Related papers: Fit Like You Sample: Sample-Efficient Generalized …
The method of generalized estimating equations (GEE) is popular in the biostatistics literature for analyzing longitudinal binary and count data. It assumes a generalized linear model (GLM) for the outcome variable, and a working…
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few…
Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text…
We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…
Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical…
Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior…
We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress…
Traditionally, in supervised machine learning, (a significant) part of the available data (usually 50% to 80%) is used for training and the rest for validation. In many problems, however, the data is highly imbalanced in regard to different…
We show that the incorporation of any new piece of information allows for improved decision making in the sense that the expected costs of an optimal decision decrease (or, in boundary cases where no or not enough new information is…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward…
We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
We study the theoretical foundations of composition in diffusion models, with a particular focus on out-of-distribution extrapolation and length-generalization. Prior work has shown that composing distributions via linear score combination…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently…
Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…
The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…