Optimizes kernel density ratios for better predictions and information measures.
problem Improving accuracy of kernel density estimates for density ratios.
method Derives an optimal weight function using calculus of variations.
result Reduces bias in kernel density estimates, leading to improved prediction posteriors and information-theoretic measures.
Normalizing flows improve density estimation from noisy data.
problem Estimating underlying density from noisy samples.
method Use normalizing flows for density estimation with arbitrary noise distributions, using amortized variational inference.
result Normalizing flows can outperform Gaussian mixtures for density deconvolution.
Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.
problem Estimating posterior densities in probabilistic models.
method Variational formulation of particle flow, Fisher-Rao gradient flow, Gaussian and Gaussian mixture approximations.
result Gaussian and Gaussian mixture approximations of Fisher-Rao particle flow reduce to Exact Daum and Huang particle flow under linear Gaussian assumptions.
Investigates tempered stable distributions and processes, including density transformations and parameter estimation.
problem Understanding the properties and applications of tempered stable distributions and processes.
method Analysis of limit distributions, parameter estimation, density transformations, and computation of p-variation indices. result Computed p-variation indices for tempered stable processes and discussed exponential stock models driven by these processes. VI approximates complex densities faster than classical methods.
problem Approximating complex probability densities.
method Optimization of a family of probability density functions using KL divergence.
result VI converges faster than Markov Chain Monte Carlo.
Paper develops a scalable distributed inference algorithm for sensor networks.
problem Efficient inference in intelligent sensor networks for location, tracking, and mapping.
method Distributed variational inference algorithm for continuous variables and large-scale data.
result Derives a separable lower bound for distributed variational inference with one-hop communication.
New integral theorems improve density function estimations.
problem Improving density function estimations.
method Integrals based on cyclic functions and Riemann sums, Fourier integral theorem, Monte Carlo methods, variational approach, Cauchy residue theorem.
result Optimal cyclic functions minimize square integrals, improving density estimations.
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed quantum state. We also introduce quantum flows, the quantum analog of normalizing flow…
Enhances mixture models with classifier-defined weights.
problem Density evaluation and sampling in mixture models.
method Introduces Classifier Weighted Mixtures (CWM) with functional weights.
result Improves expressivity in variational estimation without increasing complexity.
Neural spline flows enhance flow models with rational-quadratic splines.
problem Improving flexibility and density estimation in flow models.
method Proposes a new differentiable module based on monotonic rational-quadratic splines.
result Demonstrates improved performance in density estimation, variational inference, and generative modeling of images.
DIF extends NF with stochastic discrete latent variables for better density estimation.
problem Improving density estimation with discontinuities and fine details.
method Discretely indexed flows as an extension of Normalizing Flows with stochastic latent variables.
result DIF inherit good computational behavior of NF and can capture distributions with discontinuities.
Proposes VAE-KRnet for density estimation and variational Bayes.
problem Challenges of density estimation and posterior approximation in high dimensions.
method Combines VAE and KRnet for density estimation, incorporating mutual information maximization.
result Improves posterior approximation in high-dimensional cases.
Diffusion models adapt to low-dimensional structures for nonparametric density estimation.
problem High-dimensional statistical inference challenges.
method Viewing diffusion models as implicit density estimators and exploiting their low-dimensional structure.
result Achieves minimax optimal rate for total variation distance with factorizable density.
Bayesian state and parameter estimation for nonlinear models using variational methods.
problem Estimating states and parameters for nonlinear state-space models.
method Variational approach to approximate the intractable Bayesian distribution, resulting in an optimisation problem.
result The proposed method efficiently computes Bayesian estimates for nonlinear models, outperforming Hamiltonian Monte Carlo in numerical examples.
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
Pathfinder uses quasi-Newton optimization for variational inference.
problem Approximating complex posterior distributions efficiently.
method Pathfinder combines quasi-Newton optimization with variational methods to approximate log densities.
result Pathfinder produces draws with lower KL divergence than ADVI and comparable to HMC, requiring fewer evaluations.
We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the gradient of a variational objective. We tackle the challenge by generalizing the repa…
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
problem Estimating parameters in Gaussian location model with regularization.
method Ridge-regularized log-density-ratio estimation, variational and spectral approaches.
result Regularized variational estimator has lower risk with many observations, spectral estimator with fewer observations.
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 …
Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since…
There has recently been a steady increase in the number iterative approaches to density estimation. However, an accompanying burst of formal convergence guarantees has not followed; all results pay the price of heavy assumptions which are often unrealistic or hard to check. The Generative Adversarial Network (GAN) lite…
The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is overwhelming empirical evidence in the literature showing its success, there is relative…
Privacy-preserving synthetic data from EHRs for learning and inference.
problem Sharing sensitive EHR data while maintaining patient privacy.
method Differentially private normalizing flows for density estimation and variational inference.
result Privacy-preserving synthetic data can yield good utility at a reasonable privacy cost.
The paper analyzes numerical instability in variational flows and proposes a diagnostic method.
problem Numerical instability in variational flows affects sampling, density evaluation, and ELBO estimation.
method Treated variational flows as dynamical systems, used shadowing theory for theoretical guarantees, and developed a diagnostic procedure.
result Despite numerical instability, results from variational flows can be accurate enough for practical applications.
SoftCVI uses contrastive estimation to infer complex posteriors.
problem Estimating complex posteriors in Bayesian inference.
method Contrastive variational inference with self-generated soft labels.
result SoftCVI outperforms other variational approaches in stability and coverage.
New method trains EBMs using NFs for more accurate likelihood estimation.
problem Lack of statistical accuracy in EBMs likelihood estimation.
method Uses normalizing flows (NF) to fit an NF to an EBM during training.
result Accurate gradient for EBMs at all times, leading to a fast sampler.
UMNNs improve density estimation and variational inference without constraints.
problem Creating expressive invertible transformations without constraints.
method Proposed UMNN architecture enforcing monotonicity with a free-form neural network.
result UMNNs enhance autoregressive flows for density estimation and variational inference.
New method uses Fokker-Planck equation for sampling and inference.
problem Intractability of evaluating probability density in practical applications.
method Reformulates Fokker-Planck equation as a particle flow method, using velocity field.
result Turns intractable density evaluation into an advantage for variational inference, kernel mean embeddings, and sequential Monte Carlo.
Study exact minimax rates for density estimation over convex classes, extending previous work.
problem Deriving minimax rates for density estimation over convex density classes.
method Building on Le Cam's work, determine exact minimax rates using local metric entropy.
result Exact minimax rates derived for any convex density class, including nonparametric and parametric cases.
We show that the energy density of critical points of a class of conformally invariant variational problems with small energy on the unit 2-disk B_1 lies in the local Hardy space h^1(B_1). As a corollary we obtain a new proof of the energy convexity and uniqueness result for weakly harmonic maps with small energy on B_…
Paper proposes new density estimators for high-dimensional data.
problem Prohibitive computational cost and slow convergence rate in high-dimensional density estimation.
method Adaptive hyperbolic cross density estimators in mixed smooth Sobolev spaces.
result Proposed estimators do not suffer curse of dimensionality under Integral Probability Metrics.
Paper introduces RVNP to improve SBI in misspecified models.
problem Misspecification in simulation-based inference leads to unreliable posterior estimation.
method RVNP uses variational inference and error modeling to bridge the simulation-to-reality gap.
result RVNP can recover robust posterior inference without hyperparameters or priors.
MTCNet uses MTL to estimate crowd density and count.
problem Crowd count estimation challenges due to scale variations and perspective.
method MTL deep neural network architecture with two tasks: density estimation and count classification.
result Achieves lower MAE than state-of-the-art methods on multiple datasets.
Posterior Matching enables VAEs to model arbitrary conditional densities.
problem Modeling conditional dependencies in unsupervised learning.
method Posterior Matching framework for arbitrary conditioning.
result Posterior Matching enables VAEs to perform arbitrary conditioning without modification.
Improved VI with Price's gradient estimator for target log-density.
problem Approximating target distributions from unnormalized log-densities.
method Stochastic gradient-based variational inference with Price's gradient estimator.
result Identifies Price's gradient as the key to WVI's superior performance.
The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior of the latent variable using Kullback Leibler (KL) divergence. Although the stan…
Improved predictive posterior density estimation through optimized importance sampling.
problem Low signal-to-noise ratio in posterior predictive densities.
method Optimized importance sampling using a test-time variational proxy.
result Significantly improved estimates of predictive posterior densities.
MixFlows uses a mixture of flows for efficient variational inference.
problem Efficient and reliable variational inference for complex models.
method A new variational family of mixed flows with efficient algorithms and convergence guarantees.
result MixFlows provides more reliable posterior approximations and comparable sample quality to MCMC methods.
LGKDE learns graph density using neural networks and perturbations.
problem Graph density estimation challenges in capturing structural patterns and semantic variations.
method LGKDE uses graph neural networks to represent graphs as discrete distributions and learns graph metrics via maximum mean discrepancy.
result LGKDE outperforms state-of-the-art baselines in graph anomaly detection.
New α-divergence loss function improves neural density ratio estimation.
problem Optimization challenges in existing DRE methods, especially overfitting and high sample requirements.
method Derived α-divergence loss function (α-Div) for neural density ratio estimation. result The α-divergence loss function (α-Div) offers stable and effective optimization for DRE. Unified empirical and variational Bayes for unnormalized densities.
problem Approximating unnormalized densities using latent variable models.
method Formulate a latent variable model for Y=X+N(0,σ2Id), use ELBO as parametrization of Y's energy function, and estimate X with empirical Bayes least-squares. result UVB has higher capacity to approximate energy functions than MLPs in DEEN.
AP-CDE uses NF to estimate high-dimensional conditional densities, improving interpretability.
problem Estimating conditional densities for high-dimensional responses like images.
method Extends NF neural networks to handle high-dimensional y with a latent z. result Improves interpretation of latent components, especially zP. Paper extends information theory for efficient probabilistic modeling.
problem Efficient and data-efficient non-parametric density estimation.
method Structured generative model (SGM) using Rényi's information.
result SGM improves mutual information estimation and generative adversarial networks.
A new method for estimating complex models and high-dimensional data.
problem Difficulty in computing Hessian of log-density functions for complex models and high-dimensional data.
method Sliced score matching, which projects scores onto random vectors before comparison.
result Sliced score matching can learn deep energy-based models and produce accurate score estimates.
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice. This paper employs normalising flows as a flexible likelihood model and …
A new model combines normalizing flows with mixture components for better density estimation.
problem Lack of explicit probability density functions in deep generative models.
method Variational mixture of normalizing flows, using variational inference and neural network parameters.
result The model can perform density estimation, semi-supervised learning, and clustering.
The paper proposes a new method for density estimation using spline quasi-interpolation for clustering.
problem Density estimation and clustering modeling for multivariate data.
method Spline quasi-interpolation for mono-variate approximation, copulas for multivariate modeling.
result The proposed method achieves accurate clustering of data using copulas and spline quasi-interpolation.
BBNN improves neural network accuracy and uncertainty quantification.
problem Overfitting and lack of interpretability in probabilistic neural networks.
method Boosted Bayesian Neural Networks (BBNN) using Boosting Variational Inference (BVI).
result BBNN achieves ~5% higher accuracy and superior uncertainty quantification.