In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step size in each iteration can play a role of regularization to ensure the generalization ability of online learning algorithm. We develop a novel capacity dependen...

Within-Class Covariance Normalization (WCCN) is a powerful post-processing method for normalizing the within-class covariance of a set of data points. WCCN projects the observations into a linear sub-space where the within-class variability is reduced. This property has proven to be beneficial in subsequent recognition tasks. The central idea of this paper is to reformulate the classic WCCN as ...

For most deep learning algorithms training is notoriously time consuming. Since most of the computation in training neural networks is typically spent on floating point multiplications, we investigate an approach to training that eliminates the need for most of these. Our method consists of two parts: First we stochastically binarize weights to convert multiplications involved in computing hidd...

We present a novel semi-supervised training algorithm for learning dependency parsers. By combining a supervised large margin loss with an unsupervised least squares loss, a discriminative, convex, semi-supervised learning algorithm can be obtained that is applicable to large-scale problems. To demonstrate the benefits of this approach, we apply the technique to learning dependency parsers from...

Label propagation is a powerful and flexible semi-supervised learning technique on graphs. Neural network architectures, on the other hand, have proven track records in many supervised learning tasks. In this work, we propose a training objective for neural networks, Neural Graph Machines, for combining the power of neural networks and label propagation. The new objective allows the neural netw...

Even though there is a plethora of research in Microarray gene expression data analysis, still, it poses challenges for researchers to effectively and efficiently analyze the large yet complex expression of genes. The feature (gene) selection method is of paramount importance for understanding the differences in biological and non-biological variation between samples. In order to address this p...

Recent works have highlighted scale invariance or symmetry that is present in the weight space of a typical deep network and the adverse effect that it has on the Euclidean gradient based stochastic gradient descent optimization. In this work, we show that these and other commonly used deep networks, such as those which use a max-pooling and sub-sampling layer, possess more complex forms of sym...

The inverse of the Fisher information matrix is used in the natural gradient descent algorithm to train single-layer and multi-layer perceptrons. We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the natural gradient. When the input dimension n is much larger than the ...

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradient descent procedures, which involve parameter updates that are implicitly def...

We implement stacked denoising autoencoders, a class of neural networks that are capable of learning powerful representations of high dimensional data. We describe stochastic gradient descent for unsupervised training of autoencoders, as well as a novel genetic algorithm based approach that makes use of gradient information. We analyze the performance of both optimization algorithms and also th...