VISA improves inference efficiency for complex models.
problem Efficient approximate inference in computationally intensive models.
method Sequential sample-average approximations within a trust region.
result VISA achieves comparable accuracy with computational savings.
We use variational Gaussian approximations to analyze parametric models with unknown data-generating distributions.
problem Analyzing inference and learning in parametric models with unknown or intractable data-generating distributions.
method Replica method with variational Gaussian approximation in grand canonical formalism.
result Stationarity conditions adaptively determine parameters of the trial Hamiltonian for each dataset.
New analysis shows Bayesian model averaging is suboptimal under misspecification.
problem Generalization performance of Bayesian model averaging under model misspecification.
method Novel second-order PAC-Bayes bounds to analyze generalization performance.
result New Bayesian-like algorithms with better generalization performance.
Defines Φ-harmonic maps and studies their unstable manifolds.
problem Characterizing unstable manifolds of Φ-harmonic maps. method Extrinsic average variational method in calculus of variations.
result Every compact Φ-superstrongly unstable manifold is Φ-strongly unstable. Neural moving average model speeds up state space model inference for time series data.
problem Efficiently scaling approximate Bayesian inference for time series data.
method Proposes a novel generative model (neural moving average model) for latent temporal states in state space models.
result Achieves accurate parameter estimation in a short time for various models.
BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of implementing the variational Bayesian update equations, the user can construct model…
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic g…
IA-BMA adapts model weights to inputs for better predictions.
problem Predicting with multiple models in heterogeneous settings.
method Input adaptive Bayesian Model Averaging (IA-BMA) with an input adaptive prior and amortized variational inference.
result IA-BMA consistently delivers more accurate and better-calibrated predictions.
The paper analyzes rates for a modified gradient descent method using Stein variational gradients.
problem Improving the accuracy of gradient descent methods for complex target distributions.
method Derives finite-particle rates for regularized Stein variational gradient descent (R-SVGD).
result Establishes explicit non-asymptotic bounds for time-averaged empirical measures.
The paper connects convex functions to p-subharmonic functions and proves their equivalence.
problem Understanding the relationship between convex functions and p-subharmonic functions.
method Average principle, variational methods, and PDE techniques.
result Convex functions on R^n are p-subharmonic for every p > 1.
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use …
Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
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…
A new method averages neural network parameters to rank features robustly.
problem Neural networks' sensitivity to random initialization affects feature ranking robustness.
method Parameter averaging of multiple shallow networks trained with different random seeds.
result The averaged model discovers ground-truth feature importance consistently.
Paper proposes a method to improve variational inference for sparse networks.
problem Variational inference struggles with sparse networks, leading to inaccurate community detection.
method The method involves hard thresholding the posterior of community assignment after each iteration.
result The proposed method accurately recovers true community labels in sparse networks.
Method analyzes complexity of empirical risk landscapes for generalized linear models.
problem Understanding the complexity of empirical risk landscapes in generalized linear models.
method Kac-Rice method and replicated method from theoretical physics.
result Explicit variational formulas for the number of critical points of empirical risk landscapes.
In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our …
The paper uses Bayesian methods to infer hidden processes with unknown parameters.
problem Estimating hidden processes from noisy observations with unknown parameters.
method Variational Bayesian inference with autoregressive moving average (ARMA) and vector autoregressive (VAR) models, combined with sequential Monte Carlo (SMC) and importance sampling resampling (SISR).
result The proposed inference method accurately estimates hidden states from non-linear noisy observations.
New insights into stochastic methods for solving variational inequalities.
problem Understanding convergence behaviors of stochastic algorithms in variational inequalities.
method Re-casting SEG/SGDA as Markov Chains to analyze their probabilistic structures.
result The average iterate is asymptotically normal with a unique invariant distribution for various VIPs.
CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.
problem Traditional risk assessment methods underperform in stock market analysis.
method Derived new CV equation and used it to analyze stock performance.
result Stocks with low but positive CV grow exponentially, outperforming high-risk stocks.
SFSVI uses Gaussian mixtures to approximate neural network outputs for continual learning.
problem Learning new tasks without forgetting old ones in neural networks.
method Sequential function-space variational inference with Gaussian mixture approximation.
result Gaussian mixture SFSVI outperforms other methods in continual learning.
Derives curvature formulas for convex metric sums and conditions for positive average variation.
problem Understanding how the curvature of a convex sum of metrics changes and whether it can increase the average curvature.
method Explicit formulae for curvature of convex sums of Riemannian metrics, studying total geodesic flat torus.
result Necessary and sufficient conditions for positive average variation of curvature of \(g_t\).
Generative adversarial networks (GANs) form a generative modeling approach known for producing appealing samples, but they are notably difficult to train. One common way to tackle this issue has been to propose new formulations of the GAN objective. Yet, surprisingly few studies have looked at optimization methods desi…
A fast and scalable method for variable selection in high-dimensional Gaussian processes.
problem Inefficient variable selection in high-dimensional Gaussian processes.
method Developed a fast and scalable variational inference algorithm for spike and slab Gaussian processes.
result Consistently outperforms vanilla and sparse variational GPs while retaining similar runtimes.
A new variational inference method speeds up AMMI model estimation.
problem High-dimensional GxE interaction data in plant breeding.
method Variational inference for AMMI model.
result The new method is 2x faster with similar predictive performance.
In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the bias of variational inference can be reduced by making the distribution of the like…
Unlike human speakers, typical text-to-speech (TTS) systems are unable to produce multiple distinct renditions of a given sentence. This has previously been addressed by adding explicit external control. In contrast, generative models are able to capture a distribution over multiple renditions and thus produce varied r…
Study optimal portfolio selection using average and current profitability of risky assets.
problem Continuous-time mean-variance portfolio selection in time-varying financial markets.
method Introduced AP and CP indexes; estimated AP and CP using second-order variation of an auxiliary wealth process.
result Estimations of AP and CP are more accurate than traditional MLE.
New RL algorithm tackles non-stationary environments with flexible policy updates.
problem Non-stationary reinforcement learning with time-varying rewards and transition probabilities.
method Model-free policy-based algorithm NS-NAC with restart-based exploration and dynamic learning rates.
result Dynamic regret of ildeO(∣S∣1/2∣A∣1/2ΔT1/6T5/6) for both algorithms. New methods optimize functions faster with less gradient accuracy needed.
problem Optimizing complex functions with limited gradient accuracy.
method Hessian averaging and adaptive gradient sampling methods.
result Improved convergence rates for various function types.
While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. We propose two diagnostic algorithms to alleviate this problem. The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement f…
Variational Auto-Encoders (VAEs) are capable of learning latent representations for high dimensional data. However, due to the i.i.d. assumption, VAEs only optimize the singleton variational distributions and fail to account for the correlations between data points, which might be crucial for learning latent representa…
VCoTTA uses variational Bayesian methods to adapt models under continuous domain shifts.
problem Error accumulation in continual test-time adaptation.
method VCoTTA employs variational Bayesian techniques to update a Bayesian Neural Network (BNN) during testing, combining priors from source and teacher models.
result VCoTTA effectively mitigates error accumulation in CTTA, as shown by experimental results on three datasets.
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic splines, are well captured by genetic programming in the form of dynamical equations. …
Paper improves Bayesian inference in federated learning with new algorithm VR-FALD*.
problem Bayesian inference in federated learning with communication bottlenecks and statistical heterogeneity.
method Federated Averaging Langevin Dynamics (FALD) and VR-FALD*.
result VR-FALD* corrects client drift due to statistical heterogeneity, improving convergence.
Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also inefficient for large count values and requires averaging over many samples to reduce …
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
problem Efficiently propagating uncertainty in downstream Bayesian analysis without feedback.
method NeVI-Cut combines neural networks and normalizing flows for variational inference.
result NeVI-Cut achieves significant computational gains and higher accuracy than traditional methods.
Model predicts anti-cancer drug responses using gene and molecular data.
problem Expensive and time-consuming cancer drug discovery and tailoring.
method Uses variational autoencoders and multi-layer perceptrons to encode gene expression and drug data.
result High average R2 of 0.83 and 0.845 in predicting drug responses for breast and pan-cancer cell lines, respectively. K-Means is one of the most used algorithms for data clustering and the usual clustering method for benchmarking. Despite its wide application it is well-known that it suffers from a series of disadvantages; it is only able to find local minima and the positions of the initial clustering centres (centroids) can greatly …
Stein variational neural network ensembles improve diversity and uncertainty estimation.
problem Lack of proper Bayesian justification and diversity guarantees in deep neural network ensembles.
method Particle-based inference methods, specifically Stein variational gradient descent (SVGD), operating in weight space, function space, and hybrid settings.
result SVGD methods improve diversity and uncertainty estimation, approaching the true Bayesian posterior more closely.
Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched a…
This paper improves prediction uncertainty estimation by inferring variation from neuron activation strength.
problem Estimating prediction uncertainty from ensemble methods is expensive and inaccurate.
method Introduced randomness into model training and inferred prediction variation from neuron activation strength.
result Average R squared on MovieLens is 0.56 and on Criteo is 0.81, with strong performance in variation detection.
Proof of Graustein's theorem in different geometries.
problem Average curvature of plane ovals and convex curves in various geometries.
method Wave propagation approach for different geometries.
result The average curvature is attained at least at four points in different geometries.
New method learns robust representations by modeling environment variation.
problem Learning invariant representations across varying environments.
method Explicitly modeling variation across environments and marginalizing it out.
result Proposed method outperforms invariant-learning methods in various settings.
Paper improves particle variational inference by optimizing generalization error bound.
problem Improving the diversity of models in particle variational inference to enhance generalization.
method Develops a new second-order Jensen inequality with a repulsion term based on the loss function, leading to a tighter generalization error bound.
result The proposed PVI optimizes the generalization error bound directly, improving performance compared to existing methods.
Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology to economics. Trajectories of GBM are distributed according to the we…
A new method normalizes flow mixtures for better inference across different data types.
problem Inference failure across diverse posterior geometries in normalizing flows.
method Introduces a two-stage framework with a stable global weighting mechanism based on sEMA.
result Achieves consistent NLL improvements and stable weight trajectories over baselines.