Narrow Results

Within the field of supervised classification, the naïve Bayes (NB) classifier is a very simple and fast classification method that obtains good results, being even comparable with much more complex models. It has been proved that the NB model is strongly dependent on the estimation of conditional probabilities. In the literature, it had been shown that the classical and Laplace estimations of probabilities have some drawbacks and it was proposed a NB model that takes into account the a priori probabilities in order to estimate the conditional probabilities, which was called m-probability-estimation. With a very scarce experimentation, this approximation based on m-probability-estimation demonstrated to provide better results than NB with classical and Laplace estimations of probabilities. In this research, a new naïve Bayes variation is proposed, which is based on the m-probability-estimation version and takes into account imprecise probabilities in order to calculate the a priori probabilities. An exhaustive experimental research is carried out, with a large number of data sets and different levels of class noise. From this experimentation, we can conclude that the proposed NB model and the m-probability-estimation approach provide better results than NB with classical and Laplace estimation of probabilities. It will be also shown that the proposed NB implies an improvement over the m-probability-estimation model, especially when there is some class noise.

The human eye smooths noisy data in the process of perceiving fair shape. The shape of ordered planar noisy data is determined by constructing convex regions, called gates, around each point. The data inherits its shape from the shape of the minimal length polygonal path interpolating the gates in order. Specifically, the number of inflections in the minimal length polygonal path defines the shape of the original noisy data.

We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible. Then, we restrict this forward operator to finite-dimensional spaces so that the inverse is Lipschitz continuous. For the inverse operator, we demonstrate that there exists a neural network which is a robust-to-noise approximation of the operator. In addition, we show that these neural networks can be learned from appropriately perturbed training data. We demonstrate the admissibility of this approach to a wide range of inverse problems of practical interest. Numerical examples are given that support the theoretical findings.

In this paper, two numerical methods are presented to solve an ill-posed inverse problem for Fisher's equation using noisy data. These two methods are the Haar basis and the Legendre wavelet methods combined with the Tikhonov regularization method. A sensor located at a point inside the body is used and u(x, t) at a point x = a, 0 < a < 1 is measured and these methods are applied to the inverse problem. We also show that an exponential rate of convergence of these methods. In fact, this work considers a comparative study between the Haar basis and the Legendre wavelet methods to solve some ill-posed inverse problems. Results show that an excellent estimation of the unknown function of the inverse problem which have been obtained within a couple of minutes CPU time at Pentium(R) Dual-Core CPU 2.20 GHz.

Recent works with the BERT-based models demonstrate their generalization ability and high performance on the new domain tasks. However, this kind of model requires a large amount of data. Collecting this data can be error-prone, and it is important to know: how the errors in data affect the quality of the model. In this work, we study the impact of data with different errors – noisy data on the training of the question answering-over-text BERT-model. We use the concept of random, structural and irrelevant question noises. We study the robustness of QAT models during the training process with different settings, datasets and noise types and discuss possible reasons. We also propose a real-world domain dataset to probe our findings in a real-world scenario. The results of an experimental study showed that following developed recommendations allowed performance improvement up to 3.6% in a real-world setting.