A new sequential test for unnormalized densities.
problem Testing unnormalized densities with adaptive stopping.
method Sequential kernelized Stein discrepancy test, using non-uniform Stein kernels.
result Valid test with asymptotic lower bound for growth.
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including no…
Unified view on learning unnormalized distributions using NCE.
problem Learning unnormalized distributions across different communities.
method Noise-Contrastive Estimation (NCE) for a unified perspective.
result Established finite-sample convergence rates for exponential families.
New KSDs control moments in approximations, improving diagnostics and tests.
problem Inability of standard KSDs to control moment convergence.
method Developed alternative diffusion KSDs under sufficient conditions.
result First KSDs to exactly characterize q-Wasserstein convergence.
Paper presents a new method to learn unnormalized models efficiently.
problem Scalability issues in score matching for flexible unnormalized models.
method Connects learning objectives to Wasserstein gradient flows for scalability.
result Demonstrates improved learning of unnormalized models on manifolds.
New method estimates model discrepancy without sampling for unnormalized models.
problem Evaluating and training unnormalized density models efficiently.
method Estimate Stein discrepancy using neural network parameterized vector function.
result Method outperforms existing goodness-of-fit tests and training methods.
REGS samples from unnormalized distributions using gradient flow and neural networks.
problem Sampling from unnormalized distributions with high accuracy and efficiency.
method REGS is a particle method that iteratively transforms samples from a reference distribution to match an unnormalized target distribution using Wasserstein gradient flow and neural networks.
result REGS outperforms state-of-the-art methods in sampling from challenging multimodal distributions and real datasets.
New algorithms solve weak optimal transport problems for nonlinear costs.
problem Computing weak optimal transport with nonlinear costs.
method Mirror descent algorithms for primal and dual versions of WOT.
result Solutions for WOT and WOTUK compared with classical OT.
A new kernel Stein test assesses fit for variable-length sequential data.
problem Evaluating goodness of fit for varying-dimensional data like text documents of different lengths.
method Extends kernel Stein discrepancy (KSD) to variable-dimension settings by identifying appropriate Stein operators and proposing a novel KSD goodness-of-fit test.
result The proposed test performs well on discrete sequential data benchmarks.
Graph Laplace operators uniquely identify metrics and densities on manifolds.
problem Identifying Riemannian metrics and sampling densities from graph Laplace operators.
method Analyzing intrinsic and extrinsic graph Laplace operators on compact Riemannian manifolds.
result Graph Laplace operators uniquely determine metrics and densities under certain conditions.
Transformers improve with Fourier integral attentions.
problem Inefficiency of dot-product attention in capturing feature dependencies.
method Interpreted attention as kernel regression, proposed FourierFormer with generalized Fourier integral kernels.
result FourierFormer achieves better accuracy and reduces redundancy.
Morse neural networks improve uncertainty quantification and detection.
problem Uncertainty quantification and out-of-distribution detection.
method Generalizes unnormalized Gaussian densities to high-dimensional submanifolds using KL-divergence loss.
result Unified approach for OOD detection, anomaly detection, and continuous learning.
We investigate adversarial learning in the case when only an unnormalized form of the density can be accessed, rather than samples. With insights so garnered, adversarial learning is extended to the case for which one has access to an unnormalized form u(x) of the target density function, but no samples. Further, new c…
The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some consistent estimators have been proposed earlier, the problem of statistical efficienc…
New sampling method uses gradient-free IPS with RKHS velocity field.
problem Efficient sampling from unnormalized target densities.
method Gradient-free interacting particle systems (IPS) with RKHS velocity field.
result IPS produce high-quality samples from various target distributions.
Unified empirical and variational Bayes for unnormalized densities.
problem Approximating unnormalized densities using latent variable models.
method Formulate a latent variable model for Y=X+N(0,σ2Id), use ELBO as parametrization of Y's energy function, and estimate X with empirical Bayes least-squares. result UVB has higher capacity to approximate energy functions than MLPs in DEEN.
New CUSUM algorithm detects changes in unnormalized models.
problem Change detection in models with unknown normalization constants.
method Score-based CUSUM (SCUSUM) algorithm based on Fisher divergence and Hyvärinen score.
result Asymptotic optimality of the SCUSUM algorithm demonstrated.
CD algorithm achieves near-optimal convergence rate for unnormalized models.
problem Training unnormalized models with high efficiency.
method Non-asymptotic analysis of contrastive divergence algorithm.
result CD can achieve O(n−1/2) convergence rate under regularity assumptions. PDDS samples from unnormalized densities using iterative particle scheme.
problem Sampling from unnormalized probability densities.
method Iterative particle scheme with novel score matching loss.
result Asymptotically consistent estimates for multimodal and high-dimensional tasks.
Paper optimizes change detection in unnormalized distributions.
problem Detecting changes in unnormalized pre- and post-change distributions.
method Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration.
result Asymptotically optimal performance achieved through unbiased estimation of CUSUM statistics.
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and sco…
SQUEAK reduces space complexity for Nystrom approximations in KRR.
problem Large datasets in KRR require impractical storage space.
method SQUEAK uses unnormalized ridge leverage scores for incremental updates.
result Space complexity improved with constant factor worse than exact RLS.
We develop underdamped diffusion bridges for sampling from unnormalized densities.
problem Sampling from unnormalized densities without direct access to samples.
method Underdamped diffusion bridges with rigorous score matching equivalence.
result State-of-the-art performance in sampling across various problems.
A problem about Khovanov homology and 3-manifolds is discussed in this paper.
One-step diffusion samplers reduce sampling time and computational costs.
problem Efficient sampling from complex distributions.
method One-step diffusion, self-distillation, deterministic flow.
result Achieves competitive sample quality with fewer evaluations.
New method improves performance of Hamiltonian MCMC for log Z estimation.
problem Estimating tight bounds on log Z for unnormalized distributions.
method Uncorrected Hamiltonian Annealing (UHA) using reparameterization gradients.
result Better performance and easier parameter tuning compared to existing methods.
Single-step samplers generate high-quality samples efficiently.
problem Sampling from unnormalized distributions is computationally expensive.
method Developed consistent diffusion samplers that generate samples in a single step.
result Single-step samplers produce high-fidelity samples with less than 1% of traditional samplers' evaluations.
A new method called TemperFlow tackles multimodality in sampling from unnormalized distributions.
problem Sampling from unnormalized distributions with isolated modes.
method TemperFlow learns a sequence of tempered distributions to progressively approach the target distribution.
result TemperFlow overcomes the limitations of existing methods and achieves superior performance.
iEFM trains CNF models from unnormalized densities efficiently.
problem Training generators from energy functions or unnormalized densities.
method Iterated energy-based flow matching (iEFM) with simulation-free objective.
result iEFM outperforms existing methods in probabilistic modeling.
Proposes a method combining CNFs and rejection-resampling for sampling from unnormalized densities.
problem Sampling from unnormalized probability densities, especially multimodal ones.
method Combines continuous normalizing flows with rejection-resampling steps based on importance weights.
result The method improves sampling accuracy and performance compared to state-of-the-art methods.
Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket. This includes a categorification of brackets skein relation. Then we incorporat…
Neural density estimators are flexible families of parametric models which have seen widespread use in unsupervised machine learning in recent years. Maximum-likelihood training typically dictates that these models be constrained to specify an explicit density. However, this limitation can be overcome by instead using …
New Stein operator improves robustness in model inference.
problem Improving robustness in inference for unnormalized models.
method Density-power weighted Stein operator (γ-Stein operator). result Robust methods for goodness-of-fit testing and posterior approximation.
SoftCVI uses contrastive estimation to infer complex posteriors.
problem Estimating complex posteriors in Bayesian inference.
method Contrastive variational inference with self-generated soft labels.
result SoftCVI outperforms other variational approaches in stability and coverage.
There are two types of deep generative models: explicit and implicit. The former defines an explicit density form that allows likelihood inference; while the latter targets a flexible transformation from random noise to generated samples. While the two classes of generative models have shown great power in many applica…
Adaptive stopping in MCMC using classifier-based dynamics
problem Sampling from complex, unnormalized probability densities
method Training state-dependent neural classifiers
result Significant reduction in average trajectory lengths
We construct the universal sl(2)-tangle cohomology using an approach with webs and dotted foams. This theory depends on two parameters, and for the case of links it is a categorification of the unnormalized Jones polynomial of the link.
A new method optimizes a generalized Kullback-Leibler divergence for better simulation-based inference.
problem Optimizing likelihood functions when they are only known implicitly.
method Optimizes a generalized Kullback-Leibler divergence that accounts for normalization constants in unnormalized distributions.
result Unified approach that combines Neural Posterior Estimation and Neural Ratio Estimation.
We establish a parabolic version of Tian's C2,α-estimate for conical complex Monge-Ampere equations, which includes conical Kähler-Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical Kähler-Ricci flow in arXiv:1411.7284.
LFIS uses a time-dependent velocity field to sample from complex distributions.
problem Sampling from unnormalized density functions.
method LFIS learns a time-dependent velocity field to transport samples from a simple initial distribution to a complex target distribution.
result LFIS achieves state-of-the-art performance on various benchmark problems.
A new method for sampling from complex distributions using Langevin samplers.
problem Sampling from unnormalized Boltzmann densities.
method Probability flow ODE derived from linear stochastic interpolants, employing Langevin samplers.
result Efficient simulation of the flow with non-asymptotic convergence rate.
A new sampling method using log-concave Markov chains.
problem Sampling from unnormalized densities efficiently.
method Decomposes sampling into log-concave Markov chains with noisy measurements.
result Shows remarkable capacity to 'tunnel' between modes of a distribution.
There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence method, pseudo-likelihood, Monte Carlo maximum likelihood, and noise contrastive…
New method minimizes robust density power-based divergences for general parametric densities.
problem Computational complexity of minimizing DPD for general parametric densities.
method Stochastic approach to minimize DPD for general parametric density models.
result Proposed method can be applied to minimize other density power-based γ-divergences.
Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.
problem Understanding machine learning methods for data with varying intrinsic dimensions.
method Γ-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on intersecting manifolds of varying dimensions.
result Normalized Dirichlet energy converges to a tensorized Dirichlet energy that adapts to all dimensions simultaneously.
Generative models learn smoother densities to sample from unknown distributions.
problem Sampling from unknown distributions in high-dimensional spaces.
method Formalizes sampling problem, introduces multimeasurement noise model, derives Bayes estimator, and uses underdamped Langevin MCMC.
result Formulation leads to efficient sampling methods and theoretical connections with denoising autoencoders.
We generalize the maximal time existence of Kähler-Ricci flow in Tian-Zhang and Song-Tian to conical case. Furthermore, if the twisted canonical bundle KM+(1−β)[D] is big or big and nef, we can expect more on the limit behaviors of such conical Kähler-Ricci flow. Moreover, the results still hold for simple normal …