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We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating relationship between a response variable and its covariates. Specifically, modal regression…
For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
Advances in machine learning technologies have led to increasingly powerful models in particular in the context of big data. Yet, many application scenarios demand for robustly interpretable models rather than optimum model accuracy; as an…
The paper proposes to analyze epidemiological data using regression models which enable subject-matter (epidemiological) interpretation of such data whether with uncorrelated or correlated predictors. To this end, response functions should…
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…
We consider a circular deconvolution problem, in which the density $f$ of a circular random variable $X$ must be estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y$ of $X$. The additive measurement error is…
The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…
Compared to the conditional mean as a simple point estimator, the conditional density function is more informative to describe the distributions with multi-modality, asymmetry or heteroskedasticity. In this paper, we propose a novel…
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
This paper proposes a new method for finding the highest predictive density set or region, within the heteroscedastic regression framework. This framework enjoys the property that any highest predictive density set is a translation of some…
Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…
When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…
In many modern regression applications, the response consists of multiple categorical random variables whose probability mass is a function of a common set of predictors. In this article, we propose a new method for modeling such a…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…
Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…