Approximation Algorithms: Combinatorics, Geometry and Statistics

Pierre Alquier (ENSAE) |
Theoretical Guarantees for Approximate Bayesian Inference While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms targeting the exact posterior are prohibitively slow when both the model dimension and the sample size are large or when the likelihood is not tractable. Fast algorithms were proposed, at the price of targeting approximations of the posterior. In this talk, I will discuss two approaches. The first approach is an approximate Metropolis-Hastings algorithm (MH). In MH, a simulation from the transition kernel P requires a computation of the likelihood that might be expensive. We propose an approximation Q of P leading to a fast algorithm. We control explicity the total variation distance (TV) between the posterior and the distribution of the simulations. This algorithm was proposed in Alquier, Friel, Everitt and Boland (Statistics and Computing, 2016) under the name "Noisy-MCMC". I will also mention recent results by Rudolf and Schweizer (2018) who relaxed the assumptions of our results by using the Wasserstein distance instead of TV. The second approach is Variational Bayesian inference (VB). VB aims at approximating the posterior by a distribution in a tractable family. Thus, MCMC are replaced by an optimization algorithm which is orders of magnitude faster. VB methods have been applied in such computationally demanding applications as including collaborative filtering, NLP and text processing... However, despite nice results in practice, the theoretical properties of these approximations are usually not known. I will present conditions ensuring the asymptotic concentration of the variational approximation of the posterior around the true parameter. These results are taken from our recent works: Alquier and Ridgway (2017) and Chérief-Abdellatif and Alquier (2018). |
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Dömötör Pálvölgyi (Eötvös Loránd University) |
News about the chromatic number of the planeAt least how many colors do we need to color all the points of the plane such that every pair of points at unit distance receive different colors? This question is known as the Hadwiger-Nelson problem and until one year ago it was only known that 4 colors are needed and 7 are enough. Then in April 2018 gerontologist de Grey showed in a breakthrough result that 4 colors are not enough. His proof was computer assisted, and a collaborative Polymath project was started to find a human-verifiable proof. I will give a short introduction to the classical results, then talk about the current ongoing research with plenty of open problems. |

9h30-11h | Pierre Alquier |
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11h-11h30 | Coffee |

11h30-13h | Dömötör Pálvölgyi |

13h | Lunch |

Monika Csikos and Nabil H. Mustafa (LIGM, ESIEE Paris). The workshop is supported by ANR grant SAGA.

Contact: monika.csikos@esiee.fr.

Couprie | Michel | ESIEE / LIGM |

Cousty | Jean | ESIEE / LIGM |

Kenmochi | Yukiko | CNRS / LIGM |

Csikos | Monika | LIGM, ESIEE Paris |

Meunier | Frédéric | Ecole des Ponts ParisTech |

Mustafa | Nabil H. | LIGM, ESIEE Paris |

Romon | Pascal | UPEM |

Biswas | Ranita | Institute of Science and Technology, Austria |

Melnikova | Aleksandra | Masaryk University, Czech Republic |

Normand | Nicolas | LS2N/Université de Nantes |

Krzysztof | Ciesielski | WVU and MIPG, UPenn |

Comic | Lidija | University of Novi Sad |

Batavia | Darshan | TU Wien |

Tóth | Csaba D. | California State University Northridge |

Song | Haomin | University of Liverpool |

Nagy | Benedek | Eastern Mediterranean University |

Frosini | Andrea | Università di Firenze |

Jiménez | María José | Universidad de Sevilla |