1,345 research outputs found
End-to-End Kernel Learning with Supervised Convolutional Kernel Networks
In this paper, we introduce a new image representation based on a multilayer
kernel machine. Unlike traditional kernel methods where data representation is
decoupled from the prediction task, we learn how to shape the kernel with
supervision. We proceed by first proposing improvements of the
recently-introduced convolutional kernel networks (CKNs) in the context of
unsupervised learning; then, we derive backpropagation rules to take advantage
of labeled training data. The resulting model is a new type of convolutional
neural network, where optimizing the filters at each layer is equivalent to
learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We
show that our method achieves reasonably competitive performance for image
classification on some standard "deep learning" datasets such as CIFAR-10 and
SVHN, and also for image super-resolution, demonstrating the applicability of
our approach to a large variety of image-related tasks.Comment: to appear in Advances in Neural Information Processing Systems (NIPS
Doctor of Philosophy
dissertationThe contributions in the area of kernelized learning techniques have expanded beyond a few basic kernel functions to general kernel functions that could be learned along with the rest of a statistical learning model. This dissertation aims to explore various directions in \emph{kernel learning}, a setting where we can learn not only a model, but also glean information about the geometry of the data from which we learn, by learning a positive definite (p.d.) kernel. Throughout, we can exploit several properties of kernels that relate to their \emph{geometry} -- a facet that is often overlooked. We revisit some of the necessary mathematical background required to understand kernel learning in context, such as reproducing kernel Hilbert spaces (RKHSs), the reproducing property, the representer theorem, etc. We then cover kernelized learning with support vector machines (SVMs), multiple kernel learning (MKL), and localized kernel learning (LKL). We move on to Bochner's theorem, a tool vital to one of the kernel learning areas we explore. The main portion of the thesis is divided into two parts: (1) kernel learning with SVMs, a.k.a. MKL, and (2) learning based on Bochner's theorem. In the first part, we present efficient, accurate, and scalable algorithms based on the SVM, one that exploits multiplicative weight updates (MWU), and another that exploits local geometry. In the second part, we use Bochner's theorem to incorporate a kernel into a neural network and discover that kernel learning in this fashion, continuous kernel learning (CKL), is superior even to MKL
Neural Generalization of Multiple Kernel Learning
Multiple Kernel Learning is a conventional way to learn the kernel function
in kernel-based methods. MKL algorithms enhance the performance of kernel
methods. However, these methods have a lower complexity compared to deep
learning models and are inferior to these models in terms of recognition
accuracy. Deep learning models can learn complex functions by applying
nonlinear transformations to data through several layers. In this paper, we
show that a typical MKL algorithm can be interpreted as a one-layer neural
network with linear activation functions. By this interpretation, we propose a
Neural Generalization of Multiple Kernel Learning (NGMKL), which extends the
conventional multiple kernel learning framework to a multi-layer neural network
with nonlinear activation functions. Our experiments on several benchmarks show
that the proposed method improves the complexity of MKL algorithms and leads to
higher recognition accuracy
Bridging deep and kernel methods
There has been some exciting major progress in recent years in data analysis methods, including a variety of deep learning architectures, as well as further advances in kernel-based learning methods, which have demonstrated predictive superiority. In this paper we provide a brief
motivated survey of recent proposals to explicitly or implicitly combine kernel methods with the notion of deep learning networks.Peer ReviewedPostprint (author's final draft
Invariance of Weight Distributions in Rectified MLPs
An interesting approach to analyzing neural networks that has received
renewed attention is to examine the equivalent kernel of the neural network.
This is based on the fact that a fully connected feedforward network with one
hidden layer, a certain weight distribution, an activation function, and an
infinite number of neurons can be viewed as a mapping into a Hilbert space. We
derive the equivalent kernels of MLPs with ReLU or Leaky ReLU activations for
all rotationally-invariant weight distributions, generalizing a previous result
that required Gaussian weight distributions. Additionally, the Central Limit
Theorem is used to show that for certain activation functions, kernels
corresponding to layers with weight distributions having mean and finite
absolute third moment are asymptotically universal, and are well approximated
by the kernel corresponding to layers with spherical Gaussian weights. In deep
networks, as depth increases the equivalent kernel approaches a pathological
fixed point, which can be used to argue why training randomly initialized
networks can be difficult. Our results also have implications for weight
initialization.Comment: ICML 201
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