相关论文: On the rate of convergence of image classifiers ba…
Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Here we consider images as random variables with…
Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the…
Pattern recognition based on a high-dimensional predictor is considered. A classifier is defined which is based on a Transformer encoder. The rate of convergence of the misclassification probability of the classifier towards the optimal…
Image classification from independent and identically distributed random variables is considered. Image classifiers are defined which are based on a linear combination of deep convolutional networks with max-pooling layer. Here all the…
Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also improve the theoretical understanding of neural networks.…
A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep recurrent neural…
The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…
High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive a nonasymptotic rate for the minimax excess misclassification risk when feature dimension…
Deep convolutional neural networks have proven to be well suited for image classification applications. However, if there is distortion in the image, the classification accuracy can be significantly degraded, even with state-of-the-art…
Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts…
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…
Image distortion classification and detection is an important task in many applications. For example when compressing images, if we know the exact location of the distortion, then it is possible to re-compress images by adjusting the local…
Classification for degraded images having various levels of degradation is very important in practical applications. This paper proposes a convolutional neural network to classify degraded images by using a restoration network and an…
The state-of-the-art approaches for image classification are based on neural networks. Mathematically, the task of classifying images is equivalent to finding the function that maps an image to the label it is associated with. To rigorously…
Image classification is considered, and a hierarchical max-pooling model with additional local pooling is introduced. Here the additional local pooling enables the hierachical model to combine parts of the image which have a variable…
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables,…
In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We…
Despite the success of convolutional neural networks (CNNs) in numerous computer vision tasks and their extraordinary generalization performances, several attempts to predict the generalization errors of CNNs have only been limited to a…
Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…
We investigate multiple techniques to improve upon the current state of the art deep convolutional neural network based image classification pipeline. The techiques include adding more image transformations to training data, adding more…