A density f = f(x1, . . . , xd) on the hypercube [0, 1] d is block decreasing if, for each j ∈ {1, . . . , d}, it is a decreasing function of xj as xj → 1, when all other components are held fixed. Let us consider the class of all block decreasing densities on [0, 1]d bounded by B. We shall study the minimax risk over this class using n i.i.d.observations, the loss being measured by the L1 dist...

This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain. In the syntax it can be naturally represented by the description operator acting on the empty(fuzzy) set, because choosing an element from it...

The kernel ridge regression (KRR) approach has been successfully applied in nuclear mass predictions. Kernel function plays an important role the KRR approach. In this work, performances of different functions predictions are carefully explored. illustrated by comparing accuracies describing experimentally known nuclei and extrapolation abilities. It is found that approaches with most adopted k...

Land use is being considered as an element in determining land change studies, environmental planning and natural resource applications. The Earth’s surface Study by remote sensing has many benefits such as, continuous acquisition of data, broad regional coverage, cost effective data, map accurate data, and large archives of historical data. To study land use / cover, remote sensing as an effic...

As it is not clear how to choose an appropriate kernel function for a specific learning problem, this paper examines the performance of three kernel functions with varied parameters for online handwritten character recognition. The three kernel functions evaluated are the polynomial, complete polynomial, and radial basis functions. Results show that the three functions perform comparably with t...

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.

We give results about the learnability and required complexity of logical formulae to solve classification problems. These results are obtained by linking propositional logic with kernel machines. In particular we show that decision trees and disjunctive normal forms (DNF) can be represented by the help of a special kernel, linking regularized risk to separation margin. Subsequently we derive a...

Let B be a domain lying in the complex z plane and KB(z, t) its kernel function. A number of relationships exist between the kernel and the geometric properties of the domain. (See, for example, [l].)1 It is the purpose of the present note to relate the successive derivatives of the kernel with the domain B. If z is interior to B, we shall denote by rB(z) the shortest distance from the point z ...

In recent years, a number of kernel-based learning algorithms such as the regularization networks [1], the support vector machines [7, 4, 5], and the Gaussian process regression [8] have been investigated. These kernel machines are shown to work very well on real-world problems, given appropriate kernel functions. For general purposes, the Gaussian kernel is widely used and seems to work well [...