We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference …
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48 results for “semi-implicit posterior”
Enhances graph modeling with hyperbolic geometry and variational inference.
problem Challenges in modeling relational data with complex dependencies.
method Semi-implicit hierarchical variational Bayes with Poincaré embedding and mutual information regularization.
result Improves graph representation quality and flexibility in edge prediction and node classification.
Improved phylogenetic tree reconstruction using flexible branch length distributions.
problem Inefficient Markov chain Monte Carlo methods for large sequence datasets.
method Variational Bayesian phylogenetic inference with semi-implicit branch length distributions.
result Proposed method improves marginal likelihood estimation and branch length posterior approximation.
Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have limited expressive power due to the Gaussian assumption of latent variables. In t…
Unified theory for semi-implicit variational inference, bridging approximation and optimization.
problem Developing a statistical theory for semi-implicit variational inference.
method Unified theory combining approximation and optimization analyses.
result Unified theory characterizes SIVI's ability to recover target distributions and governs asymptotic behavior.
Proposes LBD for more robust deep learning models.
problem Improving robustness and uncertainty in deep learning models.
method Model-agnostic learnable Bernoulli dropout with joint optimization of dropout rates.
result Superior performance compared to other dropout schemes.
Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with …
Continuous semi-implicit models enable faster training and better performance in generative modeling.
problem Slow convergence in hierarchical semi-implicit models during training.
method CoSIM, a continuous semi-implicit model that incorporates a continuous transition kernel for efficient training.
result CoSIM achieves superior performance on image generation tasks compared to existing methods.
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior distribution. In turn, the expressivity of the variational family is largely limited by …
Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density function, explicit or not, as long as independent random samples can be generat…
Kernel semi-implicit variational inference improves variational inference without additional optimization.
problem Intractability of hierarchical semi-implicit distributions in variational inference.
method Kernel semi-implicit variational inference (KSIVI) using kernel methods to eliminate lower-level optimization.
result KSIVI reduces variational inference to kernel Stein discrepancy (KSD) optimization, improving expressiveness and tractability.
Semi-Implicit Variational Inference (SIVI) is improved with SIVI-SM using score matching.
problem Intractable densities in variational distributions hinder SIVI training.
method SIVI-SM uses score matching to handle intractable densities in a minimax formulation.
result SIVI-SM outperforms ELBO-based SIVI methods in Bayesian inference tasks.
Kernel SIVI improves variational inference by avoiding lower-level optimization.
problem Intractable densities in semi-implicit variational distributions.
method Kernel SIVI-SM uses a minimax formulation and kernel tricks to avoid lower-level optimization.
result Kernel Stein discrepancy (KSD) objective is computable and leads to convergence guarantees.
Thompson sampling is an efficient algorithm for sequential decision making, which exploits the posterior uncertainty to address the exploration-exploitation dilemma. There has been significant recent interest in integrating Bayesian neural networks into Thompson sampling. Most of these methods rely on global variable u…
Proposes a semi-implicit back propagation method for neural networks.
problem Challenges in training neural networks, especially gradient vanishing and small step sizes.
method Proposes a semi-implicit back propagation method using error back propagation and proximal methods.
result The proposed method leads to better performance in terms of loss decreasing and training/validation accuracy compared to SGD and ProxBP.
To combine explicit and implicit generative models, we introduce semi-implicit generator (SIG) as a flexible hierarchical model that can be trained in the maximum likelihood framework. Both theoretically and experimentally, we demonstrate that SIG can generate high quality samples especially when dealing with multi-mod…
IDAC improves reinforcement learning efficiency by modeling implicit distributions.
problem Improving sample efficiency in reinforcement learning algorithms.
method IDAC uses two DGNs for a distributional critic and a semi-implicit actor to model implicit policy distributions.
result IDAC outperforms state-of-the-art algorithms on OpenAI Gym environments.
PVI improves SIVI by directly optimizing ELBO without parametric assumptions.
problem Intractable variational densities in SIVI methods.
method Particle Variational Inference (PVI) using empirical measures to approximate optimal mixing distributions.
result PVI directly optimizes the ELBO and performs favorably compared to other SIVI methods.
Improved UIVI method shows better performance than state-of-the-art SIVI methods.
problem Estimating the likelihood of samples from complex distributions in high dimensions.
method Replaced the inner MCMC loop of UIVI with importance sampling and learned the optimal proposal distribution.
result The refined UIVI approach demonstrates superior performance or parity with state-of-the-art methods.
SGRNN models evolving graph data for better property prediction.
problem Modeling evolving graph data for property prediction.
method SGRNN uses stochastic latent variables to capture both node attribute and topology evolution, with semi-implicit variational inference and KL-divergence simplification.
result SGRNN improves property prediction on real-world datasets.
SIFG uses noisy particles to efficiently sample from complex distributions.
problem Efficient sampling from complex distributions using particle-based methods.
method SIFG introduces a semi-implicit functional gradient flow with Gaussian noise to improve sampling efficiency and accuracy.
result SIFG achieves strong theoretical convergence guarantees and efficient sampling.
In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic mar…
We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from discretizing an ordinary differential equation with a semi-implicit Euler integrat…
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit …
We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on stagger…
In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) equation. We propose the so-called Riccati met…
Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces additional latent random variables to jointly model the hidden states of a graph…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. …
FP-BMA improves generalization by encouraging flat posteriors in Bayesian Model Averaging.
problem Lack of flat posterior in approximate Bayesian inference methods hinders effective Bayesian Model Averaging.
method Proposes Flat Posterior-aware Bayesian Model Averaging (FP-BMA) and Flat Posterior-aware Bayesian Transfer Learning schemes.
result FP-BMA successfully captures flat posteriors, improving generalization performance.
New research shows CPE only occurs when Bayesian posterior underfits.
problem Model misspecification leading to CPE under perfect model specification.
method Theoretical analysis of Bayesian posterior and underfitting.
result No CPE if there is no underfitting of the Bayesian posterior.
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
SiD distills pretrained diffusion models into a fast one-step generator.
problem Efficiently distilling pretrained diffusion models into a fast generator.
method Reformulates forward diffusion processes as semi-implicit distributions and uses three score-related identities to create a loss mechanism.
result Achieves high FID performance and significantly reduces generation time.
Theoretical framework for M-posteriors connects Bayesian and frequentist statistics.
problem Connecting Bayesian and frequentist approaches in statistical inference.
method Developed a theoretical framework for M-posteriors, showing asymptotic normality and frequentist consistency.
result M-posteriors are robust and contract around M-estimators under mild conditions.
New method improves generative model performance by fully conditioning variational posteriors.
problem Inaccurate inference due to partial conditioning of variational posteriors in sequential LVMs.
method Introduces fully-conditioned approximate posteriors to improve generative model performance.
result Improves generative modelling and multi-step prediction performance.
PVI seeks a posterior that makes predictions closer to true data, not approximating the Bayesian posterior.
problem Finding meaningful posterior distributions under model misspecification.
method Predictive variational inference (PVI) seeks an optimal posterior density for close predictive matching to true data.
result PVI learns a posterior that is not the same as the Bayesian posterior, but is closer to the true data generating process.
Optimized -posteriors reduce KL divergence from true posterior in parametric misspecification.
problem Reduction of KL divergence from true posterior in parametric model misspecification.
method Derivation of Bernstein-von Mises theorem and optimization of -posteriors.
result Optimized -posteriors minimize KL divergence from true posterior, especially in severe misspecification.
This work explores how overparametrization and priors affect Bayesian neural network posteriors.
problem Symmetries, non-identifiabilities, and weight-space priors fragment and inflate BNN posteriors.
method We study the interplay between overparametrization and priors in BNN posteriors, deriving key phenomena and validating through experiments.
result Overparametrization induces structured, prior-aligned weight posterior distributions.
Adaptive method improves numerical solution of Cox-Ingersoll-Ross model.
problem Approximating solutions to the Cox-Ingersoll-Ross model efficiently.
method Path-bounded timestepping with hybrid approach, including a backstop method.
result The adaptive method is strongly convergent, with strong error control.
New priors can update posteriors without re-estimating likelihoods.
problem Degradation of classification approaches when class priors change.
method Recompute posteriors using recovered likelihoods from original posteriors and new priors.
result Dynamic update of original posteriors is possible without re-estimating likelihoods.
Bayesian learning made scalable with posteriors library.
problem Computational challenges in Bayesian learning with modern models.
method Introducing posteriors library and tempered MCMC.
result Bayesian approximations are useful and scalable.
The representation of the approximate posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the approximate posterior have a detrimental impact on the generative performance of VAEs due to the mismatch with the true posterior. We extend the class of posterior models that may be l…
When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updatingstat.ME
New decision-theoretic characterization separates belief and decision posteriors.
problem Understanding the conditions under which loss-based updating coincides with Bayesian updating.
method Decision-theoretic approach to distinguish belief and decision posteriors.
result Generalized Bayes coincides with ordinary Bayesian updating only if the loss is proportional to negative log-likelihood.
Improved MALA method for neural networks uncertainty quantification.
problem Uncertainty quantification in Bayesian neural networks.
method Corrected Stochastic MALA (csMALA) with a simplified correction term.
result Improved surrogate posterior for quantifying uncertainties in neural networks.
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the val…
New methods for scalable inference in modular models with misspecified sub-models.
problem Model misspecification in multi-modular models complicates evidence combination.
method Variational methods for approximating Cut and SMI posteriors, and Variational Meta-Posterior.
result Feasibility of analysis with multiple cuts using a single set of variational parameters.
New method controls posterior collapse in VAEs without network architecture constraints.
problem Posterior collapse in VAEs reduces diversity of generated samples.
method Introduces Latent Reconstruction (LR) loss to control posterior collapse.
result Controls posterior collapse on various datasets without architectural constraints.
This paper explores Bayesian Neural Network posteriors, uncovering symmetries and their impact.
problem Understanding the complex posterior distribution of deep Bayesian Neural Networks.
method Investigates optimal approaches for approximating posteriors, analyzes modes, and explores visualizations.
result Uncovered weight-space symmetries and their impact on the posterior, particularly scaling symmetries.
TARP tests accuracy of generative posterior estimators.
problem Assessing the accuracy of posterior estimators from generative models.
method TARP coverage testing method.
result TARP can detect inaccurate inferences in high-dimensional spaces.