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Particle-based Variational Inference with Preconditioned Functional Gradient Flow

ICLR 2023 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Variational inference theory and gradients

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use PFG instead of SVGD or SGLDHierarchical logistic regression · covtype and germanaccuracy: covtype: 75.1 -> 75.7; german: 65.1 -> 67.6Helped
Use PFG instead of SVGD or SGLDHierarchical logistic regression · covtype and germannll: covtype: 0.58 -> 0.51; german: 0.71 -> 0.64Helped
Use PFG instead of M-SVGD or pSGLDBayesian neural networks · Bostontest RMSE: 2.72$_{\pm0.17}$ -> 2.47$_{\pm0.11}$Helped
Use PFG instead of M-SVGD or pSGLDBayesian neural networks · Energytest RMSE: 0.89$_{\pm0.10}$ -> 0.48$_{\pm0.04}$Helped
Use PFG instead of SVGDParticle-based inference · Sonar, 1,000 particlestime: 19.10$_{\pm0.52}$ -> 11.56$_{\pm0.24}$Helped
Use PFG instead of SVGDParticle-based inference · Sonar, 5 particlestime: 5.20$_{\pm0.10}$ -> 7.87$_{\pm0.16}$Hurt
Use PFG instead of JKO methodsBayesian logistic regression · Covtypeaccuracy: JKO-ICNN: 75.0 -> 75.7; JKO-Variational: 75.3 -> 75.7Helped
Use diagonal preconditioning rather than identity preconditioning (ablation)PFG · ill-conditioned Gaussian samplingKL divergenceHelped
Use Hessian-aware preconditioning rather than identity (ablation)PFG · Gaussian samplingKL convergence bound: (1-σ²_d/(2σ²_1))^(2t) C_0 -> 1/4^t C_0Helped
Use a neural-network function class rather than an RBF kernel function class (ablation)Particle-based VI · 10-cluster Gaussian mixturesampling qualityHelped
Use an RBF function class rather than a linear function class (ablation)SVGD · 20-dim N(0,I) variance fittingvariance: 1.01 -> 0.35Hurt
Use a neural-network function class rather than a linear function class (ablation)PFG · 20-dim N(0,I) variance fittingvariance: 1.00 -> 0.99No clear effect

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