相关论文: A new concentration result for regularized risk mi…

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…

This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely…

Always-valid concentration inequalities are increasingly used as performance measures for online statistical learning, notably in the learning of generative models and supervised learning. Such inequality advances the online learning…

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…

We consider the problem of estimating an unknown $n_1 \times n_2$ matrix $\mathbf{\theta^*}$ from noisy observations under the constraint that $\mathbf{\theta}^*$ is nondecreasing in both rows and columns. We consider the least squares…

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances…

Empirical Risk Minimization (ERM) based machine learning algorithms have suffered from weak generalization performance on data obtained from out-of-distribution (OOD). To address this problem, Invariant Risk Minimization (IRM) objective was…

Variance regularized counterfactual risk minimization (VRCRM) has been proposed as an alternative off-policy learning (OPL) method. VRCRM method uses a lower-bound on the $f$-divergence between the logging policy and the target policy as…

Constrained optimization provides a common framework for dealing with conflicting objectives in reinforcement learning (RL). In most of these settings, the objectives (and constraints) are expressed though the expected accumulated reward.…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

Reinforcement learning (RL) in large or infinite state spaces is notoriously challenging, both theoretically (where worst-case sample and computational complexities must scale with state space cardinality) and experimentally (where function…

We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…

The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the…

A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space…

A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear models, the effect is not fully understood for arbitrary…

It is commonly believed that optimizing the reverse KL divergence results in "mode seeking", while optimizing forward KL results in "mass covering", with the latter being preferred if the goal is to sample from multiple diverse modes. We…

We consider a statistical version of curriculum learning (CL) in a parametric prediction setting. The learner is required to estimate a target parameter vector, and can adaptively collect samples from either the target model, or other…

The concept of a minimax classifier is well-established in statistical decision theory, but its implementation via neural networks remains challenging, particularly in scenarios with imbalanced training data having a limited number of…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…