Related papers: Regression on a Graph
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…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a…
Many popular piecewise regression models rely on minimizing a cost function on the model fit with a linear penalty on the number of segments. However, this penalty does not take into account varying complexities of the model functions on…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end,…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…
We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (1977)'s work, but it is able to deal with models that have a precision matrix for the…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
Noisy training set usually leads to the degradation of generalization and robustness of neural networks. In this paper, we propose using a theoretically guaranteed noisy label detection framework to detect and remove noisy data for Learning…
In this paper we present theory, algorithms and applications for regression over the max- plus semiring. We show how max-plus 2-norm regression can be used to obtain maximum likelihood estimates for three different inverse problems. Namely…
We study estimation of piecewise smooth signals over a graph. We propose a $\ell_{2,0}$-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the…
The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…