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.
We use neural networks as control variates with geometric integration techniques.
problem Analytic integration of neural network approximations for variance reduction.
method Integration domain subdivision using computational geometry for MLPs with continuous piecewise linear activation functions.
result Neural networks can be used as control variates with geometric integration methods.
NCV uses neural networks to improve Monte Carlo integration.
problem Improving variance reduction in parametric Monte Carlo integration.
method NCV combines a normalizing flow and a neural network to approximate the integrand and solve the integral equation, with a neural importance sampler to estimate the difference.
result NCV achieves state-of-the-art performance in light transport simulation with reduced noise and negligible bias.
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates approaches are well-known to reduce the variance of the estimation. These control v…
Neural SDEs reduce variance in stochastic simulations.
problem Efficiency of Monte Carlo simulations in finance.
method Use neural SDEs with control variates parameterized by neural networks.
result Prove optimality conditions for variance reduction in SDEs with infinite activity.
New method reduces training cost by using approximate gradients.
problem Training neural networks is computationally expensive.
method Uses control variates to approximate gradients without full backward pass.
result Efficacy demonstrated on a vision transformer classification task.
New method reduces variance in Bayesian inverse problems.
problem High variance in Monte Carlo estimates for inverse problems.
method Conditional neural control variates based on Stein's identity.
result Substantial variance reduction across different inverse problems.
This paper develops scalable control variates for Monte Carlo methods using stochastic optimization.
problem Reducing variance in Monte Carlo estimators for large-scale problems.
method Control variates based on Stein operators, optimized through stochastic optimization.
result Novel theoretical results and empirical validations show effective variance reduction.
We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, we first establish a global bound for the Lipschitz constant of …
VAEs analyzed using harmonic analysis, showing how variance controls frequency content and robustness.
problem Understanding and optimizing VAEs for robustness and frequency control.
method Viewing VAE latent space as Gaussian space, deriving results on variance and frequency content, and demonstrating soft Lipschitz constraints.
result Increasing encoder variance reduces high frequency content and improves adversarial robustness.
Neural networks solve variational inequalities for optimal stopping problems.
problem Solving variational inequalities for optimal stopping problems in finance.
method Proposed neural network approach using loss functions directly incorporating variational inequality on whole domain.
result Existence and convergence of neural networks whose losses converge to zero.
Exploration in environments with continuous control and sparse rewards remains a key challenge in reinforcement learning (RL). Recently, surprise has been used as an intrinsic reward that encourages systematic and efficient exploration. We introduce a new definition of surprise and its RL implementation named Variation…
The recent success of raw audio waveform synthesis models like WaveNet motivates a new approach for music synthesis, in which the entire process --- creating audio samples from a score and instrument information --- is modeled using generative neural networks. This paper describes a neural music synthesis model with fl…
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.
NOVI improves deep Gaussian process inference with neural generators and regularized Stein discrepancy.
problem Intractable exact inference in deep Gaussian processes.
method NOVI uses a neural generator to approximate the posterior distribution and minimizes Regularized Stein Discrepancy.
result NOVI achieves 93.56% classification accuracy on CIFAR10, outperforming state-of-the-art methods.
A neural network method tackles high-dimensional diffeomorphic mapping problems.
problem High-dimensional diffeomorphic mapping struggles with the curse of dimensionality.
method Combines variational principles with quasi-conformal theory for accurate, bijective mappings.
result Validated accuracy, robustness, and effectiveness in complex registration scenarios.
Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control varia…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally effic…
CLIP controls neural network stability by bounding Lipschitz constants.
problem Neural networks lack mathematical guarantees of stability, especially to adversarial examples.
method Develops a variational regularization method (CLIP) to control the Lipschitz constant of neural networks.
result CLIP provides a tighter bound on the actual Lipschitz constant compared to layer-wise methods.
Proposes a variational approach to shallow neural networks, bypassing optimization.
problem Theoretical understanding and optimization of shallow neural networks.
method Replaces discrete training with a continuum variational surrogate, proving global well-posedness and regularity.
result Optimal parameter density can be obtained by solving a single linear system, achieving O(1/N) generalization error. Analog BNNs perform similarly regardless of noise distribution shape.
problem Difficulty in precisely controlling noise distribution shape in analog devices.
method Used real device noise as the variational distribution in MFVI training.
result Predictive distributions converge to the same distribution regardless of noise shape.
This work improves variational inference by reducing gradient variance.
problem Hard optimization of flexible variational distributions.
method Control variate based on quadratic approximation of the model's mean and covariance.
result Significant improvement in gradient variance and optimization convergence.
New method reduces inference variance for faster optimization.
problem High variance in black-box variational inference.
method Joint control variate addressing both data subsampling and Monte Carlo noise.
result Significantly reduced gradient variance, leading to faster optimization.
This paper introduces the variational Rényi bound (VR) that extends traditional variational inference to Rényi's alpha-divergences. This new family of variational methods unifies a number of existing approaches, and enables a smooth interpolation from the evidence lower-bound to the log (marginal) likelihood that is co…
We develop a variational framework for SDEs driven by fractional noise.
problem Capturing long-term dependencies in SDEs driven by fractional noise.
method Markov approximation of fractional Brownian motion, variational inference, neural networks.
result Efficient variational inference of posterior path measures for neural-SDEs.
New algorithm uses control variates to improve multi-armed bandit performance.
problem Stochastic multi-armed bandits with auxiliary reward information.
method Developed UCB-CV algorithm using control variates for mean estimation.
result UCB-CV algorithm provides tighter confidence bounds and smaller variance.
Improved confidence interval estimation with control variates.
problem Estimating confidence intervals with minimal samples.
method Designing an estimation algorithm using control variates and leveraging order statistics.
result Improved asymptotic efficiency compared to existing algorithms.
A new method reduces variance in training discrete latent variable models.
problem High variance in stochastic gradient estimators for discrete latent variable models.
method Double control variates for score function estimators using Taylor expansions.
result Our method can have lower variance compared to other estimators.
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.
Optimal Control Theory optimizes neural networks, improving robustness and efficiency.
problem Optimizing deep neural networks (DNNs) for better performance and efficiency.
method Integrating Optimal Control Theory with Backpropagation to develop a new optimizer.
result Optimal Control Theoretic Neural Optimizer (OCNOpt) improves upon existing methods in robustness and efficiency.
Model learns Lagrangian dynamics from images for better prediction and control.
problem Lack of interpretability and applicability to high-dimensional data like images.
method Unsupervised neural network model that learns Lagrangian dynamics from images using a coordinate-aware VAE.
result Model infers interpretable Lagrangian dynamics, enabling long-term prediction and synthesis of controllers.
Scalable and effective exploration remains a key challenge in reinforcement learning (RL). While there are methods with optimality guarantees in the setting of discrete state and action spaces, these methods cannot be applied in high-dimensional deep RL scenarios. As such, most contemporary RL relies on simple heuristi…
Deep neural networks with their large number of parameters are highly flexible learning systems. The high flexibility in such networks brings with some serious problems such as overfitting, and regularization is used to address this problem. A currently popular and effective regularization technique for controlling the…
New method prevents neural network breakdown by combining trimmed loss and variation regularization.
problem Outlier contamination in neural network training.
method Integrates transformed trimmed loss and higher-order variation regularization.
result Ensures robustness to outlier contamination with a high functional breakdown point.
APAC-Net solves high-dimensional stochastic MFGs using neural networks.
problem High-dimensional stochastic mean-field games.
method Alternating population and control neural networks, parameterizing value and density functions.
result Solves up to 100-dimensional MFG problems.
Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the application of regularization strategies. We present a mathematical framework unifying…
Paper proposes a method to stabilize estimation of KL divergence using a discriminator in RKHS.
problem High variance and instability in estimating KL divergence using neural network discriminators.
method Developed a novel construction of the discriminator in RKHS, controlled its complexity, and proved the consistency of the estimator.
result Reduced variance and stabilized training of KL divergence estimates.
Combines control variates and adaptive importance sampling for Monte Carlo integration.
problem Improving Monte Carlo integration accuracy with control variates and adaptive sampling.
method A quadrature rule combining control variates and adaptive importance sampling.
result Non-asymptotic bound on the probabilistic error of the procedure.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
problem Efficiency of control variates in reducing variance for Monte Carlo simulations.
method Study of a specific quadrature rule using nonparametric regression-adjusted control variates.
result A specific quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under sufficient smoothness assumptions.
With the recently rapid development in deep learning, deep neural networks have been widely adopted in many real-life applications. However, deep neural networks are also known to have very little control over its uncertainty for unseen examples, which potentially causes very harmful and annoying consequences in practi…
Neural EKF improves structural dynamics prediction.
problem Accurately predicting structural response for health monitoring.
method Neural Extended Kalman Filter (Neural EKF) for learning dynamics.
result Significant predictive capabilities demonstrated on simulated and real-world data.
Paper improves variance control in importance weighted variational bounds.
problem Improving the variance of gradient estimators for IWAE.
method Develops a novel control variate that grows SNR as √K for large K.
result Empirically, the method yields superior variance reduction for generative models.
Photonic quantum reinforcement learning for control problems.
problem Solving continuous control problems with noisy quantum computers.
method Proximal policy optimization for photonic variational quantum agents.
result Photonic policy learning achieves comparable performance to classical neural networks.
ControlSHAP stabilizes Shapley value approximations using control variates.
problem High computational cost of exact Shapley values in blackbox models.
method ControlSHAP uses Monte Carlo control variates to stabilize Shapley value approximations.
result Significant reduction in Monte Carlo variability of Shapley estimates.
Generic generation and manipulation of text is challenging and has limited success compared to recent deep generative modeling in visual domain. This paper aims at generating plausible natural language sentences, whose attributes are dynamically controlled by learning disentangled latent representations with designated…
Proposes variance reduction techniques for sliced Wasserstein distance estimation.
problem Intractability of estimating sliced Wasserstein distances.
method Uses control variates based on Gaussian approximations of projected measures.
result Significant reduction in variance of SW distance estimators.
The paper studies how neural policies can be interpreted using decision trees.
problem Understanding how machine learning controllers make decisions in complex environments.
method The approach involves disentangled representation using decision trees to interpret neural policies.
result The paper shows that disentanglement of learned neural dynamics improves interpretability.
Novel neural architecture improves Bayesian experimental design efficiency.
problem Intractable evaluation of expected information gain (EIG) in Bayesian optimal experimental design.
method Develops a neural architecture that optimizes a single variational model for estimating EIG across many designs, using a lower bound for computational efficiency.
result Significantly improves accuracy in Bayesian experimental design with better sample efficiency.