Related papers: Learning Density Evolution from Snapshot Data
The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Density estimation is a versatile technique underlying many data mining tasks and techniques,ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming…
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…
While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension,…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
Learning in uncertain, noisy, or adversarial environments is a challenging task for deep neural networks (DNNs). We propose a new theoretically grounded and efficient approach for robust learning that builds upon Bayesian estimation and…
We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time…
We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…
Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…
We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…