Related papers: Statistical inference with probabilistic graphical…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…
These notes give a brief introduction to differential Harnack inequalities and summarise the main results of the mini-course ``Li-Yau and Harnack estimates for nonlocal diffusion problems'', presented by the author at the Seasonal School on…
Improved mean-field technics are a central theme of statistical physics methods applied to inference and learning. We revisit here some of these methods using high-temperature expansions for disordered systems initiated by Plefka, Georges…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…
This volume contains the post-proceedings of the Tenth International Workshop on Graph Computation Models (GCM 2019: http://gcm2019.imag.fr). The workshop was held in Eindhoven, The Netherlands, on July 17th, 2019, as part of STAF 2019…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success…
Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
Recent machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms-advection (long-range transport), diffusion-like mixing, thermodynamic processes, and forcing-are…
In this paper, we study a novel inference paradigm, termed as schema inference, that learns to deductively infer the explainable predictions by rebuilding the prior deep neural network (DNN) forwarding scheme, guided by the prevalent…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…
Neural Processes (NPs) are appealing due to their ability to perform fast adaptation based on a context set. This set is encoded by a latent variable, which is often assumed to follow a simple distribution. However, in real-word settings,…
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).