Related papers: Learning From Non-iid Data: Fast Rates for the One…
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, i.e., the rates faster than $n^{-1/2}$. The works on this subject suggested…
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than $n^{-1/2}$. The work on this subject has suggested…
We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without…
In this paper we tackle the problem of fast rates in time series forecasting from a statistical learning perspective. In a serie of papers (e.g. Meir 2000, Modha and Masry 1998, Alquier and Wintenberger 2012) it is shown that the main tools…
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…
We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all…
Continual learning, which aims to learn multiple tasks sequentially, has gained extensive attention. However, most existing work focuses on empirical studies, and the theoretical aspect remains under-explored. Recently, a few investigations…
The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…
Federated learning algorithms perform reasonably well on independent and identically distributed (IID) data. They, on the other hand, suffer greatly from heterogeneous environments, i.e., Non-IID data. Despite the fact that many research…
In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level $\lambda$. More precisely, it is assumed that the density (i) is smooth in a…
Federated learning is a promising framework to train neural networks with widely distributed data. However, performance degrades heavily with heterogeneously distributed data. Recent work has shown this is due to the final layer of the…
Can we learn a multi-class classifier from only data of a single class? We show that without any assumptions on the loss functions, models, and optimizers, we can successfully learn a multi-class classifier from only data of a single class…
We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then…
The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast…
We consider nonparametric classification with smooth regression functions, where it is well known that notions of margin in $E[Y|X]$ determine fast or slow rates in both active and passive learning. Here we elucidate a striking distinction…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
We consider the classical problem of learning rates for classes with finite VC dimension. It is well known that fast learning rates up to $O\left(\frac{d}{n}\right)$ are achievable by the empirical risk minimization algorithm (ERM) if low…
A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory hypercontractivity condition holds, the risk of the…