Related papers: Linear Convergence of Diffusion Models Under the M…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…

In this paper, we study the statistical and geometrical properties of the Kullback-Leibler divergence with kernel covariance operators (KKL) introduced by Bach [2022]. Unlike the classical Kullback-Leibler (KL) divergence that involves…

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

Motivated by the increasingly popular Score-based Generative Modeling (SGM), we study the Inexact Langevin Dynamics (ILD) and Inexact Langevin Algorithm (ILA) where a score function estimate is used in place of the exact score. We establish…

We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…

Multi-label classification (MLC) refers to the problem of tagging a given instance with a set of relevant labels. Most existing MLC methods are based on the assumption that the correlation of two labels in each label pair is symmetric,…

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions. Despite their effectiveness, their theoretical underpinnings remain relatively underdeveloped. In this work, we study…

Diffusion models (DMs) excel in photo-realistic image synthesis, but their adaptation to LiDAR scene generation poses a substantial hurdle. This is primarily because DMs operating in the point space struggle to preserve the curve-like…

This paper provides a detailed investigation of using the Kullback-Leibler (KL) Divergence as a way to compare and analyse game-levels, and hence to use the measure as the objective function of an evolutionary algorithm to evolve new…

In statistical classification/multiple hypothesis testing and machine learning, a model distribution estimated from the training data is usually applied to replace the unknown true distribution in the Bayes decision rule, which introduces a…

A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

Generative models frequently suffer miscalibration, wherein statistics of the sampling distribution, such as the fraction of generations in a given class, deviate from desired values. We frame calibration as a constrained optimization…

Diffusion models have successfully been applied to generative tasks in various continuous domains. However, applying diffusion to discrete categorical data remains a non-trivial task. Moreover, generation in continuous domains often…

In this paper, we investigate the latent geometry of generative diffusion models under the manifold hypothesis. For this purpose, we analyze the spectrum of eigenvalues (and singular values) of the Jacobian of the score function, whose…

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…