A new particle algorithm improves mean-field variational inference.
problem Efficiently approximating nonparametric posterior distributions in machine learning.
method Introduces PArticle VI (PAVI), a novel particle-based algorithm for nonparametric mean-field approximation.
result Obtains non-asymptotic error bounds for PArticle VI, providing the first end-to-end guarantee for particle-based MFVI.
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in th…
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting information from the neighbors. This process can be equivalently converted into a feedf…
Bayesian inference is used extensively to infer and to quantify the uncertainty in a field of interest from a measurement of a related field when the two are linked by a physical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large d…
A new method reduces inference cost for FwFM by allowing it to scale with item fields only.
problem High computational cost in FwFM for large field counts.
method Low-rank diagonal plus symmetric decomposition for field-wise interactions.
result Aggressive rank reduction outperforms pruning in accuracy and speed.
The inference of correlated signal fields with unknown correlation structures is of high scientific and technological relevance, but poses significant conceptual and numerical challenges. To address these, we develop the correlated signal inference (CSI) algorithm within information field theory (IFT) and discuss its n…
New algorithm improves CRF inference and learning.
problem Efficient inference and learning for dense CRFs.
method Regularized Frank-Wolfe algorithm for nonconvex CRF optimization.
result Regularized Frank-Wolfe outperforms mean field and CNN baselines.
New method improves approximate inference for Bayesian models.
problem Approximate inference for high-dimensional Bayesian models.
method Entropic regularization of mean-field variational inference.
result Improved recovery of true posterior dependency.
Bayesian ODEs with Gaussian processes infer unknown dynamics from data.
problem Estimating unknown continuous-time system dynamics from data.
method Bayesian nonparametric model using Gaussian processes, sparse variational inference, probabilistic shooting.
result Posterior predictive uncertainty scores outperform alternative methods on multiple ODE learning tasks.
Review of mean-field methods for neural network inference.
problem Understanding neural network learning from a theoretical perspective.
method Mean-field methods, high-temperature expansions, replica method, message passing algorithms.
result Equivalences and complementarities of mean-field methods.
GANs as priors improve uncertainty quantification in complex fields.
problem Bayesian inference challenges in high-dimensional, discrete fields.
method Use GANs to approximate prior distributions for Bayesian updates.
result Demonstrated efficacy on image classification, inpainting, denoising, and inverse problems.
Simulation-based inference tackles complex inverse problems in science.
problem Challenging inverse problems in complex simulations.
method Review and identification of forces driving the field.
result Expanding the audience to appreciate the impact on science.
The paper studies stability of mean-field variational inference for log-concave distributions.
problem Stability of mean-field variational inference for log-concave distributions.
method Novel approach via linearized optimal transport, lifting non-convex problem to convex optimization over transport maps.
result Dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in 2-Wasserstein distance.
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
New tractable models for complex Ising models over specific topologies.
problem Complex Ising models over specific topologies.
method Sequential application of efficient/inbrute-force inference and sampling to components.
result Improved inference and sampling quality for specific Ising models.
Enhances GNN robustness during inference using Conditional Random Fields.
problem Vulnerability of GNNs to adversarial attacks.
method Post-hoc approach using Conditional Random Fields (CRF).
result Improves robustness of GNNs across various models.
The paper develops methods for high-dimensional inference in Markov random fields.
problem Statistical inference for high-dimensional Markov random fields.
method Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization.
result The proposed methods achieve ℓ1-consistency and false discovery rate control. The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the …
TSCI improves causal inference in dynamical systems using vector fields.
problem Challenges in causal discovery with time series data in dynamical systems.
method TSCI method using vector fields to check for synchronization between learned dynamics.
result TSCI outperforms traditional methods like CCM and its generalizations.
Study infers evolutionary interactions from protein sequences using regularization methods.
problem Inferring evolutionary interactions from protein sequences.
method Regularization methods, including L2 for fields and group L1 for couplings, with parameter tuning. result Effective regularization parameters for sparse couplings improve accuracy.
We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants…
ALO-CV approximates leave-one-out error in proportional regime.
problem Estimating generalization error in high-dimensional settings.
method Developed new analysis for ALO-CV, showed consistency under strong convexity.
result ALO-CV approximates leave-one-out error up to negligible error.
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true likelihood. But due to requirement for model-specific derivation of the optimization equa…
We build a model using Gaussian processes to infer a spatio-temporal vector field from observed agent trajectories. Significant landmarks or influence points in agent surroundings are jointly derived through vector calculus operations that indicate presence of sources and sinks. We evaluate these influence points by us…
CoRMF uses RNNs to solve Ising models efficiently by ordering critical edges.
problem Solving Ising models efficiently and accurately.
method Criticality-ordered spin sequence and RNNs for mean-field factorization.
result Proves tighter error bounds than naive mean-field.
Develops a new framework for analyzing MFVI algorithms.
problem Analyzes mean field variational inference (MFVI) formulations.
method Inspired by variational Bayesian formulations, represents MFVI problem in three ways: gradient flow, Fokker-Planck-like equations, and diffusion process.
result Establishes rigorous guarantees for convergence of time-discretized coordinate ascent variational inference algorithms.
The paper analyzes mean-field variational Bayes for complex models and proposes new uncertainty quantification methods.
problem Approximating posterior distributions in complex Bayesian models with latent variables.
method Non-asymptotic analysis on mean-field variational inference, showing that a normal distribution with the MLE center approximates the posterior well.
result The mean-field approximation matches the MLE up to higher-order terms and is essentially efficient for regular parametric models.
Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not str…
A neural network model minimizes region-based free energy for faster inference in MRFs.
problem Efficient inference in complex Markov random fields (MRFs).
method Region-based Energy Neural Network (RENN) that directly minimizes region-based free energy.
result RENN outperforms other methods in marginal distribution estimation, partition function estimation, and MRF learning.
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus …
Machine learning benefits from causal inference concepts.
problem Machine learning's hard problems are related to causality.
method Introduces key concepts linking machine learning and causal inference.
result Machine learning and AI's challenges are intertwined with causality.
Paper improves variational inference on Boolean hypercube using quantum methods.
problem Improving variational inference for pairwise Markov random fields on the Boolean hypercube.
method Quantum relaxations of the Kullback-Leibler divergence for upper-bounds, primal-dual optimization, and greedy selection of hierarchies.
result Efficient algorithm and improved bounds for variational inference.
New algorithm speeds up large-scale statistical inference.
problem Efficiently solving large-scale mean-field variational inference problems.
method Developed a novel primal-dual algorithm (PD-VI) and a block-preconditioned extension (P2D-VI) for mean-field variational inference. result PD-VI and P2D-VI achieve faster convergence and better solution quality compared to existing methods. Efficiently infers time-varying sparse MRFs with strong statistical guarantees.
problem Inference of time-varying sparse MRFs with strong statistical guarantees.
method Constrained optimization with exact ℓ0 regularization, near-linear time and memory complexity. result Sharp statistical guarantees for sparsely-changing Gaussian MRFs with as few as one sample per time.
Bayesian neural networks ignore data in infinite units limit.
problem Pathological behavior of posterior in over-parameterized networks.
method Mean-field variational inference in infinite hidden units limit.
result Posterior mean converges to zero, ignoring data.
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In th…
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph part…
New method infers population dynamics from snapshots using path space optimization.
problem Recover dynamics of a population from its temporal marginals.
method Grid-free algorithm using Schrödinger bridges coupled via noisy gradient descent in mean-field limit.
result Global convergence to min-entropy estimator with end-to-end theoretical guarantees.
Paper tackles high-order inference in structured prediction tasks.
problem Maximizing a score function on the space of labels in high-order Markov random fields.
method Generative model approach with two-stage convex optimization algorithm.
result Success in general high-order inference problems driven by hyperedge expansion properties.
Rotates MFVI for better Gaussian approximations.
problem Improving variational approximations for complex distributions.
method Rotated coordinate system, PCA-based rotation, iterative Gaussianization.
result Significantly more accurate approximations with lower computational cost.
Wide BNNs with odd activations fail to approximate data under mean-field inference.
problem Theoretical limitations of mean-field variational inference in wide, deep Bayesian neural networks.
method Analysis of mean-field variational inference in fully-connected BNNs with odd activation functions and Gaussian likelihood.
result The optimal mean-field variational posterior predictive distribution converges to the prior predictive distribution as network width increases.
Ensemble Kalman Filter improves GPSSM inference for online learning.
problem Non-mean-field variational inference issues in GPSSM.
method Combining EnKF with NMF variational inference.
result Improved online learning performance and data-fitting accuracy.
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solv…
Deep Bayesian neural nets can use simpler weight approximations without sacrificing performance.
problem The need for complex weight posterior approximations in deep Bayesian neural networks.
method Theoretical and empirical analysis of mean-field variational inference in deep networks.
result Mean-field variational weight posteriors in deep networks can induce similar function-space distributions as complex approximations in shallower networks.
Surveying nonparametric inference with shape constraints, past and future.
problem Statistical inference under shape constraints.
method Historical overview and future directions.
result Outlook on future research directions.
New method for variational inference without conjugacy constraints.
problem Efficient variational inference with flexible prior and approximation families.
method Wasserstein gradient flow for mean-field approximation.
result Improved convergence and efficiency of variational inference.
NIFTy.re accelerates imaging models and expands Gaussian processes and variational inference.
problem Slow performance and limited inference strategies in NIFTy.
method Rewritten NIFTy with new modeling principles, inference strategies, and JAX integration.
result Dramatic acceleration of models and new inference capabilities.