Theoretical advances of the last decade have led to novel methodologies for probability density estimation by irregular histograms and penalized maximum likelihood. Here we consider two of them: the first one is based on the idea of minimizing the excess risk, while the second one employs the concept of the normalized maximum likelihood (NML). Apparently, the previous literature does not contain any comparison of the two approaches. To fill the gap, we provide in this paper theoretical and empirical results for clarifying the relationship between the two methodologies. Additionally, we introduce a new variant of the NML histogram. For the sake of completeness, we consider also a more advanced NML-based method that uses the measurements to approximate the unknown density by a mixture of densities selected from a predefined family.

In this survey-style paper we demonstrate the usefulness of the probabilistic modelling framework in solving not only the actual positioning problem, but also many related problems involving issues like calibration, active learning, error estimation and tracking with history. We also point out some interesting links between positioning research done in the area of robotics and in the area of wireless radio networks.

We propose a data reduction method based on a probabilistic similarity framework where tw o vectors are considered similar if they lead to similar predictions.We sho w ho w this type of a probabilistic similarity metric can be de ned both in a supervised and unsupervised manner.As a concrete application of the suggested multidimensional scaling scheme, we describe how the method can be used for producing visual images of high-dimensional data, and give several examples of visualizations obtained by using the suggested scheme with probabilistic Bayesian net w ork models.

In this paper we present a probabilistic formalization of the instance-based learning approach. In our Bayesian framework, moving from the construction of an explicit hypothesis to a data-driven instancebased learning approach, is equivalent to averaging over all the (possibly infinitely many) individual models. The general Bayesian instance-based learning framework described in this paper can be applied with any set of assumptions defining a parametric model family, and to any discrete prediction task where the number of simultaneously predicted attributes is small, which includes for example all classification tasks prevalent in the machine learning literature. To illustrate the use of the suggested general framework in practice, we show how the approach can be implemented in the special case with the strong independence assumptions underlying the so called Naive Bayes classifier. The resulting Bayesian instance-based classifier is validated empirically with public domain data sets and the results are compared to the performance of the traditional Naive Bayes classifier. The results suggest that the Bayesian instancebased learning approach yields better results than the traditional Naive Bayes classifier, especially in cases where the amount of the training data is small. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.