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.
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48 results for “variational approach”
Characterizes obstacles to variational formulation of Dirac dynamics.
problem Obstacles to variational formulation of Dirac dynamics.
method Characterizes using basic cohomology for Dirac structures and Lie algebroids.
result Characterizes the obstruction to variational formulation.
Improved Bayesian uncertainty quantification using variational bagging.
problem Inefficient and underestimating uncertainty in mean-field variational Bayes.
method Integrates bagging with variational Bayes for improved inference.
result Bagged variational posterior provides proper uncertainty quantification.
Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical work suggests that inference networks can produce suboptimal variational parameter…
Solving Statistical Mechanics Using Variational Autoregressive Networkscond-mat.stat-mech
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variation…
Variational approach to basic manifold structures.
problem Understanding basic differential geometric structures.
method Variational description of geometric structures.
result Variational formulation of manifold structures.
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densities on model parameters. In this note, we review the main variants of …
Classical approaches for approximate inference depend on cleverly designed variational distributions and bounds. Modern approaches employ amortized variational inference, which uses a neural network to approximate any posterior without leveraging the structures of the generative models. In this paper, we propose Amorti…
Variational Pseudolikelihood for Regularized Ising Inferencecond-mat.stat-mech
I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than regularized maximum pseudolikelihood inference as well as mean field and isolated spin pair appro…
A new variational method speeds up Bayesian phylogenetic inference.
problem Slow and inefficient MCMC methods in Bayesian phylogenetic inference.
method Combining subsplit Bayesian networks with variational inference for efficient tree topology and branch length estimation.
result Variational approach provides competitive performance with significantly fewer iterations.
The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.
Combines variational and evolutionary optimization for generative models.
problem Optimizing generative models with discrete latent variables.
method Truncated posteriors as variational distributions, evolutionary algorithms applied to variational parameters.
result Evolutionary algorithms effectively optimize variational bounds for generative models.
A new optimization algorithm for Gaussian Variational Inference on precision matrices.
problem Complex models with positive definite constraints on covariance matrices.
method Manifold Gaussian Variational Bayes (MGVBP) with natural gradient updates.
result Empirically validated as a feasible and efficient solution for VI in complex models.
We investigate the optimization of two probabilistic generative models with binary latent variables using a novel variational EM approach. The approach distinguishes itself from previous variational approaches by using latent states as variational parameters. Here we use efficient and general purpose sampling procedure…
Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family. Here, we introduce automatic structured variational inference (ASVI), a fully au…
A new meta-learning method using shared variational inference.
problem Meta-learning with uncertainty over model parameters.
method Shared amortized variational inference network for conditional prior and posterior.
result Prevents collapse of conditional prior to Dirac delta function.
Variational Temperingstat.ML
Variational inference (VI) combined with data subsampling enables approximate posterior inference over large data sets, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of conditionally conjugate exponential family models. This approach uses a decreasing te…
This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
problem Pathwise gradient estimators in variational inference have high variance, leading to inefficient optimization.
method Apply zero-variance control variates to pathwise gradient estimators.
result Zero-variance control variates can significantly reduce the variance of pathwise gradient estimators without requiring complex assumptions.
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The treatment of the distributions' subsets as variational parameters distinguishes …
Optimizes MCMC chains with neural control variates.
problem Reducing variance in Markov Chain Monte Carlo (MCMC) simulations.
method Uses neural networks as control variates to minimize asymptotic variance.
result Derives optimal convergence rate under various ergodicity assumptions.
Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The original approach to approximate inference in these models used variational compressio…
A new VIS approach improves log-likelihood estimation in latent variable models.
problem Challenges in achieving high log-likelihood with VI for complex posterior distributions.
method Uses forward divergence to optimize proposal distribution for better log-likelihood estimation.
result Consistently outperforms state-of-the-art baselines in log-likelihood and parameter estimation.
VBphenoR uses variational Bayes for EHR-based patient phenotyping.
problem Phenotyping patients from EHR data for targeted treatments.
method Variational Bayes Gaussian Mixture Model (GMM) and logistic regression.
result Closed-form inference for efficient patient phenotype determination.
New variational approach for privacy and fairness in data representations.
problem Learning private and fair representations while preserving relevant information.
method Variational formulation of privacy and fairness optimization problems using Lagrangians.
result Control over the trade-off between utility and privacy/fairness through a Lagrange multiplier parameter.
Mixed Variational Inferencestat.ML
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies. Variational approaches avoid this issue by explicitly minimising the Kullback-Leibler…
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…
The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem…
We propose a simple and general variant of the standard reparameterized gradient estimator for the variational evidence lower bound. Specifically, we remove a part of the total derivative with respect to the variational parameters that corresponds to the score function. Removing this term produces an unbiased gradient …
Variational Prediction simplifies Bayesian inference without test time costs.
problem Bayesian inference's computational costs and posterior predictive distribution marginalization.
method Variational Prediction learns a variational approximation to the posterior predictive distribution using a variational bound.
result Directly learns a variational approximation to the posterior predictive distribution without test time marginalization costs.
New proof of Gaffney's inequality for differential forms on manifolds with boundary.
problem Proving Gaffney's inequality for differential forms on manifolds with boundary.
method Variational approach combined with Bochner's technique.
result New proof of Gaffney's inequality for differential forms.
New method accelerates energetic variational inference using particle dynamics.
problem Efficiently solving variational inference problems with reduced computational cost.
method Particle-based variational inference with implicit scheme, inspired by energy quadratization and operator splitting.
result Significantly reduces computational cost compared to existing methods.
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restricti…
This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a matrix or a vector. By exploiting the hidden low-rank property of a high-dimens…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and to carry out Bayesian inference, however, quantification of uncertainty with vari…
The paper compares unrolling and bilevel optimization for learning variational models.
problem Learning variational models in supervised learning.
method Analyzes unrolling and bilevel optimization approaches for variational models.
result Unrolling can be better than bilevel optimization, but performance depends on parameters.
Study joint invariants on symplectic spaces, extending group and space variations.
problem Computing joint invariants on linear symplectic spaces.
method Review and extend previous work on group and space variations, relate to differential invariants.
result New computations and extensions of joint invariants.
We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). Our approach utilizes variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the …
We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a hierarchical manner using a simple reparameterizable distribution whose variational …
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…
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…
Minimal submanifolds are found as energy concentration sets in variational problems.
problem Understanding the structure of minimal submanifolds in codimension two.
method Purely variational approach, extending previous work on geodesics.
result Non-degenerate minimal submanifolds can be derived from critical maps of the Ginzburg-Landau functional.
Optimizing Variational Representations of Divergences and Accelerating their Statistical Estimationcs.LG
New method tightens variational representations of divergences for faster learning.
problem Improving tightness of variational representations of divergences for faster statistical estimation.
method Improved objective functionals constructed via an auxiliary optimization problem, leveraging neural network approximation.
result Tighter variational representations can result in significantly faster learning and more accurate estimation of divergences.
Efficiently learns from partial labels using variational inference.
problem Learning from noisy and ambiguous partial labels in crowdsourcing.
method Amortized variational inference for probabilistic posterior approximation.
result Achieves state-of-the-art performance in accuracy and efficiency.
Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are approximated by Gaussian sampling. These approaches are of particular interest …
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dy…
A new recursive mixture estimation algorithm improves VAE inference efficiency and accuracy.
problem Inaccurate posterior approximation in traditional VAEs.
method Recursive mixture estimation algorithm using functional gradient approach for iterative component selection.
result Significantly higher test data likelihood compared to state-of-the-art methods on benchmark datasets.