AMF-VI uses adaptive mixtures of flows for robust VI across diverse distributions.
problem Inconsistent behavior of single-flow models across different distributions.
method Sequential expert training of individual flows and adaptive global weight estimation via likelihood-driven updates.
result AMF-VI achieves lower negative log-likelihood and stable gains in transport metrics across various posterior families.
Improves sequence modeling with a flow-based recurrent mixture density network.
problem Sequence modeling and sequence-to-sequence mapping applications.
method Generalized recurrent mixture density networks using normalized flow transformations.
result Significantly improved fit to image sequences measured by log-likelihood.
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
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.
We propose two neural network based mixture models in this article. The proposed mixture models are explicit in nature. The explicit models have analytical forms with the advantages of computing likelihood and efficiency of generating samples. Computation of likelihood is an important aspect of our models. Expectation-…
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.
Paper uses GMM and MAF for probabilistic classification, outperforming simpler models.
problem Classifying data with complex distributions.
method Density estimation using Gaussian Mixture Model and Masked Autoregressive Flow.
result Proposed classifiers outperform simpler models like linear discriminant analysis.
Study improves flow-based model training from few samples.
problem Training flow-based models from limited data.
method Sharp analysis of two-layer autoencoder with finite sample complexity.
result Generative flow approximates target density with rate Θ_n(1/n).
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.
Model accurately gates ocean microbes from high-frequency flow cytometry data.
problem Gating of high-frequency flow cytometry data for ocean microbes is challenging.
method Trend filtered mixture of experts with smooth parameter variation.
result Model accurately matches human-annotated gating and corrects errors.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
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.
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.
The paper studies scaling limits of Wasserstein metrics on Gaussian mixture models.
problem Understanding the scaling limits of Wasserstein metrics on Gaussian mixture models.
method Scaling limit approach on Gaussian mixture models, including inhomogeneous and extended models.
result Existence of the limit of the Wasserstein metric after renormalization for GMMs with zero variance.
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a geographical area. Other settings include domains where unsuitable recordings are discard…
Paper introduces Tensor Gauge Flow Models for better data encoding.
problem Lack of expressive flow dynamics in existing Generative Flow Models.
method Incorporates higher-order Tensor Gauge Fields into the Flow Equation.
result Tensor Gauge Flow Models achieve improved generative performance.
HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.
problem Tackles heavy-tailed data in various domains with rare events.
method Proposes a framework using clock-conditioned Gaussian sources and truncated logsignature features.
result Improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and baselines.
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
problem Learning dynamics of SGD for a neural network classifying Gaussian mixture.
method Applying dynamical mean-field theory to track SGD dynamics in high dimensions.
result Reveals how SGD navigates the non-convex loss landscape.
Develops a framework for distilling flow models from few steps.
problem Improving few-step sampling in diffusion models for better performance.
method Local approximation errors and dynamical amplification controlled through analytical tractability.
result Deep residual compositions efficiently approximate long-horizon transport with controlled global error.
Transformers can learn mixture of linear models efficiently.
problem Existence and generalization of in-context learning for mixture models.
method Theoretical analysis and gradient flow optimization.
result Transformers achieve a prediction error of O ( d / n ) \mathcal{O}(\sqrt{d/n}) O ( d / n ) with high probability. Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
problem Improving generative models' performance.
method Integrates L ∞ _{\infty} ∞ -algebra into Generative Flow Models, leveraging higher geometry and symmetries. result Substantial performance improvements on Gaussian Mixture Model datasets.
Smooth flows for physical systems with smooth energies and forces.
problem Smooth energies for physical simulations and force computation.
method Smooth mixture transformations on compact intervals and hypertori, using root-finding and the inverse function theorem.
result Smooth flows allow training by force matching and use as molecular dynamics potentials.
A new method for categorical variational inference using discrete normalizing flows.
problem Challenges in optimizing variational approximations for discrete latent variables.
method Differentiable reparameterization using a mixture of discrete normalizing flows.
result Improves optimization of evidence lower bound and reduces sensitivity to hyperparameters.
Model predicts phytoplankton subpopulations based on environmental factors.
problem Predicting phytoplankton dynamics under changing environmental conditions.
method Sparse mixture of multivariate regressions model.
result Identifies environmental covariates influencing phytoplankton subpopulations.
A new clustering method estimates non-linear boundaries and automatically selects the number of clusters.
problem Discriminative clustering with non-linear boundaries and data abnormalities.
method Regularized mutual information objective function with a mixture of Gaussian and uniform distributions.
result Automatic selection of the number of components and estimation of non-linear boundaries.
New method reduces mixture model evaluation cost for large models.
problem Computational infeasibility of evaluating all mixture components.
method Combining EM and Metropolis-Hastings for stochastic sampling.
result Significantly reduced computational cost for large models.
Improved phylogenetic inference using VBPI-Mixtures for tree topology and branch length.
problem Multimodality of tree-topology posterior distributions in phylogenetic inference.
method VBPI-Mixtures algorithm that uses mixture learning within the BBVI framework.
result VBPI-Mixtures captures tree-topology distributions better than VBPI.
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.
Mixture components improve VAE performance by increasing latent flexibility.
problem Improving variational autoencoder (VAE) performance through more flexible latent representations.
method Modeling mixture components with separate encoder networks and analyzing their impact on ELBO.
result Increasing the number of mixture components improves VAE performance on various datasets.
A new method learns quantization boundaries in continuous space using tessellation.
problem Mapping between discrete and continuous distributions is difficult.
method Constructs normalizing flows on convex polytopes with exact likelihood evaluations.
result Improves likelihood evaluation and quantization learning across various data modalities.
New GM layers improve neural network performance.
problem Improving neural network performance.
method Employing Gaussian mixture models and Wasserstein gradient flows.
result GM layers achieve comparable performance to two-layer networks.
Theoretical work on mode collapse in variational inference models.
problem Mode collapse in variational inference models, where models focus on a few modes instead of all possible ones.
method Theoretical investigation of mode collapse in Gaussian mixture models, identifying key low-dimensional statistics and equations governing their evolution.
result Mode collapse is present even in favorable scenarios, driven by mean alignment and vanishing weight mechanisms.
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
problem Approximating Gaussian and mixture-of-Gaussians filtering for complex systems.
method Variational approximation via gradient-flow representation on Wasserstein metric space.
result Competitive performance in posterior representation and parameter estimation for systems with multiplicative noise and multi-modal distributions.
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.
problem Mode collapse in variational inference for multimodal distributions.
method Analyzed annealing strategies for Gaussian mixtures, derived formulas, and tested on neural networks.
result Appropriately chosen annealing schemes can robustly prevent mode collapse.
Generative models improve angular variable simulation in high dimensions.
problem Lack of flexibility and scalability in simulating multivariate angular variables.
method Introducing generative adversarial networks, normalizing flows, and flow matching.
result Deep learning methods outperform classical parametric models in complex data structures.
A new framework enhances generative modeling by learning local flows over complex manifolds.
problem Limited expressivity of current normalizing flows for low-dimensional manifolds.
method Vector quantized local normalizing flows (VQ-Flows) using a VQ-AE atlas and conditional flows.
result Enhanced modeling of complex data distributions over manifolds.
This study examines biases in flow matching samplers using finite-sample estimation.
problem Biases in flow matching samplers when using finite-sample surrogates.
method Finite-sample plug-in estimation and hierarchy of empirical FM models.
result Exact empirical minimizer and smoothed plug-in regime identified for affine conditional flows.
Identifying components and estimating mixing weights in unlabeled finite mixtures under marginal independence.
problem Identifying components and estimating mixing weights in unlabeled finite mixtures.
method Proving structural results and extending them to observable mixtures.
result Identifying components and estimating mixing weights under marginal independence.
Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order fl…
MDNs offer a data-efficient alternative to diffusion and flow models for multimodal scientific learning.
problem Capturing multimodal conditional uncertainty in scientific inverse problems.
method Mixture Density Networks (MDNs) as explicit parametric density estimators.
result MDNs achieve superior generalization, interpretability, and sample efficiency in scientific tasks.
New algorithm for fitting Gaussian mixtures using Wasserstein-Fisher-Rao geometry.
problem Hard problem of fitting Gaussian mixture models to data computationally.
method Gradient descent over Wasserstein-Fisher-Rao geometry for probability measures.
result Established convergence guarantees for the proposed algorithm.
Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for m…
There has been great interest recently in applying nonparametric kernel mixtures in a hierarchical manner to model multiple related data samples jointly. In such settings several data features are commonly present: (i) the related samples often share some, if not all, of the mixture components but with differing weight…
New method models fat-tailed distributions with anisotropic tail-adaptive flows.
problem Gaussian-based variational inference fails to accurately capture tail decay in fat-tailed distributions.
method Improved theory on tails of flows, developed anisotropic tail-adaptive flows (ATAF).
result ATAF models tail-anisotropy, outperforming prior work on synthetic and real-world targets.
iGNN tackles inverse graph prediction using invertible neural networks.
problem Inverse graph prediction problem in data analysis and machine learning.
method Developed invertible graph neural network (iGNN) to solve inverse prediction problem on graphs.
result iGNN model allows efficient generation from output labels and forward prediction.
Normalizing flows transform a latent distribution through an invertible neural network for a flexible and pleasingly simple approach to generative modelling, while preserving an exact likelihood. We propose FlowGMM, an end-to-end approach to generative semi supervised learning with normalizing flows, using a latent Gau…
Bi-Lipschitz flows approximate a wide range of distributions.
problem Characterizing the expressivity of bi-Lipschitz normalizing flows.
method Linking score regularity to transport map bi-Lipschitzness via probability flow ODE.
result Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are L 1 L^1 L 1 -dense among all probability densities.