This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.
problem The gap between maximum likelihood and score matching objectives for score-based diffusion ODEs.
method High-order denoising score matching to maximize likelihood.
result Score-based diffusion ODEs achieve better likelihood on synthetic and CIFAR-10 data.
Neural score matching improves high-dimensional causal inference by using neural networks for balancing scores.
problem Impracticality of traditional matching methods in high-dimensional datasets due to the curse of dimensionality.
method Develops neural networks to create non-trivial, multivariate balancing scores for high-dimensional causal inference.
result Neural score matching outperforms other methods in treatment effect estimation and reducing imbalance on high-dimensional datasets.
Improved score matching methods for estimating score functions and Hessians without high dimensionality.
problem Estimating score functions and Hessians efficiently in high-dimensional data.
method Implicit score matching and denoising score matching, leveraging Gagliardo-Nirenberg inequalities.
result Achieves convergence rates similar to denoising score matching and estimates Hessians without dimensionality issues.
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been completely resolved for score matching. First, we provide a formal link between maxim…
Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density functions. We show this difficulty can be mitigated by projecting the scores onto random…
The paper establishes bounds for score-matching in causal discovery and generative modeling.
problem Estimating causal relationships from data.
method Training a deep neural network to estimate the score function and applying it to causal discovery.
result Bounds on the error rate of causal discovery methods using score-matching.
Improves score estimation for noised targets using known clean scores.
problem Poor score estimation at low noise levels in Denoising Score Matching.
method Introduces Target Score Identity and Target Score Matching loss.
result Score estimates are more accurate at low noise levels.
DDSME outperforms SME in estimating multimodal distributions.
problem Efficiency of score matching in multimodal distributions.
method Diffusion-based denoising score matching (DDSME) compared to vanilla score matching (SME).
result DDSME avoids the error bound deterioration of SME with increasing mode separation.
This work interprets diffusion score matching using normalizing flows for better model training and evaluations.
problem Limitations of diffusion score matching when dealing with certain types of distributions.
method The approach involves interpreting the diffusion matrix using normalizing flows to provide better interpretation and usage of diffusion score matching.
result Diffusion score matching is equivalent to the original score matching evaluated in the transformed space defined by the normalizing flow.
Develops Hamiltonian Score Matching and Generative Flows for machine learning.
problem Estimating score functions and designing generative models.
method Introduces Hamiltonian velocity predictors (HVPs) for score matching and generative flows.
result Hamiltonian Generative Flows (HGFs) rival leading generative modeling techniques.
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
Robust score matching improves parameter estimation in contaminated data.
problem Parameter estimation in data contaminated by outliers.
method Geometric median of means to develop a robust score matching procedure.
result Consistent parameter estimates in contaminated data settings.
Score matching fails for general point processes, a new estimator improves accuracy.
problem Score matching estimators fail for general point processes.
method Introduced a weighted score matching estimator for point processes.
result The weighted score matching estimator accurately estimates model parameters on synthetic and real data.
Score matching method improves image generation quality.
problem Score matching method underperforms GANs in metrics like Fréchet Inception Distance.
method DSM-ALS with denoising and improved sampling techniques.
result Score matching methods can match GANs in image generation quality.
Semi-Implicit Variational Inference (SIVI) is improved with SIVI-SM using score matching.
problem Intractable densities in variational distributions hinder SIVI training.
method SIVI-SM uses score matching to handle intractable densities in a minimax formulation.
result SIVI-SM outperforms ELBO-based SIVI methods in Bayesian inference tasks.
ScoreMatchingRiesz improves debiased machine learning and policy effects estimation.
problem Improving debiased machine learning and policy effects estimation.
method Score matching and Riesz representer estimation.
result Estimates policy path for continuous treatments, improving interpretability.
Score matching method improves density estimation for truncated data on manifolds.
problem Density estimation for truncated data on manifolds with intractable normalising constant.
method Truncated score matching extended to Riemannian manifolds with boundary.
result Score matching estimator approximates true parameter values with low error.
New bounds for score matching in polynomial exponential families.
problem Understanding the sample complexity of score matching for polynomial exponential families.
method Non-asymptotic sample complexity analysis for score matching.
result First finite sample bounds for score matching in polynomial exponential families.
Heuristic weighting improves denoising score matching without requiring noise distribution assumptions.
problem Improving denoising score matching without assuming noise distribution.
method Demonstrated heteroskedasticity, derived optimal weighting functions, and provided theoretical and empirical comparisons.
result Heuristical weighting function can achieve lower variance than optimal weighting, facilitating more stable and efficient training.
This paper improves change-point detection for complex data streams using denoising score matching.
problem Timely identification of distributional shifts in high-dimensional, complex data streams.
method Score-based CUSUM change-point detection with denoising score matching.
result Denoising score matching enhances detection power by effectively controlling noise scale.
Study improves denoising score matching under relaxed manifold assumptions.
problem Improving denoising score matching under relaxed manifold assumptions.
method Model density with nonparametric Gaussian mixtures, relax manifold assumption, derive non-asymptotic bounds.
result Non-asymptotic bounds on approximation and generalization errors, rates of convergence determined by intrinsic dimension.
New score matching method estimates local intrinsic dimension efficiently.
problem Quantifying the local intrinsic dimension of complex data.
method Denoising score matching loss and equivalent implicit score matching loss.
result Denoising score matching loss is a highly competitive and scalable LID estimator.
New algorithm speeds up causal discovery for network data.
problem Scalability issues in score-matching for temporal network data.
method Developed a new parent-finding subroutine for DAGs, improving score matching efficiency.
result Efficiency-lifted score matching for both i.i.d. and temporal data on networks.
Adapts score matching for missing data in flexible settings.
problem Learning data distribution with missing data.
method Adapted score matching to handle missing data, providing two approaches: importance weighting and variational.
result Variational approach performs best in high-dimensional settings.
Score matching offers efficient estimation for certain distributions.
problem Estimating probability distributions with intractable constants.
method Score matching as an alternative to maximum likelihood.
result Score matching is computationally and statistically efficient for certain distributions.
Paper proposes a new method for training diffusion models using Markov operators.
problem Training efficiency and accuracy in diffusion models.
method Operator-informed score matching using spectral decomposition of Markov operators.
result Improved score matching for both low and high-dimensional distributions.
Large learning rates prevent memorization in denoising score matching.
problem Memorization of training data in diffusion-based generative models.
method Investigating the role of large learning rates in the small-noise regime, proving that they prevent convergence to the empirical optimal score.
result Large learning rates prevent memorization by making it impossible for the learned score to be arbitrarily close to the empirical optimal score.
A new method improves data generation quality by correcting score mismatches.
problem Score mismatch issue in conditional score-based data generation methods.
method Denoising Likelihood Score Matching (DLSM) loss for classifier training.
result The proposed method outperforms previous methods on Cifar-10 and Cifar-100 benchmarks.
A new method for generating samples without training, using smoothed score matching.
problem Generating samples efficiently and without training.
method Moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD).
result The method enables fast, robust, training-free sampling with competitive sample fidelity and diversity.
Generalized score matching for densities on general domains.
problem Estimating density functions on complex, non-standard domains.
method A generalized score matching approach for densities on general domains.
result The method provides theoretical guarantees and empirical advantages.
New method recovers causal graphs from data scores in non-linear models.
problem Recovering causal graphs from data scores in non-linear models.
method Score matching algorithms and efficient Jacobian approximation.
result New method, SCORE, is competitive and faster than state-of-the-art methods.
AR-CSM models use derivatives of univariate log-conditionals to estimate joint distributions efficiently.
problem Scalability and stability issues in training autoregressive models.
method Parameterize joint distribution using derivatives of univariate log-conditionals and introduce Composite Score Matching (CSM) for efficient training.
result AR-CSM models are more scalable and stable compared to previous score matching algorithms.
A new variational inference method using Gaussian score matching.
problem Approximating posterior distributions in Bayesian statistics.
method Score matching principle applied to variational inference.
result Gaussian score matching VI (GSM-VI) is faster and requires fewer gradient evaluations.
Paper efficiently infers differential parameters in time-varying models using time score matching.
problem Efficiently inferring differential parameters in time-varying probabilistic models.
method Directly estimates the differential parameter using time score matching and proves consistency of the method.
result Consistent estimation of parameter derivatives in high-dimensional settings.
Automated denoising score matching handles nonlinear diffusion processes.
problem Nonlinear diffusion processes limit generative modeling and property estimation.
method Local-DSM using local increments and Taylor expansions.
result Tractable training and score estimation for nonlinear diffusion processes.
Improves generative models by using heavy-tailed noise in score matching.
problem High-dimensional limitations of Gaussian noise in generative models.
method Extended DSM to generalised normal distribution, relaxed key assumptions, developed iterative noise scaling algorithm.
result Heavy-tailed DSM leads to improved generative performance.
SMRL uses score matching for efficient RL with exponential family models.
problem Efficient reinforcement learning with unknown transition models.
method Score matching for parameter estimation of exponential family models.
result Achieves online regret of O ( d H 3 T ) O(d\sqrt{H^3T}) O ( d H 3 T ) . A new machine learning model uses score matching to estimate probability densities efficiently.
problem Estimating probability density functions is challenging.
method Introduced a product Jacobi-Theta Boltzmann machine (pJTBM) and used score matching for efficient fitting.
result The pJTBM can fit probability densities more efficiently than the RTBM using score matching.
Score matching efficiency tied to distribution isoperimetric properties.
problem Understanding when score matching is as efficient as maximum likelihood.
method Connecting score matching efficiency to isoperimetric constants of distributions.
result Score matching is statistically efficient when the distribution has a small isoperimetric constant.
Score matching errors are not sufficient for measuring diffusion model quality.
problem The L 2 L^2 L 2 score matching error is not a reliable measure of diffusion model performance. method Decomposed score errors into gradient and solenoidal components and analyzed their geometric properties.
result Only the gradient component of the score error affects the marginal distributional quality.
Propensity score matching improves fairness in machine learning models.
problem Bias in training data affects fairness metrics in machine learning models.
method Propensity score matching to evaluate and mitigate bias in test data.
result FairMatch significantly reduces bias in test data without sacrificing predictive performance.
A new method for training diffusion models using likelihood matching.
problem Training efficient and accurate diffusion models.
method Likelihood Matching approach, quasi-likelihood approximation, score and Hessian estimation.
result Consistent matching of first two transitional moments between diffusion steps.
New algorithm learns bridged diffusion processes without time-reversals.
problem Learning bridged diffusion processes efficiently and accurately.
method Score matching with Doob's h-transform, avoiding time-reversals.
result Outperforms existing methods in learning bridged diffusion processes.
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyvärinen [2005] …
New method improves SBI efficiency and scalability.
problem Scalability issues in SBI methods for large datasets.
method Langevin dynamics with score matching, exploiting likelihood structure.
result Structured score network enhances statistical efficiency and scalability.
Simplifies denoising score matching for manifold learning.
problem Learning distributions on manifolds is computationally intensive.
method Modifies denoising score matching to implicitly account for the manifold.
result Reduces computational burden while maintaining efficiency.
Paper bridges score estimation to parameter and density estimation in DDPMs.
problem Efficiently estimating scores for generative models.
method Introduces a framework linking score estimation to parameter and density estimation.
result Denoising score-matching in DDPMs is asymptotically efficient for parameter estimation.
Enhances learning of structured distributions using nonlinear denoising score matching.
problem Learning structured distributions from noisy data.
method Latent Nonlinear Denoising Score Matching (LNDSM) integrating nonlinear dynamics with VAE-based latent score matching.
result LNDSM achieves superior sample quality and variability compared to structure-agnostic methods.