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This article investigates the use of random feature neural networks for learning Kolmogorov partial (integro-)differential equations associated to Black-Scholes and more general exponential L\'evy models. Random feature neural networks are…
Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
Recent works demonstrated the existence of a double-descent phenomenon for the generalization error of neural networks, where highly overparameterized models escape overfitting and achieve good test performance, at odds with the standard…
Deep learning algorithms are responsible for a technological revolution in a variety of tasks including image recognition or Go playing. Yet, why they work is not understood. Ultimately, they manage to classify data lying in high dimension…
Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the…
In the contemporary of deep learning, where models often grapple with the challenge of simultaneously achieving robustness against adversarial attacks and strong generalization capabilities, this study introduces an innovative Local Feature…
Learning to rank with biased click data is a well-known challenge. A variety of methods has been explored to debias click data for learning to rank such as click models, result interleaving and, more recently, the unbiased learning-to-rank…
A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…
One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
Pairwise learning or dyadic prediction concerns the prediction of properties for pairs of objects. It can be seen as an umbrella covering various machine learning problems such as matrix completion, collaborative filtering, multi-task…
Deep neural networks can achieve remarkable generalization performances while interpolating the training data perfectly. Rather than the U-curve emblematic of the bias-variance trade-off, their test error often follows a "double descent" -…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Consider the classical supervised learning problem: we are given data $(y_i,{\boldsymbol x}_i)$, $i\le n$, with $y_i$ a response and ${\boldsymbol x}_i\in {\mathcal X}$ a covariates vector, and try to learn a model $f:{\mathcal…
We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes…