Related papers: Regression on a Graph
We assume a nonparametric regression model where the signal is given by the sum of a piecewise constant function and a smooth function. To detect the change-points and estimate the regression functions, we propose PCpluS, a combination of…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context…
Regression is fundamental in computer vision and is widely used in various tasks including age estimation, depth estimation, target localization, \etc However, real-world data often exhibits imbalanced distribution, making regression models…
Classical regression has a simple geometric description in terms of a projection of the training labels onto the column space of the design matrix. However, for over-parameterized models -- where the number of fit parameters is large enough…
Sharpness-aware minimization (SAM) is known to improve the generalization performance of neural networks. However, it is not widely used in real-world applications yet due to its expensive model perturbation cost. A few variants of SAM have…
We consider the problem of joint estimation of the parameters of $m$ linear dynamical systems, given access to single realizations of their respective trajectories, each of length $T$. The linear systems are assumed to reside on the nodes…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
Increasing practical interest has been shown in regression problems where the errors, or disturbances, are centred in a way that reflects particular characteristics of the mechanism that generated the data. In economics this occurs in…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
We present an estimation procedure for nonlinear mixed-effects models in which the population trajectory is represented by penalized splines and adapted to individuals via subject-specific transformation parameters. By exploiting the mixed…
Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…
Signed networks, characterized by edges labeled as either positive or negative, offer nuanced insights into interaction dynamics beyond the capabilities of unsigned graphs. Central to this is the task of identifying the maximum balanced…
In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…
We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…