Related papers: Generalised additive and index models with shape c…
Shape restrictions on functional regression coefficients such as non-negativity, monotonicity, convexity or concavity are often available in the form of a prior knowledge or required to maintain a structural consistency in functional…
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either…
An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well…
In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex,…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…
Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of…
Generalized Additive Models (GAMs) balance predictive accuracy and interpretability, but manually configuring their structure is challenging. We propose using the multi-objective genetic algorithm NSGA-II to automatically optimize GAMs,…
Generalized Additive Models (GAMs) can be used to create non-linear glass-box (i.e. explicitly interpretable) models, where the predictive function is fully observable over the complete input space. However, glass-box interpretability…
In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of…
Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape…
We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish…
Sparse generalized additive models (GAMs) are an extension of sparse generalized linear models which allow a model's prediction to vary non-linearly with an input variable. This enables the data analyst build more accurate models,…
The Generalized Additive Model (GAM) is a powerful tool and has been well studied. This model class helps to identify additive regression structure. Via available test procedures one may identify the regression structure even sharper if…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
We consider an additive partially linear framework for modelling massive heterogeneous data. The major goal is to extract multiple common features simultaneously across all sub-populations while exploring heterogeneity of each…
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…
Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to…