We develop a framework for approximating collapsed Gibbs sampling in generative latent variable cluster models. Collapsed Gibbs is a popular MCMC method, which integrates out variables in the posterior to improve mixing. Unfortunately for many complex models, integrating out these variables is either analytically or co…
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48 results for “Intractable integral”
Bayesian approach for inhomogeneous Poisson process intensity estimation.
problem Intractable integral in likelihood of Gaussian Cox process.
method Joint modeling of intensity and cumulative intensity as transformed Gaussian process; exact MCMC sampler.
result Exact posterior inference without approximations.
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
problem Estimating intractable integrals in complex models.
method Probabilistic, model-based approach using Gaussian processes.
result Comprehensive review and systematic taxonomy of Bayesian quadrature methods.
Improves accuracy of SMCI estimators without expanding sum regions.
problem Intractable multiple summations in evaluating expectations on the Ising model.
method Combining multiple SMCI estimators using generalized least squares (GLS).
result The proposed method can improve accuracy without combinatorial explosion.
A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricingq-fin.CP
Improved path integral method for financial derivatives pricing.
problem Analytical intractability of financial derivative pricing models.
method Generalized semi-classical path integral approach to time-dependent Hamiltonians.
result Accuracy and computational efficiency of the path integral approach for derivatives pricing.
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm r…
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we …
A new model DKMPP integrates covariates and uses an integration-free method for spatio-temporal point processes.
problem Training intractable deep spatio-temporal point processes with multimodal covariates.
method DKMPP uses a deep kernel to model complex relationships and an integration-free score matching method.
result DKMPP and score-based estimators outperform baseline models in spatio-temporal point processes.
Distilling Model Knowledgestat.ML
Top-performing machine learning systems, such as deep neural networks, large ensembles and complex probabilistic graphical models, can be expensive to store, slow to evaluate and hard to integrate into larger systems. Ideally, we would like to replace such cumbersome models with simpler models that perform equally well…
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intract…
We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods that use both an inference network and a refinement procedure to output samples f…
SING improves state inference in latent SDE models for better drift function estimation.
problem Intractable posterior inference in latent SDE models.
method Natural gradient variational inference.
result SING provides faster and more reliable inference in latent SDE models.
A new method combines AIS and SMCI for efficient evaluation of Ising models.
problem Efficiently evaluating expectations on Ising models under various temperatures.
method Combining Annealed Importance Sampling (AIS) and Spatial Monte Carlo Integration (SMCI).
result The proposed method performs efficiently in both high- and low-temperature regions.
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lo…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model uncertainty. Variational methods have been used for approximating intractable integrals t…
Discrete integration in a high dimensional space of n variables poses fundamental challenges. The WISH algorithm reduces the intractable discrete integration problem into n optimization queries subject to randomized constraints, obtaining a constant approximation guarantee. The optimization queries are expensive, which…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (Møller et al., 2006; Murray et al., 2006) for tackling this pr…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information availab…
Hybrid model combines continuous and tractable probabilistic models.
problem Intractable probabilistic inference in continuous latent-space models.
method Continuous mixtures of tractable probabilistic models with finite integration points.
result Hybrid models achieve state-of-the-art performance in density estimation.
A new method improves inference for complex Bayesian models.
problem Bayesian inference for doubly intractable distributions is computationally challenging.
method Monte Carlo Stein variational gradient descent (MC-SVGD) approach.
result The method achieves substantial computational gains over existing algorithms.
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-defined convex program, we must retain the conve…
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.
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.
We prove in this paper that the weighted volume of the set of integral transportation matrices between two integral histograms r and c of equal sum is a positive definite kernel of r and c when the set of considered weights forms a positive definite matrix. The computation of this quantity, despite being the subject of…
Paper uses referenced thermodynamic integration for Bayesian model selection in a complex COVID-19 transmission model.
problem Bayesian model selection with uncertainty and misleading metrics.
method Referenced thermodynamic integration for intractable high-dimensional distributions.
result Favourable convergence performance in model selection for COVID-19 transmission.
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.
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which implies that the joint distribution given the ODE's and GP kernels is also Gaussian di…
Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions …
Efficient Bayesian decision-making with intractable likelihoods.
problem Bayesian decision-making under intractable likelihoods.
method Learning surrogate models and using simulation-based inference and Bayesian optimization.
result Optimal actions can be learned with fewer simulations than posterior inference.
New method for efficient inference over complex parameter spaces.
problem Challenges in Bayesian inference for high-dimensional, intractable likelihoods.
method Arbitrary Marginal Neural Ratio Estimation (AMNRE) for simulation-based inference.
result Efficient inference over arbitrary subsets of parameters without numerical integration.
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed distributions and distributions with analytically intractable densities turns out to be…
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates approaches are well-known to reduce the variance of the estimation. These control v…
We propose an algorithm which predicts each subsequent time step relative to the previous timestep of intractable short rate model (when adjusted for drift and overall distribution of previous percentile result) and show that the method achieves superior outcomes to the unbiased estimate both on the trained dataset and…
Gradient-based MCMC for discrete spaces improves sampling performance.
problem Sampling in discrete spaces using traditional methods is challenging.
method Introduced new discrete Metropolis-Hastings samplers inspired by MALA, with a novel preconditioning technique.
result Demonstrated strong empirical performance across various challenging sampling problems.
Develops algorithm to differentiate Metropolis-Hastings for optimization.
problem Optimizing intractable densities with discrete components.
method Fuses stochastic automatic differentiation with Markov chain coupling schemes.
result Unbiased and low-variance gradient estimator for intractable densities.
Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimationcs.LG
A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.
problem Quantifying uncertainty in neural network predictions.
method Proposes a single-model approach integrating Gaussian distribution with softmax outputs, using mean-field approximation.
result Competitive performance on uncertainty estimation tasks and outperforms many methods on out-of-distribution detection.
A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniques to sample from the posterior, such as Markov chain Monte Carlo (…
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.
Investor maximizes utility from an unknown claim using robust optimization.
problem Maximizing utility from an unknown contingent claim.
method Robust optimization with quantile formulation and variational inequalities.
result Optimal trading strategy and utility indifference price determined.
Bayesian optimization is a sample-efficient approach to solving global optimization problems. Along with a surrogate model, this approach relies on theoretically motivated value heuristics (acquisition functions) to guide the search process. Maximizing acquisition functions yields the best performance; unfortunately, t…
Generative Bayesian Filtering improves inference in complex models without explicit density evaluations.
problem Performing posterior inference in complex nonlinear and non-Gaussian state-space models.
method Generative Bayesian Filtering (GBF) extends GBC to dynamic settings using deep neural networks for recursive posterior inference. Generative-Gibbs sampler bypasses density evaluations for parameter learning.
result GBF significantly outperforms likelihood-free approaches in accuracy and robustness for intractable state-space models.
A new MCMC method for GPs tackles computational burden and intractable likelihoods.
problem High computational burden and intractable likelihoods in Gaussian process models.
method Combines variationally sparse Gaussian processes with pseudo-marginal MCMC.
result Asymptotically exact inference with computational gains for large datasets.
Proposes exact inference for continuous-time Gaussian process dynamics.
problem Inexact inference methods for continuous-time Gaussian process dynamics are impractical for irregularly-sampled data.
method Uses higher-order numerical integrators to discretize dynamics with arbitrary accuracy and proposes multistep and Taylor integrators for exact inference.
result Demonstrates accurate representation of continuous-time systems through exact GP inference.
Paper generalizes tensor-train approximation for complex random variables.
problem Characterizing intractable high-dimensional random variables.
method Extends inverse Rosenblatt transform to general reference measures and integrates into deep variable transformation framework.
result Deep inverse Rosenblatt transport significantly expands tensor approximations for complex random variables.
QT improves inference in complex PGMs with hidden variables.
problem Intractable learning and prediction errors in undirected PGMs with hidden variables.
method Query training (QT) learns a worse model to improve marginal inference.
result QT produces better marginals for a given inference algorithm than the original model.
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild dif…
New method for MCMC models without perfect or sequential samplers.
problem Bayesian inference for complex models with intractable terms.
method Utilizes tractable independence model to construct unbiased estimates.
result Scalable method for high-dimensional models.
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.