no code implementations • 29 Oct 2024 • Martin Gjorgjevski, Nicolas Keriven, Simon Barthelmé, Yohann de Castro
We show that in Latent Position Models this estimator tends to a Nadaraya Watson estimator in the latent space, and that its rate of convergence is in fact the same.
1 code implementation • 31 Oct 2022 • Simon Barthelmé, Nicolas Tremblay, Pierre-Olivier Amblard
Finally, an interesting by-product of the analysis is that a realisation from a DPP is typically contained in a subset of size O(m log m) formed using leverage score i. i. d.
no code implementations • 15 Oct 2021 • Yusuf Pilavci, Pierre-Olivier Amblard, Simon Barthelmé, Nicolas Tremblay
Large dimensional least-squares and regularised least-squares problems are expensive to solve.
2 code implementations • 23 Mar 2018 • Nicolas Tremblay, Simon Barthelmé, Pierre-Olivier Amblard
We apply our results to both the k-means and the linear regression problems, and give extensive empirical evidence that the small additional computational cost of DPP sampling comes with superior performance over its iid counterpart.
no code implementations • 5 Mar 2018 • Simon Barthelmé, Pierre-Olivier Amblard, Nicolas Tremblay
In this work we show that as the size of the ground set grows, $k$-DPPs and DPPs become equivalent, meaning that their inclusion probabilities converge.
no code implementations • 5 Mar 2017 • Nicolas Tremblay, Pierre-Olivier Amblard, Simon Barthelmé
For large graphs, ie, in cases where the graph's spectrum is not accessible, we investigate, both theoretically and empirically, a sub-optimal but much faster DPP based on loop-erased random walks on the graph.
no code implementations • 11 Jun 2014 • Simon Barthelmé, Nicolas Chopin
Here we show that inferring the parameters of a unnormalised model on a space $\Omega$ can be mapped onto an equivalent problem of estimating the intensity of a Poisson point process on $\Omega$.