On the rates of convergence for learning with convolutional neural networks
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908467775668224 |
|---|---|
| author | Yang, Yunfei Feng, Han Zhou, Ding-Xuan |
| author_facet | Yang, Yunfei Feng, Han Zhou, Ding-Xuan |
| contents | We study approximation and learning capacities of convolutional neural networks (CNNs) with one-side zero-padding and multiple channels. Our first result proves a new approximation bound for CNNs with certain constraint on the weights. Our second result gives new analysis on the covering number of feed-forward neural networks with CNNs as special cases. The analysis carefully takes into account the size of the weights and hence gives better bounds than the existing literature in some situations. Using these two results, we are able to derive rates of convergence for estimators based on CNNs in many learning problems. In particular, we establish minimax optimal convergence rates of the least squares based on CNNs for learning smooth functions in the nonparametric regression setting. For binary classification, we derive convergence rates for CNN classifiers with hinge loss and logistic loss. It is also shown that the obtained rates for classification are minimax optimal in some common settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rates of convergence for learning with convolutional neural networks Yang, Yunfei Feng, Han Zhou, Ding-Xuan Machine Learning Statistics Theory We study approximation and learning capacities of convolutional neural networks (CNNs) with one-side zero-padding and multiple channels. Our first result proves a new approximation bound for CNNs with certain constraint on the weights. Our second result gives new analysis on the covering number of feed-forward neural networks with CNNs as special cases. The analysis carefully takes into account the size of the weights and hence gives better bounds than the existing literature in some situations. Using these two results, we are able to derive rates of convergence for estimators based on CNNs in many learning problems. In particular, we establish minimax optimal convergence rates of the least squares based on CNNs for learning smooth functions in the nonparametric regression setting. For binary classification, we derive convergence rates for CNN classifiers with hinge loss and logistic loss. It is also shown that the obtained rates for classification are minimax optimal in some common settings. |
| title | On the rates of convergence for learning with convolutional neural networks |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2403.16459 |