Advances in Probabilistic Modeling and Inference

The field of probabilistic modeling and inference is rapidly advancing, with a focus on developing innovative methods for complex data analysis and simulation. Recent research has emphasized the importance of robust and efficient algorithms for inverse problems, Bayesian inference, and stochastic processes. Notably, the development of new criteria for rapid mixing of Glauber dynamics and the application of Gaussian process tilted nonparametric density estimation have shown promise in addressing long-standing challenges in statistical physics and machine learning. Furthermore, advances in diffusion models, such as the Gaussian mixture flow matching model and dimension-free convergence of diffusion models, have demonstrated improved performance in generative tasks and high-dimensional sampling. Overall, the field is moving towards more efficient, scalable, and accurate methods for probabilistic modeling and inference. Noteworthy papers include: Rapid Mixing on Random Regular Graphs beyond Uniqueness, which confirms a conjecture on the mixing behavior of the hardcore model on random regular graphs. Gaussian Mixture Flow Matching Models, which proposes a novel model that generalizes previous diffusion and flow matching models.

Sources

Effects of Interpolation Error and Bias on the Random Mesh Finite Element Method for Inverse Problems

Rapid Mixing on Random Regular Graphs beyond Uniqueness

Shape reconstruction of inclusions based on noisy data via monotonicity methods for the time harmonic elastic wave equation

Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching

Stochastic Variational Inference with Tuneable Stochastic Annealing

Efficient Rejection Sampling in the Entropy-Optimal Range

TabRep: Training Tabular Diffusion Models with a Simple and Effective Continuous Representation

Gaussian Mixture Flow Matching Models

Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures

Quantifying uncertainty in inverse scattering problems set in layered environments

Systematic Parameter Decision in Approximate Model Counting

A Method for Generating Connected Erdos-Renyi Random Graphs

A Metropolis-Adjusted Langevin Algorithm for Sampling Jeffreys Prior

On Mixed-Precision Iterative Methods and Analysis for Nearly Completely Decomposable Markov Processes

Asymptotic Variance in the Central Limit Theorem for Multilevel Markovian Stochastic Approximation

Dissimilar Batch Decompositions of Random Datasets

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