Target class measurements, if available from automatic target recognition systems, can be incorporated into multiple target tracking algorithms to improve measurement-to-track association accuracy. In this work, the performance of the classifier is modeled as a confusion matrix, whose entries are target class likelihood functions that are used to modify the update equations of the recently deri...

We extend the fractional genetic programming scheme with data elements that are no more scalar, but instead are similar to probability density functions. The extension straightforwardly fits into fractional programming, in which data elements are blended from several values. In the case of our previous work, the blend produced a single scalar value. The extension proposes to build an approximat...

We present an approach for the estimation of probability density functions (pdf) given a set of observations. It is based on the use of feedforward multilayer neural networks with sigmoid hidden units. The particular characteristic of the method is that the output of the network is not a pdf, therefore, the computation of the network’s integral is required. When this integral cannot be performe...

The paper introduces a new framework for learning probability density functions. A theoretical analysis suggests that we can tailor a distribution for a class of tasks by training it to fit a small subsample. Experimental evidence is given to support the theoretical analysis.

Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least the probability density function (pdf), which to estimate is classically a time consumpting and/or less accurate hard task, that may make decisions to fail....

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate thes...

This paper introduces an objective function that seeks to minimise the average total number of bits required to encode the joint state of all of the layers of a Markov source. This type of encoder may be applied to the problem of optimising the bottom-up (recognition model) and top-down (generative model) connections in a multilayer neural network, and it unifies several previous results on the...

There exist many approaches to discern a functional relationship between two variables. A functional model is useful for two reasons: Firstly, if the function is a relatively simple model in the plane, it provides us with qualitative information about the relationship. Secondly, given a fixed value for one variable, the other one can be calculated as a means for prediction. In this paper an app...

Partial likelihood (PL) establishes a sufficiently general framework to develop and study statistical properties of nonlinear techniques in signal processing. In [I], we present the theorem by which the fundamental information-theoretic relationship for learning on the P L cost, the equivalence of likelihood maximization and relative entropy minimization, is established. In this paper, we refor...

The state price density of a basket, even under uncorrelated Black–Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short time and small volatility expansions, respectively. The method works for gene...