相关论文: Two Lectures on Iterative Coding and Statistical M…

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…

These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…

These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…

These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…

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...).

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a…

The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…

The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a…

This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Finite Fields by J.-P. Serre and organised at Centro de ciencias…

Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message passing techniques, namely warning and survey…

One of the most popular methods of the machine learning prediction explanation is the SHapley Additive exPlanations method (SHAP). An imprecise SHAP as a modification of the original SHAP is proposed for cases when the class probability…

Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…

We describe an implementation of a hybrid statistical/symbolic approach to repairing parser failures in a speech-to-speech translation system. We describe a module which takes as input a fragmented parse and returns a repaired meaning…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…

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…

The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or…

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…

We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent…

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…