Related papers: A Novel Bayesian Classifier using Copula Functions

With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal…

The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…

This paper presents a versatile technique for the purpose of feature selection and extraction - Class Dependent Features (CDFs). We use CDFs to improve the accuracy of classification and at the same time control computational expense by…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated -- amongst the inputs that receive…

There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated)…

In this work, we investigated the application of score-based gradient learning in discriminative and generative classification settings. Score function can be used to characterize data distribution as an alternative to density. It can be…

This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well known copulas are…

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

Bayesian optimization (BO) methods choose sample points by optimizing an acquisition function derived from a statistical model of the objective. These acquisition functions are chosen to balance sampling regions with predicted good…

When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…

We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…

In this work, we show that under specific choices of the copula, the lasso, elastic net, and $g$-prior are particular cases of `copula prior,' for regularization and variable selection method. We present `lasso with Gauss copula prior' and…

We give improved and almost optimal testers for several classes of Boolean functions on $n$ inputs that have concise representation in the uniform and distribution-free model. Classes, such as $k$-junta, $k$-linear functions, $s$-term DNF,…

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…

Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses new…

When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…

Classifiers based on probabilistic graphical models are very effective. In continuous domains, maximum likelihood is usually used to assess the predictions of those classifiers. When data is scarce, this can easily lead to overfitting. In…