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.
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.
Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.
Generalizes moment-matching for exponential families with conditioning or hidden data.
problem Generalizing moment-matching conditions for exponential families with conditioning or hidden data.
method First-principles explanation and self-contained derivation of generalized moment-matching conditions.
result Derives generalized moment-matching conditions for conditional exponential families and hidden data.
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.
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.
New method uses neural exponential families for likelihood-free inference.
problem Bayesian Likelihood-Free Inference with intractable likelihood.
method Score Matching neural conditional exponential families for approximate likelihood.
result State-of-the-art performance in posterior sampling for intractable likelihood models.
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
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.
Directly estimates Fisher score for likelihood maximization.
problem Intractable likelihood functions with model simulations.
method Gradient-based optimization using local score matching and linear parameterization.
result Efficient approximation of Fisher score improves likelihood maximization.
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.
ABI bypasses likelihood intractability with nonparametric distribution matching.
problem Approximate Bayesian computation's inefficiency in high-dimensional settings and under diffuse priors.
method Adaptive Bayesian Inference (ABI) compares posterior distributions directly using nonparametric distribution matching and MSW distance.
result ABI significantly outperforms other methods in high-dimensional or dependent observation regimes.
DFM simplifies CNF training without interpolants.
problem Efficiently training CNFs with computationally expensive ODE solving.
method DFM optimizes dual vector fields for bijective transformations.
result DFM outperforms CNF trained with FM or ML objectives.
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.
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…
Method infers parameters in complex diffusion processes.
problem Parameter inference in high-dimensional, non-linear diffusion processes.
method Differentiable score matching to approximate diffusion bridges, used in an importance sampler.
result Numerically stable framework for parameter inference and diffusion mean estimation.
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study this problem from a statistical framework in which one of the graphs is an errorfu…
New method trains energy-based models faster and more stably.
problem Training efficiency and stability of energy-based models.
method EBFlow with score-matching objectives.
result EBFlow achieves significant speedup and better performance.
Resultant improves likelihood-based U-OOD detection across various tasks.
problem Improving likelihood-based U-OOD detection performance.
method Resultant combines post-hoc prior and dataset entropy-mutual calibration techniques.
result Resultant achieves new state-of-the-art U-OOD detection performance.
DTM improves dLLM fine-tuning stability and performance.
problem Intractable sequence-level marginal likelihoods for masked diffusion models.
method Discrete Tilt Matching (DTM) recasts dLLM fine-tuning as state-level matching of local unmasking posteriors under reward tilting.
result DTM yields strong gains on Sudoku and Countdown while remaining competitive on MATH500 and GSM8K.
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.
Graph Energy Matching improves generation quality for molecular graphs.
problem Discrete energy-based models struggle with efficient and high-quality sampling for graph generation.
method Inspired by transport-map optimization, Graph Energy Matching learns a permutation-invariant potential energy to guide sampling.
result GEM matches or surpasses discrete diffusion baselines on molecular graph benchmarks.
Score matching fails to train VAEs robustly, revealing autoencoding loss insights.
problem Catastrophic failure of variational score matching on VAE models.
method Analysis of existing variational score matching objectives and their equivalence to autoencoding losses.
result Score matching methods fail to produce robust VAE models, predicting poor performance.
SFM matches flows on statistical manifolds for better discrete generation.
problem Discrete generation on statistical manifolds with strong prior assumptions.
method Statistical Flow Matching (SFM) on manifold of categorical distributions using Fisher information metric.
result SFM achieves higher sampling quality and likelihood than other models.
This paper tackles matching two complete graphs with correlated edge weights in geometric models.
problem Matching two complete graphs with edge weights correlated through latent geometries.
method Derives an approximate maximum likelihood estimator for recovering hidden vertex correspondence.
result The estimator provably achieves perfect recovery under certain noise conditions.
New bounds show BBVI's gradient variance matches SGD conditions, improving parameterization efficiency.
problem Understanding and improving the convergence of black-box variational inference (BBVI).
method Showed BBVI satisfies matching gradient variance bounds corresponding to the ABC condition for smooth and quadratically-growing log-likelihoods.
result Proven BBVI's gradient variance matches SGD conditions, with superior dimensional dependence for mean-field parameterization.
Study connects database alignment and planted matching using Gaussian features.
problem Identify matching between correlated user features in anonymized databases.
method Derived results for database alignment and planted matching, showing connections and thresholds.
result Performance thresholds for database alignment converge to planted matching when feature dimensionality is sufficiently high.
Matching correlated VAR time series databases by recovering matching permutations.
problem Matching perturbed and permuted correlated VAR time series.
method Probabilistic framework modeling, maximum likelihood estimator (MLE), linear assignment, convex relaxations.
result Recovery guarantees for perfect or partial recovery of matching permutations, thresholds for σ. Unified theory for causal inference using various methods.
problem Estimating causal effects in ATE estimation.
method Riesz regression, covariate balancing, DRE, TMLE, matching estimator.
result Unified theory integrating multiple methods for ATE estimation.
Proposes a non-adversarial method for distribution matching.
problem Stability and optimization challenges in adversarial matching methods.
method Non-adversarial VAE-based matching method with alignment upper bounds.
result Demonstrates applicability of non-adversarial matching methods without modifying original architectures.
New efficient algorithm for approximate PML distribution.
problem Computing the profile maximum likelihood (PML) distribution efficiently.
method Exploiting sparsity structure and new matrix rounding algorithm.
result First provable computationally efficient implementation of PseudoPML.
TRACE improves conformal prediction for multi-dimensional outputs.
problem Challenges in constructing valid and informative conformal prediction regions for multi-dimensional outputs.
method TRACE uses transport alignment in diffusion and flow matching models to define nonconformity scores.
result TRACE yields valid and adaptive conformal prediction regions for multimodal and non-convex distributions.
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined as minimising an expec…
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.
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. Previous work has yielded several approaches to this problem, with theoretical re…
CatFlow uses variational flow matching for efficient graph generation.
problem Graph generation tasks, especially for categorical data.
method Variational flow matching for categorical data, computationally efficient.
result CatFlow achieves strong results on graph generation tasks.
A new layer, funnel, reduces dimensionality in flows for better performance.
problem Training high-dimensional models efficiently and accurately.
method Constructing dimension-reducing surjective flows using the funnel layer.
result The funnel layer improves model performance with a smaller latent space.
A method merges two pretrained diffusion experts to improve image quality and likelihood.
problem Trade-off between image quality and data likelihood in diffusion models.
method Combining two pretrained diffusion experts by switching between them along the denoising trajectory.
result The merged model consistently matches or outperforms its base components, improving or preserving both likelihood and sample quality.
Cold posteriors in BNNs harm performance, likely due to incorrect likelihood.
problem Cold posteriors in Bayesian neural networks degrade performance.
method Developed a generative model explaining cold posteriors and matched it to the tempered likelihoods.
result Cold posteriors are a result of using the wrong likelihood for image classification datasets.
This paper resolves the all-or-nothing phase transition in graph matching.
problem Recovering vertex correspondence between edge-correlated random graphs.
method Analysis of mutual information, truncated second-moment computation, and maximum likelihood estimator.
result Sharp thresholds for correct matching in both dense and sparse graphs.
A new method uses ABC-SMC to infer hybrid models in bioprocesses with limited data.
problem Inference of hybrid models in bioprocesses with limited real data and high uncertainties.
method Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) and linear Gaussian dynamic Bayesian network (LG-DBN) for posterior distribution approximation.
result The method accelerates hybrid model inference and supports process monitoring and robust control.
Unified framework for simulation-based inference learns a single model for multiple tasks.
problem Simulation-based inference for multiple tasks with limited model retraining.
method Unified flow-matching generative model with query-aware masking distribution.
result Competitive performance on various inference tasks and real-world problems.
Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks, alternative non-likelihood training criteria have been proposed. Whilst not necessarily…
Geometrically, high-likelihood regions in DGMs are unlikely to generate OOD data.
problem The paradox of high-likelihood OOD detection in deep generative models.
method Local intrinsic dimension estimation to identify high-likelihood regions that do not generate OOD data.
result A method pairing likelihoods and LID estimates for reliable OOD detection.
Generative Adversarial Networks (GANs) can achieve state-of-the-art sample quality in generative modelling tasks but suffer from the mode collapse problem. Variational Autoencoders (VAE) on the other hand explicitly maximize a reconstruction-based data log-likelihood forcing it to cover all modes, but suffer from poore…
SMURF-THP improves Transformer Hawkes process models by providing uncertainty quantification.
problem Uncertainty quantification for Transformer Hawkes process predictions.
method Score matching for learning the score function of event arrival times.
result SMURF-THP outperforms likelihood-based methods in confidence calibration.
Dual training method for EBMs with overparametrized neural networks.
problem Training EBMs with non-convex energies is challenging.
method Derive variational principles and dual GDA algorithm for feature-learning regime.
result Dual GDA algorithm performs best with similar time scales for features and particles.