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Found 33 papers, 6 papers with code
The Central Spanning Tree Problem
Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing.
Generative Modeling of Discrete Joint Distributions by E-Geodesic Flow Matching on Assignment Manifolds
This paper introduces a novel generative model for discrete distributions based on continuous normalizing flows on the submanifold of factorizing discrete measures.
On the Universality of Coupling-based Normalizing Flows
We present a novel theoretical framework for understanding the expressive power of coupling-based normalizing flows such as RealNVP.
Quantum State Assignment Flows
This paper introduces assignment flows for density matrices as state spaces for representing and analyzing data associated with vertices of an underlying weighted graph.
On the Convergence Rate of Gaussianization with Random Rotations
Gaussianization is a simple generative model that can be trained without backpropagation.
Whitening Convergence Rate of Coupling-based Normalizing Flows
For the first time, we make a quantitative statement about this kind of convergence: We prove that all coupling-based normalizing flows perform whitening of the data distribution (i. e. diagonalize the covariance matrix) and derive corresponding convergence bounds that show a linear convergence rate in the depth of the flow.
A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling
We devise an entropy-regularized difference-of-convex-functions (DC) decomposition of this potential and show that the basic geometric Euler scheme for integrating the assignment flow is equivalent to solving the G-PDE by an established DC programming scheme.
Self-Certifying Classification by Linearized Deep Assignment
We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm.
Multi-view Monocular Depth and Uncertainty Prediction with Deep SfM in Dynamic Environments
3D reconstruction of depth and motion from monocular video in dynamic environments is a highly ill-posed problem due to scale ambiguities when projecting to the 2D image domain.
Learning System Parameters from Turing Patterns
The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes.
Learning Linearized Assignment Flows for Image Labeling
An exact formula is derived for the parameter gradient of any loss function that is constrained by the linear system of ODEs determining the linearized assignment flow.
Assignment Flows for Data Labeling on Graphs: Convergence and Stability
The assignment flow recently introduced in the J.
Self-Assignment Flows for Unsupervised Data Labeling on Graphs
This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given.
Learning Adaptive Regularization for Image Labeling Using Geometric Assignment
We study the inverse problem of model parameter learning for pixelwise image labeling, using the linear assignment flow and training data with ground truth.
Approximate Variational Inference Based on a Finite Sample of Gaussian Latent Variables
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals.
Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment
Experiments demonstrate a beneficial effect in both directions: adaptivity of labels improves image labeling, and steering label evolution by spatially regularized assignments leads to proper labels, because the assignment flow for supervised labeling is exactly used without any approximation for label learning.
Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment
We introduce a novel approach to Maximum A Posteriori inference based on discrete graphical models.
Sum-Product Graphical Models
SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a class of models that incorporate context specific independence.
Symmetry-free SDP Relaxations for Affine Subspace Clustering
We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces.
Joint Recursive Monocular Filtering of Camera Motion and Disparity Map
Monocular scene reconstruction is essential for modern applications such as robotics or autonomous driving.
A Geometric Approach to Color Image Regularization
Our energy is a non-convex, non-smooth higher-order vectorial total variation approach and promotes color consistent image filtering via a coupling term.
Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization
Sum-Product Networks with complex probability distribution at the leaves have been shown to be powerful tractable-inference probabilistic models.
Multicuts and Perturb & MAP for Probabilistic Graph Clustering
We present a probabilistic graphical model formulation for the graph clustering problem.
Partial Optimality by Pruning for MAP-Inference with General Graphical Models
We propose a novel polynomial time algorithm to obtain a part of its optimal non-relaxed integral solution.
Globally Optimal Joint Image Segmentation and Shape Matching Based on Wasserstein Modes
While the overall functional is non-convex, non-convexity is confined to a low-dimensional variable.
Solving QVIs for Image Restoration with Adaptive Constraint Sets
In the present paper we prove uniqueness for a larger class of problems and in particular independent of the image size.
A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems
However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.
Probabilistic Intra-Retinal Layer Segmentation in 3-D OCT Images Using Global Shape Regularization
With the introduction of spectral-domain optical coherence tomography (OCT), resulting in a significant increase in acquisition speed, the fast and accurate segmentation of 3-D OCT scans has become evermore important.
Global MAP-Optimality by Shrinking the Combinatorial Search Area with Convex Relaxation
We consider energy minimization for undirected graphical models, also known as MAP-inference problem for Markov random fields.
Shape from Texture using Locally Scaled Point Processes
Shape from texture refers to the extraction of 3D information from 2D images with irregular texture.
Contour Manifolds and Optimal Transport
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions.
Convex Variational Image Restoration with Histogram Priors
We present a novel variational approach to image restoration (e. g., denoising, inpainting, labeling) that enables to complement established variational approaches with a histogram-based prior enforcing closeness of the solution to some given empirical measure.
