Paper addresses the disparity between sampled and mean representations in disentangled learning.
problem Disparity between sampled and mean representations in disentangled learning.
method Proposes a method to eliminate the disparity by proving and utilizing the relationship between total correlation of sampled and mean representations for multivariate normal distributions.
result Demonstrates that a factorized mean representation can have lower total correlation than the sampled representation.
Variational language models seek to estimate the posterior of latent variables with an approximated variational posterior. The model often assumes the variational posterior to be factorized even when the true posterior is not. The learned variational posterior under this assumption does not capture the dependency relat…
We propose a novel approach to approximate complex high-dimensional posteriors using neural samplers.
problem Accurately capturing complex, multimodal, and correlated posteriors in high-dimensional spaces.
method Implicit variational inference with neural samplers and local linearisation bounds.
result Our method enables implicit distributions over tens of millions of latent variables, recovering correlations across layers in large Bayesian neural networks.
Paper proposes PSIPS for identifying Pareto set with correlated objectives.
problem Identifying the best answer among items with multiple conflicting metrics.
method Posterior sampling in stopping and sampling rules for structure and correlation.
result PSIPS is asymptotically optimal and demonstrates good empirical performance.
Gaussian OBFS proves strong consistency in feature selection with correlations.
problem Feature selection consistency in the presence of correlations.
method Proves strong consistency of Gaussian OBFS under mild conditions.
result Identifies selected features and rates of convergence for different feature types.
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…
This work tackles posterior collapse in conditional and hierarchical VAEs.
problem Posterior collapse in VAEs leads to poor latent variable representations.
method Theoretical analysis of linear conditional and hierarchical VAEs, empirical validation.
result Theoretical and empirical evidence of posterior collapse causes in conditional and hierarchical VAEs.
Enhances multimodal generation with Normalizing Flows and correlation analysis.
problem Generating coherent cross-modal data from multiple sources.
method Uses Deep Canonical Correlation Analysis for shared information, Normalizing Flows for diversity, and Product of Experts for scalability.
result Improves likelihood, diversity, and coherence in conditional generation.
New SMC sampler improves diffusion model sampling efficiency.
problem Sampling generative diffusion models efficiently.
method Constructs correlated observation paths and designs a sampler.
result Improved statistical efficiency, especially under outlier conditions.
We make a minimal, but very effective alteration to the VAE model. This is about a drop-in replacement for the (sample-dependent) approximate posterior to change it from the standard white Gaussian with diagonal covariance to the first-order autoregressive Gaussian. We argue that this is a more reasonable choice to ado…
This paper benchmarks Bayesian models' ability to estimate predictive correlations, especially for active learning.
problem Benchmarking how accurately Bayesian models estimate predictive correlations, especially in active learning.
method Considered transductive active learning as a benchmark, introduced meta-correlations and cross-normalized likelihoods.
result Meta-correlations and cross-normalized likelihoods can efficiently evaluate predictive correlations and are consistent with TAL performance.
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corre…
A framework for navigating environments with spatially correlated obstacles and uncertain blockage status.
problem Navigation in environments with spatially correlated obstacles of uncertain blockage status.
method Modeling spatial correlation with Gaussian Random Field, developing Bayesian belief updates, proposing a two-stage learning framework with offline and online phases.
result Consistent performance gains over baselines in environments with adversarial interruptions or clustered natural hazards.
Bayesian method for dynamic correlation matrices improves accuracy and responsiveness.
problem Challenges in estimating time-varying correlation matrices, including slow adaptation, insufficient regularization, and diffuse uncertainty.
method Low-rank factor representation with dynamic shrinkage prior and multivariate factor stochastic volatility model.
result Improved accuracy and responsiveness compared to competing methods in various challenging scenarios.
Proposes a method to calibrate data for more accurate linear correlation testing.
problem Inaccurate Pearson's correlation coefficient due to sample size and data non-normality.
method Predictive data calibration using machine learning to condition data on expected linear relationship.
result Calibrated Pearson's correlation coefficient yields a calibrated p-value and r estimate for posterior probability interpretation.
Bayesian priors for neural networks are improved by incorporating weight correlations and tail behavior.
problem Improving Bayesian priors for neural networks to better reflect true beliefs and performance.
method Analyzed summary statistics of neural network weights in different architectures and incorporated these observations into new priors.
result Improved performance on image classification datasets by using new priors that account for weight correlations and tail behavior.
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Global inducing points improve Bayesian neural network performance.
problem Improving Bayesian neural network performance.
method Adapting correlated approximate posterior to all layers in a Bayesian neural network and deep Gaussian processes using learned global inducing points.
result State-of-the-art performance on CIFAR-10 (86.7%) without data augmentation or tempering.
Variational inference transforms posterior inference into parametric optimization thereby enabling the use of latent variable models where otherwise impractical. However, variational inference can be finicky when different variational parameters control variables that are strongly correlated under the model. Traditiona…
A new algorithm for bandits with hierarchical rewards.
problem Learning from correlated rewards in complex hierarchies.
method Hierarchical Thompson Sampling (HierTS) for Gaussian hierarchies.
result Hierarchical Thompson Sampling reduces regret by non-constant factors in the number of actions.
Enhances hashing for fast retrieval with correlated bits.
problem Fast retrieval and small memory footprint for large-scale information retrieval.
method Employing Boltzmann machine distribution as variational posterior to model correlations among hash code bits.
result Significant performance gains achieved by effectively modeling correlations among hash code bits.
Meta-learning improves Bayesian causal discovery by sampling from the posterior.
problem Difficulty in estimating the full posterior over causal structures due to large number of possible graphs and functional relationships.
method Proposes a Bayesian meta-learning model that encodes key properties of the posterior and allows for sampling causal structures.
result Meta-Bayesian causal discovery allows for reliable sampling from the posterior over causal structures.
Temporal coarse-graining of multi-sector default count data generates effective correlation matrices and rank copulas.
problem Explaining the difference in default dependence between monthly and annual aggregation.
method Dynamic low-rank state-space model with AR(1) latent credit-state factors.
result Effective correlation matrices and rank copulas are generated from monthly default count data.
Variational Auto-Encoders (VAEs) have been widely applied for learning compact, low-dimensional latent representations of high-dimensional data. When the correlation structure among data points is available, previous work proposed Correlated Variational Auto-Encoders (CVAEs), which employ a structured mixture model as …
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
A scalable method for efficient inference in Gaussian process regression networks.
problem Intractable inference in Gaussian process regression networks (GPRN).
method Tensorization of output space, tensor/matrix-normal variational posteriors, joint optimization, and exploiting Kronecker product structure.
result Captures posterior dependencies and improves inference quality for large number of outputs.
New research challenges the flatness-generalization link in deep neural networks.
problem The correlation between flatness of the loss landscape and generalization in deep neural networks is questioned.
method The study examines various flatness measures and popular SGD variants, finding some break the flatness-generalization link. It proposes using logP(f), a global quantity, as a predictor of generalization. result The log of Bayesian prior upon initialization, logP(f), is a significantly more robust predictor of generalization than flatness measures. This paper models default data to capture dynamic dependence across sectors.
problem Static models fail to explain monthly default dependence.
method Dynamic low-rank state-space model for monthly multi-sector default-count data.
result Effective correlation matrices and copulas are induced from monthly data.
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior distribution where we explicitly model the covariance among the input and output dimensions…
Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully exploits GPU parallelism. However, such simple approximate posteriors are often insuf…
In many domains, scientists build complex simulators of natural phenomena that encode their hypotheses about the underlying processes. These simulators can be deterministic or stochastic, fast or slow, constrained or unconstrained, and so on. Optimizing the simulators with respect to a set of parameter values is common…
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily …
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically either uses MCMC schemes which target the joint posterior of the parameters and some…
Bayesian neural networks show good correlation between out-of-sample performance and Bayesian evidence.
problem Improving the out-of-sample performance of Bayesian neural networks.
method Numerical sampling of Bayesian posterior, ensembling over architectures, analysis of evidence vs. model size.
result Good correlation between out-of-sample performance and Bayesian evidence; ensembling improves performance.
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of inducing points. The inference is accurate only when data points have strong corre…
New MCMC methods improve efficiency for large network inference.
problem Efficiency of Metropolis within Gibbs for large networks.
method Combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo.
result New methods outperform Metropolis within Gibbs on synthetic and real networks.
Temporal aggregation reveals latent default correlation from monthly data.
problem Understanding effective default correlation from monthly default data.
method Temporal coarse-graining of latent default-probability paths.
result Temporal coarse-graining improves identifiability and reduces over-allocation of long-horizon fluctuations.
Study quantifies information borrowing in hierarchical Bayesian models.
problem Impact of shared hyperparameters on posterior inference.
method Non-asymptotic framework, nested hierarchical prior distribution, integrated risk measure.
result Deeper hierarchical models outperform nested ones under certain conditions.
Study uses regression and ML for COVID-19 mortality forecasting.
problem Forecasting COVID-19 mortality during the first wave in Spain.
method Cyclical curve log-regression, multivariate time series spatial residual correlation analysis, Bayesian approach, machine learning.
result Empirical analysis shows ML regression models perform better than traditional methods.
Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Bayesian inference in models where the posterior distribution is analytical intractable or computationally costly to evaluate directly. It operates by introducing additional auxiliary variables into the model and form an extended target distribution, w…
Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.
problem Understanding effective default correlation in corporate defaults.
method Temporal coarse-graining of latent default-probability paths, applied to corporate default-count data.
result Temporal coarse-graining provides a scale-consistent baseline that improves identifiability and reduces over-allocation of long-horizon fluctuations.
We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably…
We propose multivariate nonstationary Gaussian processes for jointly modeling multiple clinical variables, where the key parameters, length-scales, standard deviations and the correlations between the observed output, are all time dependent. We perform posterior inference via Hamiltonian Monte Carlo (HMC). We also prov…
The paper presents a novel approach to multi-output regression using probabilistic circuits.
problem Capturing correlations between multiple output dimensions in large-scale regression problems.
method Employing a mixture of single-output Gaussian process experts encoded via a probabilistic circuit.
result The method can capture correlations between output dimensions and often outperforms other approaches.
This paper explores approximations for fully Bayesian Gaussian Process Regression.
problem Learning in Gaussian Process models through hyperparameter adaptation.
method Two approximation schemes: Hamiltonian Monte Carlo and Variational Inference.
result Predictive performance analysis on various benchmark datasets.
A method predicts posterior PCs for faster uncertainty quantification in imaging.
problem Uncertainty visualization in image restoration models is limited by per-pixel variances.
method Neural Posterior Principal Components (NPPC) method for predicting PCs in a single forward pass.
result Orders of magnitude faster uncertainty quantification compared to posterior samplers.
Statistical inference of analytically non-tractable posteriors is a difficult problem because of marginalization of correlated variables and stochastic methods such as MCMC and VI are commonly used. We argue that stochastic KL divergence minimization used by MCMC and VI is noisy, and we propose instead EL_2O, expectati…