We prove that a particular deep network architecture is more efficient at approximating radially symmetric functions than the best known 2 or 3 layer networks. We use this architecture to approximate Gaussian kernel SVMs, and subsequently improve upon them with further training. The architecture and initial weights of the Deep Radial Kernel Network are completely specified by the SVM and theref...

This paper investigates the ability of several models of Support Vector Machines (SVMs) with alternate kernel functions to predict the probability of occurrence of Essential Hypertension (HT) in a mixed patient population. To do this a SVM was trained with 13 inputs (symptoms) from the medical dataset. Different kernel functions, such as Linear, Quadratic, Polyorder (order three), Multi Layer P...

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for other methods the spectral information can be used to estimate the excess risk. An important question remains on how close the sample eigenvalues/eigenvectors a...

----In statistical practices, difficulties of missing data are universal. Several techniques are used to handle this dilemma of missing data. They include both old approaches, which require only a small amount of mathematical computations and new approaches, which require additional difficult computations that are ever easier for social work researchers to carry out the statistical programming ...

Radial convolution operators on free groups with non-negative kernel of weak type (2, 2) and of restricted weak type (2, 2) are characterized. Estimates of weak type (p, p) are obtained as well for 1 < p < 2.

Knowledge of noun phrase anaphoricity might be profitably exploited in coreference resolution to bypass the resolution of non-anaphoric noun phrases. However, it is surprising to notice that recent attempts to incorporate automatically acquired anaphoricity information into coreference resolution have been somewhat disappointing. This paper employs a global learning method in determining the an...

the prediction of lithology is necessary in all areas of petroleum engineering. this means that todesign a project in any branch of petroleum engineering, the lithology must be well known. supportvector machines (svm’s) use an analytical approach to classification based on statistical learningtheory, the principles of structural risk minimization, and empirical risk minimization. in thisresearc...

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions an O(D) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigo...

We show that support vector machines of the 1-norm soft margin type are universally consistent provided that the regularization parameter is chosen in a distinct manner and the kernel belongs to a specific class}the so-called universal kernels}which has recently been considered by the author. In particular it is shown that the 1-norm soft margin classifier with Gaussian RBF kernel on a compact ...

In this paper, the effects of using multi RBF kernel for an online LSSVR on modeling and control performance are investigated. The Jacobian information of the system is estimated via online LSSVR model. Kernel parameter determines how the measured input is mapped to the feature space and a better plant model can be achieved by discarding redundant features. Therefore, introducing flexibility in...