Deep QMC ansatzes improve variational QMC accuracy.
problem Improving variational QMC accuracy with neural network ansatzes.
method Analysis of deep neural network ansatzes PauliNet and FermiNet convergence to fixed-node limit.
result Deep QMC ansatzes can reach fixed-node limit with large network sizes.
Quantum neural tangent kernels help understand variational quantum circuits in machine learning.
problem Designing and predicting performance of variational quantum circuits.
method Using quantum neural tangent kernels and dynamical equations for loss functions.
result Analytical solutions for training dynamics in variational quantum circuits.
Paper derives CLT for Bayesian neural networks trained with variational inference.
problem Analyzing the fluctuation behavior of Bayesian neural networks trained with different variational inference schemes.
method Rigorous derivation of CLT for three variational inference schemes: idealized, Bayes-by-Backprop, and Minimal VI.
result Minimal VI scheme has larger variances but is more computationally efficient.
Study of particle system for sampling from probability densities.
problem Sampling from probability densities with unknown normalization.
method Interacting particle system and non-local nonlinear PDE.
result Empirical measure converges to solution of PDE.
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. …
Variational autoencoders struggle with inference quality due to recognition network limitations.
problem Inference suboptimality in variational autoencoders.
method Examined approximate inference in terms of variational distribution capacity and recognition network quality.
result Inference quality is more influenced by recognition network limitations than variational distribution complexity.
We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor structures. We construct a compact classifying space for regular singular Briesk…
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.
The paper studies the dimension of limit sets using variational principles and stationary measures.
problem Calculating the Hausdorff dimension of limit sets of Anosov representations and the Rauzy gasket.
method Established variational principles for affinity exponents and Rauzy gaskets, combined with dimension formulas of stationary measures.
result Yields the equality between the Hausdorff dimensions and affinity exponents in both settings.
TM-VI uses flexible transformation models to approximate complex posteriors in Bayesian models.
problem Approximating complex posteriors in Bayesian models with limited flexibility.
method Transformation models for variational inference (TM-VI).
result TM-VI allows accurate approximation of complex posteriors in models with one parameter and works in a mean-field fashion for multi-parameter models.
Study Edgeworth expansion for quadratic variation estimator with noise.
problem Estimating quadratic variation with noise and error.
method Martingale embedding, Malliavin calculus, stable central limit theorems.
result Obtained a second order expansion for the joint density of estimators.
Meta-CVs leverage task similarity to reduce variance with limited data.
problem Reducing variance in Monte Carlo estimators with few samples.
method Meta-learning control variates for related tasks.
result Meta-CVs lead to significant variance reduction in settings with limited data.
New proof of Donaldson-Uhlenbeck-Yau theorem using variational approach.
problem Proving Donaldson-Uhlenbeck-Yau theorem for slope stable holomorphic vector bundles.
method Variational approach, focusing on Bergman kernel asymptotics.
result Elementary proof of Donaldson-Uhlenbeck-Yau theorem with uniform coercivity.
We derive a continuum model from discrete elastic models on smooth manifolds.
problem Modeling stress-free configurations in geometrically-incompatible elastic systems.
method Variational convergence of discrete models to a continuum model.
result No stress-free configurations unless the manifold is flat.
The paper analyzes how graph-based functionals converge to continuum limits.
problem Analyzing functionals on k-NN graphs for data clouds. method Large sample asymptotics and variational limits of graph cut functionals.
result The solution to graph cut optimization converges to a continuum variational problem.
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.
AVO improves variational inference by encouraging exploration in latent space.
problem Biasing the true posterior to be unimodal limits the density learned in variational inference.
method Inspired by Annealed Importance Sampling, AVO incorporates energy tempering into the optimization objective.
result AVO facilitates learning by encouraging exploration in latent space, improving robustness and benefits.
Unified variational inference framework reveals GAN's limitations and proposes improvements.
problem Limitations of GAN training and lack of completeness in loss function.
method Reinterpretation of variational inference and revealing special cases of GAN, VAE, etc.
result Proposes a regularization term to improve GAN training stability.
A new algorithm improves topic model accuracy in small data sets.
problem Limited data leads to inaccurate topic model identification.
method Developed a novel variational message passing algorithm (ALBU) for LDA.
result ALBU learns latent distributions more accurately than Variational Bayes (VB) in small data sets.
Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on E=[0,∞]d\{(0,0,...,0)} and models another regular variation on the sub-cone E(2)=E\∪i=1dLi, where Li is the $i…
This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.
problem Estimating shared subspace across multiple datasets with varying degrees of misalignment.
method Angle-based Joint and Individual Variation Explained (AJIVE) method, a two-stage spectral approach.
result AJIVE's performance in high signal-to-noise ratio (SNR) regimes and its non-diminishing error in low-SNR settings.
ED-VAE improves VAEs by explicitly including entropy components in ELBO.
problem Limitations of traditional VAEs with ELBO in generating high-quality samples and interpreting latent spaces.
method Introduces ED-VAE, a re-formulation of ELBO that includes entropy and cross-entropy components.
result Significantly enhances model flexibility and improves interpretability and generative performance.
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description is proved. A formal notion of 'spin' force is discovered as a by-product of the v…
The paper analyzes Bayesian neural networks trained with VI, proving a law of large numbers for different schemes.
problem Training Bayesian neural networks with variational inference.
method Analyzes three training schemes: exact estimation, Bayes by Backprop, and Minimal VI.
result All training schemes converge to the same mean-field limit.
New path-gradient estimator for continuous normalizing flows.
problem Limitation of simple Gaussian variational distributions in complex applications.
method Proposed a path-gradient estimator for continuous normalizing flows.
result Empirical evidence of superior performance of the new estimator.
Novel framework discovers SPDEs from limited data.
problem Discovering SPDEs from limited data.
method Combines stochastic calculus, variational Bayes, and sparse learning.
result Accurately identifies SPDEs from limited data.
Study energy functional's second variation on manifolds, proving Morse index bounds.
problem Understanding the stability and index of phase transition interfaces.
method Extending gradient theory to minimal hypersurfaces, proving upper semicontinuity of stability operator eigenvalues.
result Upper bounds for the Morse index of limit interfaces without multiplicity or orientability conditions.
New method clusters matrix-variate data with outliers.
problem Clustering matrix-variate data with outliers.
method Iterative approach using subset log-likelihoods.
result Extends OCLUST algorithm to matrix-variate normal data.
Paper proposes efficient multivariate spatial Fay-Herriot models using variational autoencoders.
problem Estimating population characteristics in small areas with limited data.
method Integrates multivariate spatial Fay-Herriot model with variational autoencoders to leverage spatial structure efficiently.
result Significant computational efficiency improvements for high-dimensional datasets.
Improves Gaussian process models for large datasets.
problem Complexity and memory limitations in Gaussian process models.
method Combines variational sparse approximation and state-space formulation.
result Significant computational and memory savings for large datasets.
SGD implicitly performs variational inference for deep networks, converging to limit cycles.
problem Understanding the implicit regularization in deep neural networks using SGD.
method Proving SGD minimizes an average potential over the posterior distribution with entropic regularization.
result SGD converges to limit cycles rather than classical convergence for deep networks.
Study adiabatic limits of calibrated submanifolds in Riemannian geometry.
problem Understanding the behavior of calibrated submanifolds under adiabatic limits.
method Define a 1-parameter family of forms and study their adiabatic limit, showing it is a generalized calibration.
result Adiabatic calibrated submanifolds are anisotropic minimal in the classical sense.
HYVINT generates hypergraphs with intensity-driven incidence formation and variational learning.
problem Challenges in generating hypergraphs with mechanistic interpretation and limited latent space.
method HYVINT uses intensity-driven incidence formation and a lower-bound variational estimator for latent representations.
result HYVINT achieves strong fidelity and novelty on synthetic and real-world hypergraphs.
The paper exposes VAEs' limitations in learning marginal distributions and proposes VAE-GAN hybrids as a solution.
problem VAEs fail to learn marginal distributions in latent and visible spaces.
method Analyzed VAEs and proposed VAE-GAN hybrids as a solution.
result VAE-GAN hybrids are harder to scale, evaluate, and use for inference compared to VAEs.
Study neural communication systems with bandwidth-limited channels.
problem Reliable message transmission despite noisy channels.
method Jointly model compression and error correction with neural networks; introduce prior for missing information; use auxiliary latent variables.
result Joint neural communication systems outperform separate models under expected information loss.
Develops variational Bayesian neural network for complex biomedical applications.
problem High computational cost of Markov Chain Monte Carlo in BNN.
method Variational Bayes inference for posterior consistency and classification accuracy.
result Developed statistical theory for posterior consistency and prediction accuracy.
In this short paper, we re-derive the Bochner formula for the Laplacian by considering local variations of volume. The derivation is rooted in the fact that the Laplacian of a function measures the volume variation along the flow of the gradient vector of the function. Possible extensions of this approach/technique are…
Quantized Variational Inference improves ELBO optimization with fast convergence.
problem Maximizing Evidence Lower Bound (ELBO) for variational inference.
method Optimal Voronoi Tesselation for variance-free gradients, Richardson extrapolation for asymptotic improvement.
result Quantized Variational Inference leads to fast convergence with comparable computational cost.
New minimax rates for total variation denoising in higher dimensions, showing limitations of linear smoothers.
problem Estimating functions with bounded total variation over high-dimensional grids.
method Minimax analysis, focusing on linear and non-linear estimators.
result Linear estimators like Laplacian smoothing and eigenmaps are suboptimal for total variation denoising in higher dimensions.
Mean field Gaussian inference limits mutual information to regularize neural networks.
problem Understanding and quantifying the regularization effect of mean field Gaussian inference.
method Empirically observed and theoretically quantified mutual information limitation through noise.
result Bounding mutual information between parameters and data effectively regularizes neural networks.
This research explores neural SDEs as deep latent Gaussian models in the diffusion limit.
problem Deep latent Gaussian models with time-inhomogeneous Markov chains and Gaussian perturbations.
method Develops variational inference for neural SDEs using stochastic automatic differentiation in Wiener space.
result The limiting latent object is an Itô diffusion process governed by neural nets.
Variational Inference shows promise for Bayesian GARCH model estimation.
problem Bayesian estimation of GARCH-family models using Monte Carlo sampling.
method Variational Inference as an alternative to Monte Carlo sampling.
result Variational Inference is a reliable and competitive method for Bayesian learning in GARCH-like models.
VLBM learns MDP transitions from limited data, improving OPE performance.
problem Limited coverage of state and action space in offline trajectories.
method VLBM uses variational inference with RSA and branching architecture.
result VLBM outperforms existing OPE methods on deep OPE benchmark.
Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in Rn≥2 as an sharp upper bound of the variational (1,n)∋p-capacity radius, this paper settles a restriction/variant of S.-T. Yau's \cite[Problem 59]{Yau} from the surface area to t…
New algorithm limits regret in changing MDPs.
problem Reinforcement learning in MDPs with time-varying rewards and transitions.
method Proposed an algorithm with performance guarantees for non-stationary policies.
result First variational regret bound for general RL setting.
The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group…
Boosting Variational Inference improves posterior approximations with adaptive step-sizes.
problem Limited resources hinder the widespread adoption of Boosting Variational Inference.
method Characterized global curvature impact, introduced local curvature, and developed an approximate backtracking algorithm.
result New theoretical convergence rates and experimental validation demonstrate improved performance.
Two new methods for variational inference without tractable densities.
problem Challenges in variational inference due to computationally intractable probability density functions.
method Introduces wild variational inference methods that do not require tractable density functions.
result Significant improvement in stochastic gradient Langevin dynamics (SGLD) step size adjustment.