Related papers: Estimating composite functions by model selection
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…
This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1} w(x) f(x)$, where the weight function $w$ and the total weight $W=\int w(x) f(x) dx$ may not be known. The length-biased and…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al. (2017) described an algorithm for this problem whose…
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum…
We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…
Let $\mathbf{x}_j = \mathbf{\theta} + \mathbf{\epsilon}_j$, $j=1,\dots,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim\mathcal{N}(\mathbf{\theta},\mathbf{\Sigma})$ with unknown mean $\mathbf{\theta} \in \mathbb{R}^d$ and…
We study a Bayesian approach to estimating a smooth function in the context of regression or classification problems on large graphs. We derive theoretical results that show how asymptotically optimal Bayesian regularization can be achieved…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…