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In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
Bayesian optimisation is a popular technique for hyperparameter learning but typically requires initial exploration even in cases where similar prior tasks have been solved. We propose to transfer information across tasks using learnt…
We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a…
Frequentist and Bayesian methods differ in many aspects, but share some basic optimal properties. In real-life classification and regression problems, situations exist in which a model based on one of the methods is preferable based on some…
In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…
Bayesian nonparametric mixture models offer a rich framework for model based clustering. We consider the situation where the kernel of the mixture is available only up to an intractable normalizing constant. In this case, most of the…
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model.…
Linear regression analysis focuses on predicting a numeric regressand value based on certain regressor values. In this context, k-Nearest Neighbors (k-NN) is a common non-parametric regression algorithm, which achieves efficient performance…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…
This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…
Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, it is proposed to base comparisons on the predictive distributions of linear readouts from intermediate representations. In…
We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random…
Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a non-negative integer. We treat both the Poisson and Negative Binomial families as models for the…