Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
New method uses Gaussian ODE filtering to approximate likelihoods for fast ODE inverse problems.
problem Intractable forward models in likelihood-free inference, especially for ODEs.
method Gaussian ODE filtering to construct local Gaussian likelihood approximations.
result New solvers outperform standard likelihood-free approaches on benchmark systems.
Neural networks estimate spatial process likelihoods efficiently.
problem Challenges in estimating spatial processes with slow or intractable likelihoods.
method Convolutional neural networks trained on a classification task to learn likelihood function.
result Neural likelihood surfaces provide fast and accurate parameter estimation.
Two synthetic likelihood methods learn EBM of likelihood from simulator data for SBI.
problem Conduct inference from experimental observations using high-fidelity simulators.
method Learn conditional EBM of likelihood using synthetic data conditioned on parameters.
result Learned likelihood combined with prior yields posterior estimate for sampling.
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.
Develops methods for constructing likelihoods and priors for Bayesian networks.
problem Learning parameters and structure of Bayesian networks from limited data.
method Introduces assumptions for constructing likelihoods and priors from small assessments.
result Allows construction of likelihoods and priors for a wide range of network structures.
Proposes Likelihood Regret for VAEs to improve OOD detection.
problem VAEs can assign high likelihoods to OOD samples, making traditional likelihood thresholds unreliable.
method Introduces Likelihood Regret, a new OOD score for VAEs.
result Empirical results show Likelihood Regret outperforms existing methods for VAEs.
New method improves causal structure discovery with Prior-Fitted Networks.
problem Errors in likelihood estimation limit proper causal structure discovery.
method Amortized causal discovery with Prior-Fitted Networks.
result Significant gains in structure recovery compared to baselines.
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.
Unified contrastive learning for likelihood-free inference.
problem Parameter inference in models with intractable likelihood.
method Unified contrastive learning scheme for both density ratio and direct posterior estimation.
result Unified approach clarifies method selection and comparison.
New method estimates marginal likelihood for deep learning models using training data alone.
problem Estimation difficulties in marginal likelihood for model selection in deep learning.
method Scalable marginal likelihood estimation based on Laplace's method and Gauss-Newton approximations.
result Estimate outperforms cross-validation and manual tuning on various datasets.
This study benchmarks likelihood-free inference methods for models with heavy-tailed or discrete data.
problem Comparing likelihood-free inference methods for models with structural features like heavy-tails or discreteness.
method Four approaches: MLE, NBE, EOT, and AW-NBE are evaluated using simulations.
result The choice of evaluation tools is crucial for models with extremes and discrete data.
New method resolves nonidentifiability in mixture models.
problem Nonidentifiability in marginal models of mixture models.
method Introducing an effective temperature to generalize the marginal likelihood.
result Maximization of the generalized likelihood leads to unique results.
A new ABC method uses variational approximations for efficient inference.
problem Computational challenges in Bayesian inference for complex models.
method Variational approximation for log-posterior, empirical likelihood for estimating expected log-likelihood, differential entropy estimation.
result Posterior consistency established for the proposed method.
New method estimates latent gene expression factors without overlap with known confounders.
problem Estimating latent variance components in gene expression data with known confounders.
method Restricted maximum-likelihood method maximizing likelihood on orthogonal subspace.
result Method reduces runtime and attains greater likelihood values than gradient-based optimizers.
Paper develops methods for estimating and forecasting integer-valued trawl processes.
problem Estimation and forecasting of continuous-time integer-valued trawl processes.
method Composite likelihood methods, focusing on pairwise likelihood.
result Consistency and asymptotic normality of the estimator in the short memory case.
New analysis shows entropy term cancels out in likelihood-based OOD detection.
problem Curious likelihood values for out-of-distribution data.
method Decomposed average likelihood into KL divergence and entropy terms.
result Entropy term explains OOD behaviour and cancels out in expectation.
A new two-step MH method for Bayesian EL computation.
problem Complex likelihood support in Bayesian EL.
method Hierarchical Metropolis Hastings with reversible jump MCMC.
result Improved sampling from BayesEL posteriors.
Develops an empirical likelihood framework for random forests and ensembles.
problem Quantifying the statistical uncertainty of random forests and ensembles.
method Empirical likelihood framework exploiting the incomplete U U U -statistic structure of ensemble predictions. result Modified empirical likelihood statistic achieves accurate coverage and practical reliability.
We present Sequential Neural Likelihood (SNL), a new method for Bayesian inference in simulator models, where the likelihood is intractable but simulating data from the model is possible. SNL trains an autoregressive flow on simulated data in order to learn a model of the likelihood in the region of high posterior dens…
The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is ver…
A new method improves likelihood-free Bayesian inference by transforming summary statistics and using efficient Variational Bayes.
problem Incorrectly assuming normally distributed summary statistics in likelihood-free Bayesian inference.
method Wasserstein Gaussianization transformation combined with robust BSL and efficient Variational Bayes.
result Highly efficient and reliable approximate Bayesian inference for likelihood-free problems.
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.
Develops likelihood-based methods for trawl processes, improving forecasting accuracy.
problem Statistical modeling of trawl processes with heavy tails and long memory.
method Composite likelihood estimation as a stochastic optimization problem, using gradient descent methods.
result New gradient estimators with significantly reduced variance for trawl processes.
The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields…
New method calculates DMN log-likelihood faster.
problem Precise and fast computation of DMN log-likelihood.
method Derived a closed form expression using gamma function properties.
result Closed form calculation is faster with same accuracy.
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…
New methods improve statistical accuracy of complex models without high computational cost.
problem Improving statistical accuracy of complex models without high computational cost.
method Neural posterior and likelihood estimation (NPE and NLE) methods.
result NPE and NLE methods have similar theoretical guarantees to ABC and BSL, but achieve accuracy at a reduced computational cost.
We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method is used to form the noisy log-likelihood estimates using computationally costly …
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…
Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.
problem Overfitting in maximum likelihood estimation.
method Introduces a regularization approach based on gauge symmetry in Kullback-Leibler divergence.
result The method provides a theoretically guaranteed optimal model without frequent hyperparameter tuning.
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.
New method improves simulation-based inference by avoiding model misspecification.
problem Inefficient parameter estimation for models with intractable likelihoods.
method Proposes a robust SNL method with additional adjustment parameters.
result Demonstrates more accurate point estimates and uncertainty quantification.
Develops clustering methods based on likelihood and convergence proved.
problem Hard clustering based on likelihood.
method k-MLE, k-Bregman, k-VARs approaches.
result Convergence proved for clustering methods.
New approach combines likelihood and adversarial losses for better precipitation predictions.
problem Spatially inconsistent precipitation projections from likelihood-based models.
method Fuses likelihood-based and adversarial losses for generative models.
result Improves spatial consistency in precipitation downscaling.
Likelihood-free methods are an established approach for performing approximate Bayesian inference for models with intractable likelihood functions. However, they can be computationally demanding. Bayesian synthetic likelihood (BSL) is a popular such method that approximates the likelihood function of the summary statis…
A new method speeds up quantum state estimation.
problem Exponential growth in sample size and dimension for quantum state tomography.
method Stochastic mirror descent with Burg entropy.
result Optimization error vanishes at a O ( ( 1 / t ) d log t ) O (\sqrt{ ( 1 / t ) d \log t }) O ( ( 1/ t ) d log t ) rate. 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.
Geodesic descent optimizes likelihood in dually flat spaces.
problem Maximum likelihood estimation in exponential families.
method m-geodesic and e-geodesic updates on dually flat spaces.
result Geodesic updates can reach maximum likelihood estimator in one step.
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.
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.
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.
A new method trains and samples from energy-based models using diffusion recovery likelihood.
problem Training and sampling high-dimensional datasets with energy-based models is challenging.
method Trains EBMs with a diffusion recovery likelihood method, maximizing conditional probabilities of data at different noise levels.
result Generates high-fidelity images with low FID and inception scores, and accurately estimates normalized data density.
Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian Computation' methods, but recent work suggests that approaches based on deep neural condi…
Parametric statistical models that are implicitly defined in terms of a stochastic data generating process are used in a wide range of scientific disciplines because they enable accurate modeling. However, learning the parameters from observed data is generally very difficult because their likelihood function is typica…
This research improves neural likelihood approximation for Bayesian inverse problems.
problem Challenges in modeling and inference for high-dimensional Bayesian inverse problems.
method Develops a strictly convex approximation framework for neural likelihood.
result Empirical minimizers converge to the true likelihood as sample size increases.
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.
New method improves community detection for large networks.
problem Inefficient community detection for large sparse networks.
method Decouples row and column labels in likelihood function for fast alternating maximization.
result Strongly consistent estimates of communities with provable convergence guarantee.