相关论文: Rademacher upper bounds for cross-validation error…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability has been first introduced by \cite{DEWA79}…
Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an…
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…
In the task of comparing two classification algorithms, the widely-used McNemar's test aims to infer the presence of a significant difference between the error rates of the two classification algorithms. However, the power of the…
Cross validation is a central tool in evaluating the performance of machine learning and statistical models. However, despite its ubiquitous role, its theoretical properties are still not well understood. We study the asymptotic properties…
Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is…
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…
We show a Talagrand-type concentration inequality for Multi-Task Learning (MTL), using which we establish sharp excess risk bounds for MTL in terms of distribution- and data-dependent versions of the Local Rademacher Complexity (LRC). We…
Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this…
Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific…
The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this…
This paper describes a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
This paper studies V-fold cross-validation for model selection in least-squares density estimation. The goal is to provide theoretical grounds for choosing V in order to minimize the least-squares loss of the selected estimator. We first…
In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond…
Group number selection is a key problem for group panel data modeling. In this work, we develop a cross-validation (CV) method to tackle this problem. Specifically, we split the panel data into two data folds on the time span, with group…
In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
The error or variability of machine learning algorithms is often assessed by repeatedly re-fitting a model with different weighted versions of the observed data. The ubiquitous tools of cross-validation (CV) and the bootstrap are examples…