We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian network models, namely networks that include hidden variables, where asymptotic ap…
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48 results for “likelihood evaluation”
Benchmark of Likelihood-Free Inference Methods based on Neural and Optimal Transport Approachesstat.ME
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.
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 …
Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explici…
HollowFlow speeds up likelihood evaluation for large-scale models.
problem Prohibitive scaling of sample likelihood computations in flow-based models.
method Introduces HollowFlow, a flow-based generative model using a NoBGNN with a block-diagonal Jacobian structure.
result Achieves up to O(n^2) speed-up in likelihood evaluation for large systems.
This work evaluates deep generative models using RD curves, providing a more comprehensive quality assessment.
problem Quantitative evaluation of deep generative models is challenging, especially for implicit models.
method Proposes using rate distortion (RD) curves to evaluate and compare deep generative models, approximating the entire curve with similar computations to log-likelihood estimation.
result Approximating the entire RD curve provides a more comprehensive quality assessment than scalar-valued metrics.
A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these rese…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them susceptible to estimation errors. We thus propose to replace each…
Normalizing flow regression approximates posterior distributions without additional sampling.
problem Bayesian inference with computationally expensive likelihood evaluations.
method Normalizing flow regression (NFR) for offline inference.
result NFR yields a tractable posterior approximation through regression on existing log-density evaluations.
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…
Improved MCMC sampling for expensive, irregular likelihoods.
problem Bayesian inference challenges with irregular, expensive likelihoods.
method Adapt subset samplers, introduce data-driven proxies, adaptive controller.
result Improved HINTS algorithm achieves best sampling error in fixed budget.
Framework for Bayesian inference using GP emulated MH sampler for noisy likelihoods.
problem Approximate Bayesian inference with limited noisy log-likelihood evaluations.
method Gaussian process emulates MH sampler for log-likelihood evaluations; sequential experimental design selects evaluation points.
result Approximate sampler is sample-efficient and robust to GP assumptions.
This paper introduces a method to estimate log-likelihood in VAE models.
problem Difficulty in comparing models trained via ELBO due to lack of log-likelihood.
method Introduces a general upper bound to approximate model evidence.
result Efficiently approximates model evidence and compares to other bounds.
A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio under model and true distributions. When the likelihood ratio is unknown, it can b…
New method uses approximate KLD for intractable likelihood models.
problem Designing experiments for models with intractable likelihoods.
method Derive a lower bound of KLD utility, express it in terms of entropies, and evaluate efficiently.
result Demonstrated the performance of the proposed method through numerical examples.
Bayesian method infers contextual bandit policies robustly.
problem Inference of contextual bandit policies in small sample sizes.
method Empirical likelihood for Bayesian inference.
result Accurate uncertainty measurements and policy comparison.
SCALLOP improves likelihood flow maps for efficient Boltzmann generation.
problem Efficient estimation of model likelihood in flow-based generative models.
method SCALLOP introduces a Hutchinson-free likelihood distillation objective for scalable flow-based models.
result SCALLOP achieves up to 10x inference speedup while improving performance.
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…
Improves likelihood-free inference by using a new sampling approach to avoid biased data collection.
problem Efficient Bayesian inference without likelihood evaluation for real-world datasets.
method Introduces Neural Proposal (NP) to sample simulation inputs i.i.d. for unbiased posterior inference.
result Demonstrates improved performance, especially for multi-modal posteriors, through experiments.
Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to the gradient or a large number of likelihood evaluations. We introduce here a n…
In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering met…
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…
Bayesian Learning of Conditional Kernel Mean Embeddings for Automatic Likelihood-Free Inferencestat.ML
In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they demand large quantities of simulation calls. Critically, hyperpara…
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.
Deep Bayes Factorsstat.ME
Deep learning improves Bayes factor computation for likelihood-free models.
problem Computing Bayes factors for likelihood-free models is challenging.
method Proposes a deep learning estimator of Bayes factors using simulated data.
result Establishes consistency of the Deep Bayes Factor estimator.
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood that identifies a probability measure which lies in the neighbor…
We approximate differential entropy for efficient Bayesian experimental design.
problem Efficiently estimating expected information gain in large-scale inference problems.
method Approximate differential entropy using Monte Carlo or quasi-Monte Carlo surrogates.
result Our approach achieves comparable or better convergence rates than state-of-the-art methods.
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a classifier to distinguish between pairs of parameter-observation samples generated using…
Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transf…
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte…
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.
Optimizing full likelihoods adapts loss scales and shapes for robust modeling.
problem Rigid loss functions limit model adaptability and robustness.
method Optimize full likelihoods with adjustable parameters.
result Adaptive tuning of loss scales and shapes improves model robustness.
A new concordance loss improves model performance and reliability in survival prediction.
problem Inconsistent evaluation of deep survival models using likelihood losses.
method Proposed a value-monotone concordance loss (SCL) to improve reliability and optimization.
result SCL achieves comparable discrimination and is the best or within one standard deviation of the best C-index across multiple datasets.
VBMC+VIQR outperforms noisy models in Bayesian inference.
problem Bayesian inference with noisy likelihoods in complex models.
method Gaussian process surrogates, expected information gain, variational interquantile range.
result VBMC+VIQR achieves state-of-the-art performance in noisy inference benchmarks.
New criterion improves predictive evaluation in weighted inference scenarios.
problem Improving predictive evaluation in scenarios with different likelihoods for estimation and evaluation.
method Developed the posterior covariance information criterion (PCIC) to handle weighted likelihood inference.
result PCIC is asymptotically unbiased for quasi-Bayesian generalization error in weighted inference.
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes that tie parameters of an underlying theory and measurement apparatus to hig…
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.
Python package for estimating Hurst exponent in fBm.
problem Estimating Hurst exponent in fractional Brownian motion.
method Whittle's likelihood method applied to fractional Gaussian noise.
result Implementation achieves state-of-the-art accuracy and speed.
Generates multimodal safety-critical scenarios for robustness evaluation of decision-making algorithms.
problem Lack of comprehensive evaluation of neural network robustness under real-world scenarios.
method Proposes a flow-based multimodal scenario generator using weighted likelihood maximization and gradient-based sampling.
result Demonstrates improved testing efficiency and multimodal modeling capability compared to traditional methods.
Deep Gaussian Processes improve likelihood-free inference for complex distributions.
problem Limited flexibility of Bayesian Optimization with GPs for multimodal distributions.
method Proposes Deep Gaussian Processes (DGPs) as a surrogate model for likelihood-free inference.
result DGPs outperform GPs on multimodal distributions while maintaining comparable performance on unimodal cases.
Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matchingstat.ML
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.
Markov random fields (MRFs) are difficult to evaluate as generative models because computing the test log-probabilities requires the intractable partition function. Annealed importance sampling (AIS) is widely used to estimate MRF partition functions, and often yields quite accurate results. However, AIS is prone to ov…
Deep learning and genetic algorithms speed up cosmological Bayesian inference.
problem Substantial computational demands in Bayesian inference for cosmological parameter estimation.
method Deep learning using feedforward neural networks to approximate likelihood functions dynamically, optimized with genetic algorithms.
result Significant speed-up in Bayesian inference process for cosmological models and datasets.
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix …
Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Meansstat.ML
This work studies a unified approach to ensemble aggregation using likelihood perspective.
problem Density aggregation in machine learning, focusing on improving ensemble predictions.
method Normalized generalized mean of order r in the log-likelihood framework.
result The optimal range for r is [0,1], providing a principled justification for linear and geometric pooling.
New RL algorithm GDPO improves DLM reasoning efficiency.
problem Adapting RL to DLMs for efficient, unbiased likelihood estimation.
method Group Diffusion Policy Optimization (GDPO) using semi-deterministic Monte Carlo.
result GDPO outperforms existing methods on math, reasoning, and coding benchmarks.
Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task.…
In this paper we study the probabilistic properties of the posteriors in a speech recognition system that uses a deep neural network (DNN) for acoustic modeling. We do this by reducing Kaldi's DNN shared pdf-id posteriors to phone likelihoods, and using test set forced alignments to evaluate these using a calibration s…