Intrinsic Signal Models Defined by the High-Dimensional, Small-Sample Limit
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915515063074816 |
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| author | Mototake, Yoh-ichi Taguchi, Y-h. |
| author_facet | Mototake, Yoh-ichi Taguchi, Y-h. |
| contents | The detection of a signal variable from multiple variables that contain many noise variables is often approached as a variable selection problem under a given objective variable. This is nothing more than building a supervised model of a signal by specifying the signal as the objective variable. On the other hand, such a supervised model does not work effectively under high-dimensional and small-sample-size conditions, as the estimation of model parameters becomes indeterminate. We propose an ``intrinsic signal model'' that enables signal detection under high-dimensional and small-sample-size conditions without external signal definitions. The proposed intrinsic signal model is based on the assumption that the datasets in this world are generated from a certain dynamical system, and variables generated from dynamical systems with small correlation lengths are considered noisy variables. That is, the variables that maintain the data structure generated from a dynamical system under high-dimensional and small-sample-size conditions, corresponding to the limit of a sample size of 0, are modeled as always signal variables. In this study, we showed that with such a signal model, the Taguchi method provides an effective way of detecting signals. The proposed signal model was validated by generating a dataset with a globally coupled map system, which is a high-dimensional dynamical system. Furthermore, we validated the model with Gene Expression Data which are not explicitly generated from a dynamical system; as a result, we observed a signal structure consistent with that of the signal model proposed in this study. The results suggest that the proposed signal model is valid for a wide range of datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06522 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Intrinsic Signal Models Defined by the High-Dimensional, Small-Sample Limit Mototake, Yoh-ichi Taguchi, Y-h. Data Analysis, Statistics and Probability Machine Learning The detection of a signal variable from multiple variables that contain many noise variables is often approached as a variable selection problem under a given objective variable. This is nothing more than building a supervised model of a signal by specifying the signal as the objective variable. On the other hand, such a supervised model does not work effectively under high-dimensional and small-sample-size conditions, as the estimation of model parameters becomes indeterminate. We propose an ``intrinsic signal model'' that enables signal detection under high-dimensional and small-sample-size conditions without external signal definitions. The proposed intrinsic signal model is based on the assumption that the datasets in this world are generated from a certain dynamical system, and variables generated from dynamical systems with small correlation lengths are considered noisy variables. That is, the variables that maintain the data structure generated from a dynamical system under high-dimensional and small-sample-size conditions, corresponding to the limit of a sample size of 0, are modeled as always signal variables. In this study, we showed that with such a signal model, the Taguchi method provides an effective way of detecting signals. The proposed signal model was validated by generating a dataset with a globally coupled map system, which is a high-dimensional dynamical system. Furthermore, we validated the model with Gene Expression Data which are not explicitly generated from a dynamical system; as a result, we observed a signal structure consistent with that of the signal model proposed in this study. The results suggest that the proposed signal model is valid for a wide range of datasets. |
| title | Intrinsic Signal Models Defined by the High-Dimensional, Small-Sample Limit |
| topic | Data Analysis, Statistics and Probability Machine Learning |
| url | https://arxiv.org/abs/2304.06522 |