We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating non-normalized models without computing the normalization constant are not applicable …
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48 results for “intractable normalizing constants”
Bayesian inference uses Stein discrepancy for robustness in intractable likelihoods.
problem Intractable likelihoods in Bayesian inference.
method Generalised Bayesian inference with Stein discrepancy as the loss function.
result Robust generalised posteriors with closed form or accessible using MCMC.
Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant,…
Leveraging Nested MLMC for Sequential Neural Posterior Estimation with Intractable Likelihoodsstat.CO
Paper proposes nested MLMC for SNPE with intractable likelihoods.
problem Estimating posterior distributions from intractable likelihoods.
method Nested MLMC for loss function and gradients, with convergence results.
result Effective methods for approximating complex multimodal posteriors.
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.
This paper shows how to perform likelihood inference for complex graphical models efficiently.
problem Intractable normalizing constants in fully and partially observed exponential family graphical models.
method Using a technique from Geyer (1991), the paper estimates the normalizing constant and its gradient.
result Full likelihood-based analysis is feasible and computationally efficient for these models.
Develops a new Bayesian inference method for discrete data.
problem Computational challenges in discrete state spaces, especially intractable likelihoods.
method Uses a discrete Fisher divergence to update beliefs about model parameters, circumventing the intractable normalising constant.
result Establishes statistical properties of the generalised posterior and proposes a calibration approach.
Computing partition functions, the normalizing constants of probability distributions, is often hard. Variants of importance sampling give unbiased estimates of a normalizer Z, however, unbiased estimates of the reciprocal 1/Z are harder to obtain. Unbiased estimates of 1/Z allow Markov chain Monte Carlo sampling of "d…
NEO combines orbits to sample and estimate complex distributions.
problem Sampling and normalizing complex distributions.
method NEO-IS and NEO-MCMC using invertible maps and orbits.
result NEO provides unbiased estimators and explores multimodal targets.
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] …
A new method normalizes EBM training by introducing a learnable parameter.
problem Training energy-based models with maximum likelihood is challenging due to intractable normalisation constants.
method Proposes a self-normalised log-likelihood (SNL) objective that introduces a learnable parameter representing the normalisation constant.
result The SNL objective is a lower bound of the log-likelihood and can be directly optimised using stochastic gradient techniques.
New MCMC methods use auxiliary variables to sample from intractable distributions.
problem Sampling from distributions with unknown normalizing constants.
method Unified Markov chain Monte Carlo framework with auxiliary variables.
result New algorithms outperform existing methods on synthetic and real datasets.
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-o…
New variational flows improve Monte Carlo and normalization tasks.
problem Intractable global optimum in expressive variational families.
method Constructing asymptotically exact variational flows from involutive MCMC kernels.
result Provable total variation convergence of new variational families.
Robust Score Matchingstat.ML
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.
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…
Contrastive divergence (CD) is a promising method of inference in high dimensional distributions with intractable normalizing constants, however, the theoretical foundations justifying its use are somewhat shaky. This document proposes a framework for understanding CD inference, how/when it works, and provides multiple…
Neural network estimates network models efficiently.
problem Estimating flexible ERGMs is challenging due to intractable normalizing constants.
method Trains a neural network on parameter-simulation pairs to invert and estimate parameters quickly and in parallel.
result The method performs well in practice and accommodates extra network statistics.
We propose Learned Accept/Reject Sampling (LARS), a method for constructing richer priors using rejection sampling with a learned acceptance function. This work is motivated by recent analyses of the VAE objective, which pointed out that commonly used simple priors can lead to underfitting. As the distribution induced …
The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally intractable. We provide accurate approximations that make it possible to numericall…
New method trains EBMs using NFs for more accurate likelihood estimation.
problem Lack of statistical accuracy in EBMs likelihood estimation.
method Uses normalizing flows (NF) to fit an NF to an EBM during training.
result Accurate gradient for EBMs at all times, leading to a fast sampler.
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable, leading to extensive study of approximation methods. Iterative variational methods…
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.
Normalizing flows improve density estimation from noisy data.
problem Estimating underlying density from noisy samples.
method Use normalizing flows for density estimation with arbitrary noise distributions, using amortized variational inference.
result Normalizing flows can outperform Gaussian mixtures for density deconvolution.
Causal Posterior Estimation improves Bayesian inference in complex models.
problem Bayesian inference in models with intractable likelihood functions.
method Normalizing flow-based approximation with conditional dependence structure.
result Improved accuracy in posterior inference through direct incorporation of model structure.
Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel . DPPs possess desirable properties, such as exact sampling or analyticity of the moments, but learning the parameters of kernel through like…
Researchers study the normalizing constant of a continuous categorical distribution.
problem Understanding the normalizing constant of the continuous categorical distribution.
method Characterize numerical behavior and present theoretical and methodological advances.
result The normalizing constant can be written in closed form using elementary functions.
Classifies special submanifolds with specific curvature properties.
problem Classifying submanifolds with constant Moebius curvature and flat normal bundle.
method Analyzes isometric immersions with constant Moebius curvature and flat normal bundle.
result Classifies submanifolds with these curvature properties.
A faster method for density estimation using denoising score matching with random Fourier features.
problem Intractability of normalizing constant in density estimation.
method Denoising Score Matching with Random Fourier Features.
result The method is computationally faster and scalable to complex high-dimensional data.
Paper proposes efficient method to calculate Fisher-Bingham distribution normalizing constant.
problem Efficiently calculating the normalizing constant of Fisher-Bingham distributions.
method Numerical integration with continuous Euler transform to Fourier-type integral representation.
result The method is fast and accurate, applicable to high-dimensional distributions.
2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.
problem Characterizing submanifolds with constant curvature in space forms.
method Analyzing submanifolds with flat normal connection or codimension 2.
result 2-stein submanifolds have constant curvature under specified conditions.
FNFs model parameter-dependent densities by combining a fixed flow with a polynomial parameter-dependent transformation.
problem Learning a separate flow for every parameter configuration is intractable.
method Factorizable Normalizing Flows (FNFs) represent the parameter-dependent density as a fixed flow for a reference configuration and a learnable polynomial transformation factorized over parameters.
result FNFs enable the recovery of the combined effect of multiple parameters without sampling their joint space, providing a scalable and interpretable solution.
Inverts operator on hyperbolic surfaces, constructing invariant distributions.
problem Constructing explicit inversion formula for X-ray normal operator.
method First, inversion formula for attenuated normal operator on Poincaré disk and closed hyperbolic surfaces. Then, explicit construction of invariant distributions.
result Explicit construction of invariant distributions with prescribed pushforward.
A new method improves Bayesian inference for multimodal posteriors.
problem Insensitivity to well-separated modes in multimodal posteriors.
method Weighted Kernel Stein Discrepancy method.
result Significantly improved mode sensitivity compared to standard KSD-Bayes.
We analyze subsets of Carnot groups that have intrinsic constant normal, as they appear in the blowup study of sets that have finite sub-Riemannian perimeter. The purpose of this paper is threefold. First, we prove some mild regularity and structural results in arbitrary Carnot groups. Namely, we show that for every co…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximat…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we study a class of minimum distance estimators for intractable generative models, tha…
The paper characterizes surfaces in 4D space forms with flat normal connection.
problem Characterizing surfaces in 4D space forms with specific geometric properties.
method Analyzing linearly dependent conditions and using properties of sectional curvature.
result Characterizations of space-like and time-like surfaces with flat normal connection.
Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimizationcs.LG
The paper studies estimating the normalizing constant using queries to a black-box function in RKHS.
problem Estimating the normalizing constant of a function in a reproducing kernel Hilbert space.
method Combines Bayesian quadrature and Bayesian optimization approaches, considering different levels of difficulty based on the parameter λ.
result The difficulty of estimating the normalizing constant varies between Bayesian quadrature and Bayesian optimization, even with noisy function evaluations.
Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group manifolds or, more generally, for symmetric spaces. This paper extends the scope of …
Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chose…
In this paper we proof that the Holomorphic angle for compact minimal surfaces in the sphere with constant Contact angle and with a parallel normal vector field must be constant.
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
DGFS improves sampling from complex densities by optimizing partial trajectories.
problem Sampling from intractable high-dimensional density functions.
method DGFS uses a flow function to break down the training process into short partial trajectory segments, leveraging intermediate learning signals.
result DGFS achieves more accurate estimates of the normalization constant.
The study shows how to foliate convex hypersurfaces in affine space with constant curvature.
problem Finding convex hypersurfaces with constant Gauss-Kronecker curvature in affine space.
method Solving a Monge-Ampère equation with specific boundary conditions.
result Regular domains in affine space are foliated by complete convex hypersurfaces with constant Gauss-Kronecker curvature.
New method improves sample diversity and efficiency from complex distributions.
problem Sampling from intractable un-normalized distributions with high auto-correlation.
method Stein self-repulsive dynamics using a repulsive force to push samples away from past trajectories.
result Significantly decreases auto-correlation and increases effective sample size.
Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Mo…
We classify the connected pseudo-Riemannian manifolds of signature with so that at each point of the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes and so that the skew-symmetric curvature operator is not nilpotent for at least …