10 citations · 21 across the 8 of their papers we have counts for
9 papers
Differentiable Kernel Ridge Regression for Deep Learning Pipelines
Jean-Marc Mercier, Gabriele Santin
Deep neural networks dominate modern machine learning, while alternative function approximators remain comparatively underexplored at scale. In this work, we revisit kernel methods…
A class of kernel-based scalable algorithms for data science
Philippe G. LeFloch, Jean-Marc Mercier, Shohruh Miryusupov
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with la…
Extrapolation and generative algorithms for three applications in finance
Philippe G. LeFloch, Jean-Marc Mercier, Shohruh Miryusupov
For three applications of central interest in finance, we demonstrate the relevance of numerical algorithms based on reproducing kernel Hilbert space (RKHS) techniques. Three use c…
Reproducing kernel methods for machine learning, PDEs, and statistics
Philippe G. LeFloch, Jean-Marc Mercier, Shohruh Miryusupov
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the…
A class of mesh-free algorithms for some problems arising in finance and machine learning
Philippe G. LeFloch, Jean-Marc Mercier
We introduce a numerical methodology, referred to as the transport-based mesh-free method, which allows us to deal with continuous, discrete, or statistical models in the same unif…
Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions
Philippe G. LeFloch, Jean-Marc Mercier
We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functi…
The Transport-based Mesh-free Method (TMM) and its applications in finance: a review
Philippe G. LeFloch, Jean-Marc Mercier
We review a numerical technique, referred to as the Transport-based Mesh-free Method (TMM), and we discuss its applications to mathematical finance. We recently introduced this met…
An algorithm (CoDeFi) for overcoming the curse of dimensionality in mathematical finance
Philippe G. LeFloch, Jean-Marc Mercier
We present an algorithm (CoDeFi) which overcomes the curse of dimensionality (CoD) in scientific computations and, especially, in mathematical finance (Fi). Our method applies a br…
Revisiting the method of characteristics via a convex hull algorithm
Philippe G. LeFloch, Jean-Marc Mercier
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we describe a novel numerical algorithm - the convex hull algorithm (CHA) - i…