Related papers: When is the mode functional the Bayes classifier?
Under mild conditions, it is shown the strong consistency of the Bayes estimator of the density. Moreover, the Bayes risk (for some common loss functions) of the Bayes estimator of the density (i.e. the posterior predictive density) reaches…
We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds…
Naive Bayes classifiers, a family of classifiers that are based on the popular Bayes' probability theorem, are known for creating simple yet well performing models, especially in the fields of document classification and disease prediction.…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper, we argue that part of…
The Naive Bayesian classifier is a popular classification method employing the Bayesian paradigm. The concept of having conditional dependence among input variables sounds good in theory but can lead to a majority vote style behaviour.…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
Neural networks for semantic segmentation can be seen as statistical models that provide for each pixel of one image a probability distribution on predefined classes. The predicted class is then usually obtained by the maximum a-posteriori…
Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…
We present a framework and analysis of consistent binary classification for complex and non-decomposable performance metrics such as the F-measure and the Jaccard measure. The proposed framework is general, as it applies to both batch and…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
Abstaining classifiers have been widely used in cost-sensitive applications to avoid ambiguous classification and reduce the cost of misclassification. Previous abstaining classification models rely on cost information, such as a cost…
Upper and lower bounds are derived for the mode(s) of the negative binomial distribution of order k, type I, with parameters r and p, which are employed to establish an explicit formula for the mode(s) in terms of r and k when p equals 0.5.…
A mode of a probability vector is a local maximum with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability vectors. Related to this is the concept of…
Filtered probability spaces (called "filtrations" for short) are shown to satisfy such a topological zero-one law: for every property of filtrations, either the property holds for almost all filtrations, or its negation does. In particular,…
The focal loss has demonstrated its effectiveness in many real-world applications such as object detection and image classification, but its theoretical understanding has been limited so far. In this paper, we first prove that the focal…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review…