Continuously-Adaptive Discretization for Message-Passing (CAD-MP) is a new message-passing algorithm for approximate inference. Most message-passing algorithms approximate continuous probability distributions using either: a family of continuous distributions such as the exponential family; a particle-set of discrete samples; or a fixed, uniform discretization. In contrast, CAD-MP uses a discre...

Many supervised induction algorithms require discrete data, even while real data often comes in a discrete and continuous formats. Quality discretization of continuous attributes is an important problem that has effects on speed, accuracy and understandability of the induction models. Usually, discretization and other types of statistical processes are applied to subsets of the population as th...

This report investigates a technique to calculate the distributions of discretization errors for a model of advection-diffusion-reaction with stochastic noise in problem data. The focus is on operator-split discretization methods. The error is decomposed into components due to the splitting and due to the discretization within each component. We present a method to estimate the distributions of...

The finite-difference time-domain (FDTD) method is an explicit time discretization scheme for Maxwell’s equations. In this context it is well-known that explicit time discretization schemes have a stability induced time step restriction. In this paper, we recast the spatial discretization of Maxwell’s equations, initially without time discretization, into a more convenient format, called the FD...

There is still lack of clarity about the best manner in which to handle numeric attributes when applying Bayesian network classifiers. Discretization methods entail an unavoidable loss of information. Nonetheless, a number of studies have shown that appropriate discretization can outperform straightforward use of common, but often unrealistic parametric distribution (e.g. Gaussian). Previous st...

Discretization is a process of dividing a continuous attribute into a finite set of intervals to generate an attribute with small number of distinct values, by associating discrete numerical value with each of the generated intervals. Discretization is usually performed prior to the learning process and has played an important role in data mining and knowledge discovery. The results of CAIM are...

In diffuse optical tomography (DOT), the discretization error in the numerical solutions of the forward and inverse problems results in error in the reconstructed optical images. In this first part of our work, we analyse the error in the reconstructed optical absorption images, resulting from the discretization of the forward and inverse problems. Our analysis identifies several factors which ...

One of the ways to solve classification problems with realvalue attributes using a Learning Classifier System is the use of a discretization algorithm, which enables traditional discrete knowledge representations to solve these problems. A good discretization should balance losing the minimum of information and having a reasonable number of cut points. Choosing a single discretization that achi...

An empirical investigation of the interaction of sample size and discretization – in this case the entropy-based method CAIM (Class-Attribute Interdependence Maximization) – was undertaken to evaluate the impact and potential bias introduced into data mining performance metrics due to variation in sample size as it impacts the discretization process. Of particular interest was the effect of dis...

The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi level) and it finds application, for example, in the numerical renormalization group (NRG) approach to quantum impurity problems (Kondo model), where the conti...