Related papers: Risk Bounds For Distributional Regression
We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$. Under this setting, we prove bounds for…
We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…
In this paper, we provide extended convolution bounds for the Fr\'{e}chet problem and discuss related implications in quantitative risk management. First, we establish a new form of inequality for the Range-Value-at-Risk (RVaR). Based on…
Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…
We present novel lower bounds on the mean square error (MSE) of the location estimation of an emitting source via a network where the sensors are deployed randomly. The sensor locations are modeled as a homogenous Poisson point process. In…
We consider two-stage recourse models in which the second-stage problem has integer decision variables and uncertainty in the second-stage cost vector, technology matrix, and the right-hand side vector. Such mixed-integer recourse models…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
We develop a formalism for constructing stochastic upper bounds on the expected full sample risk for supervised classification tasks via the Hilbert coresets approach within a transductive framework. We explicitly compute tight and…
There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood,…
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
A new risk bound is presented for the problem of convex/concave function estimation, using the least squares estimator. The best known risk bound, as had appeared in \citet{GSvex}, scaled like $\log(en) n^{-4/5}$ under the mean squared…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…