Sig-LSTM	Accuracy: 0.992 NLL: 0.047
time-series-classification-on-auslan	GP-Sig-GRU	Accuracy: 0.978 NLL: 0.123
time-series-classification-on-auslan	GP-KConv1D	Accuracy: 0.784 NLL: 1.900
time-series-classification-on-auslan	GP-Sig	Accuracy: 0.925 NLL: 0.550
time-series-classification-on-auslan	GP-LSTM	Accuracy: 0.880 NLL: 0.650
time-series-classification-on-auslan	GP-Sig-LSTM	Accuracy: 0.983 NLL: 0.106
time-series-classification-on-auslan	GP-GRU	Accuracy: 0.949 NLL: 0.248
time-series-classification-on-cmusubject16	GP-Sig-LSTM	Accuracy: 1.000 NLL: 0.088
time-series-classification-on-cmusubject16	GP-GRU	Accuracy: 0.993 NLL: 0.089
time-series-classification-on-cmusubject16	GP-Sig	Accuracy: 0.979 NLL: 0.089
time-series-classification-on-cmusubject16	GP-Sig-GRU	Accuracy: 1.000 NLL: 0.040
time-series-classification-on-cmusubject16	GP-LSTM	Accuracy: 0.924 NLL: 0.270
time-series-classification-on-cmusubject16	GP-KConv1D	Accuracy: 0.897 NLL: 0.255
time-series-classification-on-digitshapes	GP-Sig-LSTM	Accuracy: 1.000 NLL: 0.008
time-series-classification-on-digitshapes	GP-Sig-GRU	Accuracy: 1.000 NLL: 0.035
time-series-classification-on-digitshapes	GP-KConv1D	Accuracy: 1.000 NLL: 0.035
time-series-classification-on-digitshapes	GP-Sig	Accuracy: 1.000 NLL: 0.021
time-series-classification-on-digitshapes	GP-LSTM	Accuracy: 1.000 NLL: 0.013
time-series-classification-on-digitshapes	GP-GRU	Accuracy: 0.812 NLL: 0.727
time-series-classification-on-ecg	GP-KConv1D	Accuracy: 0.760 NLL: 0.543
time-series-classification-on-ecg	GP-LSTM	Accuracy: 0.782 NLL: 0.496
time-series-classification-on-ecg	GP-GRU	Accuracy: 0.734 NLL: 0.601
time-series-classification-on-ecg	GP-Sig-LSTM	Accuracy: 0.816 NLL: 0.402
time-series-classification-on-ecg	GP-Sig-GRU	Accuracy: 0.832 NLL: 0.431
time-series-classification-on-ecg	GP-Sig	Accuracy: 0.848 NLL: 0.356
time-series-classification-on-japanesevowels	GP-Sig-LSTM	Accuracy: 0.981 NLL: 0.080
time-series-classification-on-japanesevowels	GP-Sig	Accuracy: 0.982 NLL: 0.069
time-series-classification-on-japanesevowels	GP-KConv1D	Accuracy: 0.986 NLL: 0.067
time-series-classification-on-japanesevowels	GP-LSTM	Accuracy: 0.982 NLL: 0.061
time-series-classification-on-japanesevowels	GP-Sig-GRU	Accuracy: 0.985 NLL: 0.053
time-series-classification-on-japanesevowels	GP-GRU	Accuracy: 0.986 NLL: 0.052
time-series-classification-on-kickvspunch	GP-Sig-GRU	Accuracy: 0.820 NLL: 0.493
time-series-classification-on-kickvspunch	GP-LSTM	Accuracy: 0.620 NLL: 0.696
time-series-classification-on-kickvspunch	GP-KConv1D	Accuracy: 0.700 NLL: 0.662
time-series-classification-on-kickvspunch	GP-GRU	Accuracy: 0.600 NLL: 0.674
time-series-classification-on-kickvspunch	GP-Sig	Accuracy: 0.900 NLL: 0.224
time-series-classification-on-kickvspunch	GP-Sig-LSTM	Accuracy: 0.900 NLL: 0.301
time-series-classification-on-libras	GP-GRU	Accuracy: 0.742 NLL: 1.110
time-series-classification-on-libras	GP-Sig-LSTM	Accuracy: 0.921 NLL: 0.320
time-series-classification-on-libras	GP-Sig	Accuracy: 0.923 NLL: 0.259
time-series-classification-on-libras	GP-KConv1D	Accuracy: 0.698 NLL: 1.608
time-series-classification-on-libras	GP-LSTM	Accuracy: 0.776 NLL: 0.911
time-series-classification-on-libras	GP-Sig-GRU	Accuracy: 0.899 NLL: 0.346
time-series-classification-on-netflow	GP-LSTM	Accuracy: 0.928 NLL: 0.251
time-series-classification-on-netflow	GP-Sig	Accuracy: 0.937 NLL: 0.189
time-series-classification-on-netflow	GP-KConv1D	Accuracy: 0.945 NLL: 0.168
time-series-classification-on-netflow	GP-GRU	Accuracy: 0.926 NLL: 0.194
time-series-classification-on-netflow	GP-Sig-GRU	Accuracy: 0.921 NLL: 0.259
time-series-classification-on-netflow	GP-Sig-LSTM	Accuracy: 0.931 NLL: 0.218
time-series-classification-on-pems	GP-Sig	Accuracy: 0.820 NLL: 0.520
time-series-classification-on-pems	GP-GRU	Accuracy: 0.769 NLL: 0.784
time-series-classification-on-pems	GP-Sig-GRU	Accuracy: 0.775 NLL: 1.100
time-series-classification-on-pems	GP-Sig-LSTM	Accuracy: 0.763 NLL: 0.704
time-series-classification-on-pems	GP-LSTM	Accuracy: 0.745 NLL: 1.194
time-series-classification-on-pems	GP-KConv1D	Accuracy: 0.794 NLL: 0.537
time-series-classification-on-pendigits	GP-Sig-LSTM	Accuracy: 0.928 NLL: 0.289
time-series-classification-on-pendigits	GP-Sig-GRU	Accuracy: 0.902 NLL: 0.399
time-series-classification-on-pendigits	GP-KConv1D	Accuracy: 0.946 NLL: 0.181
time-series-classification-on-pendigits	GP-GRU	Accuracy: 0.951 NLL: 0.187
time-series-classification-on-pendigits	GP-Sig	Accuracy: 0.955 NLL: 0.146
time-series-classification-on-pendigits	GP-LSTM	Accuracy: 0.953 NLL: 0.185
time-series-classification-on-shapes	GP-KConv1D	Accuracy: 1.000 NLL: 0.012
time-series-classification-on-shapes	GP-Sig	Accuracy: 1.000 NLL: 0.011
time-series-classification-on-shapes	GP-GRU	Accuracy: 0.867 NLL: 0.168
time-series-classification-on-shapes	GP-Sig-GRU	Accuracy: 1.000 NLL: 0.012
time-series-classification-on-shapes	GP-LSTM	Accuracy: 1.000 NLL: 0.016
time-series-classification-on-shapes	GP-Sig-LSTM	Accuracy: 1.000 NLL: 0.014
time-series-classification-on-uwave	GP-GRU	Accuracy: 0.763 NLL: 1.168
time-series-classification-on-uwave	GP-LSTM	Accuracy: 0.870 NLL: 0.745
time-series-classification-on-uwave	GP-KConv1D	Accuracy: 0.947 NLL: 0.189
time-series-classification-on-uwave	GP-Sig	Accuracy: 0.964 NLL: 0.140
time-series-classification-on-uwave	GP-Sig-GRU	Accuracy: 0.968 NLL: 0.121
time-series-classification-on-uwave	GP-Sig-LSTM	Accuracy: 0.970 NLL: 0.113
time-series-classification-on-wafer	GP-LSTM	Accuracy: 0.966 NLL: 0.105
time-series-classification-on-wafer	GP-GRU	Accuracy: 0.994 NLL: 0.029
time-series-classification-on-wafer	GP-Sig-GRU	Accuracy: 0.978 NLL: 0.081
time-series-classification-on-wafer	GP-Sig	Accuracy: 0.965 NLL: 0.105
time-series-classification-on-wafer	GP-KConv1D	Accuracy: 0.984 NLL: 0.085
time-series-classification-on-wafer	GP-Sig-LSTM	Accuracy: 0.988 NLL: 0.048
time-series-classification-on-walkvsrun	GP-Sig-GRU	Accuracy: 1.000 NLL: 0.030
time-series-classification-on-walkvsrun	GP-GRU	Accuracy: 1.000 NLL: 0.028
time-series-classification-on-walkvsrun	GP-LSTM	Accuracy: 1.000 NLL: 0.048
time-series-classification-on-walkvsrun	GP-KConv1D	Accuracy: 1.000 NLL: 0.066
time-series-classification-on-walkvsrun	GP-Sig-LSTM	Accuracy: 1.000 NLL: 0.030
time-series-classification-on-walkvsrun	GP-Sig	Accuracy: 1.000 NLL: 0.023

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