Related papers: Oracle inequalities for square root analysis estim…

We generalize the bridge between analysis and synthesis estimators by Elad, Milanfar and Rubinstein (2007) to rank deficient cases. This is a starting point for the study of the connection between analysis and synthesis for total variation…

Following recent success on the analysis of the Slope estimator, we provide a sharp oracle inequality in term of prediction error for Graph-Slope, a generalization of Slope to signals observed over a graph. In addition to improving upon…

We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a…

We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric…

We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we…

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

We derive oracle inequalities for the problems of isotonic and convex regression using the combination of $Q$-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities…

Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar…

We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…

Partial penalized tests provide flexible approaches to testing linear hypotheses in high dimensional generalized linear models. However, because the estimators used in these tests are local minimizers of potentially non-convex…

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive…

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…

We introduce a general approach to prove oracle properties in context tree selection. The results derive from a concentration condition that is verified, for example, by mixing processes. Moreover, we show the superiority of the oracle…

This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in…

Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…

We develop early stopping rules for growing regression tree estimators. The fully data-driven stopping rule is based on monitoring the global residual norm. The best-first search and the breadth-first search algorithms together with linear…

We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…