Related papers: Adaptive spectral regularizations of high dimensio…
We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…
We study the non-parametric estimation of an unknown density f with support on R+ based on an i.i.d. sample with multiplicative measurement errors. The proposed fully data driven procedure is based on the estimation of the Mellin transform…
This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller…
Second-order information -- such as curvature or data covariance -- is critical for optimisation, diagnostics, and robustness. However, in many modern settings, only the gradients are observable. We show that the gradients alone can reveal…
A low rank matrix X has been contaminated by uniformly distributed noise, missing values, outliers and corrupt entries. Reconstruction of X from the singular values and singular vectors of the contaminated matrix Y is a key problem in…
Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…
We study the problem of estimating $\beta \in \mathbb{R}^p$ from its noisy linear observations $y= X\beta+ w$, where $w \sim N(0, \sigma_w^2 I_{n\times n})$, under the following high-dimensional asymptotic regime: given a fixed number…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
We develop a unified matrix-spectral framework for analyzing stability and interpretability in deep neural networks. Representing networks as data-dependent products of linear operators reveals spectral quantities governing sensitivity to…
We study the problem of exact support recovery: given an (unknown) vector $\theta \in \left\{-1,0,1\right\}^D$, we are given access to the noisy measurement $$ y = X\theta + \omega,$$ where $X \in \mathbb{R}^{N \times D}$ is a (known)…
We propose a method for learning linear models whose predictive performance is robust to causal interventions on unobserved variables, when noisy proxies of those variables are available. Our approach takes the form of a regularization term…
Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are…
This paper considers statistical inference for the explained variance $\beta^{\intercal}\Sigma \beta$ under the high-dimensional linear model $Y=X\beta+\epsilon$ in the semi-supervised setting, where $\beta$ is the regression vector and…