Related papers: On model selection consistency of regularized M-es…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
While there are many studies on weight regularization, the study on structure regularization is rare. Many existing systems on structured prediction focus on increasing the level of structural dependencies within the model. However, this…
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
The problem of model selection arises in a number of contexts, such as compressed sensing, subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper generalizes the notion of…
When multiple models are considered in regression problems, the model averaging method can be used to weigh and integrate the models. In the present study, we examined how the goodness-of-prediction of the estimator depends on the…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model…
This work is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set $S \subset {\mathbb R}^d$. The general aim is to identify (via stochastic…
In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…
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…
We focus on semiparametric regression that has played a central role in statistics, and exploit the powerful learning ability of deep neural networks (DNNs) while enabling statistical inference on parameters of interest that offers…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…