Related papers: Refined Error Bounds for Several Learning Algorith…
In this paper, we provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems. The originality of our work is that we propose to use the confusion matrix of a classifier as…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…
In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable…
This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to…
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the…
With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active…
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…
This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms with Markovian noise. As a corollary, we also obtain…
Algorithms which minimize the averaged loss have been widely designed for dealing with noisy labels. Intuitively, when there is a finite training sample, penalizing the variance of losses will improve the stability and generalization of the…
We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite…
We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating…
Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises…
In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…
We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…
New bounds on classification error rates for the error-correcting output code (ECOC) approach in machine learning are presented. These bounds have exponential decay complexity with respect to codeword length and theoretically validate the…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
We consider the problem of training a model under the presence of label noise. Current approaches identify samples with potentially incorrect labels and reduce their influence on the learning process by either assigning lower weights to…
The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…
We study the efficient PAC learnability of halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, each label is independently flipped with some probability which is controlled by an adversary. This noise model…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…