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Found 31 papers, 6 papers with code
All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on Graphs
The fields of effective resistance and optimal transport on graphs are filled with rich connections to combinatorics, geometry, machine learning, and beyond.
OTClean: Data Cleaning for Conditional Independence Violations using Optimal Transport
Ensuring Conditional Independence (CI) constraints is pivotal for the development of fair and trustworthy machine learning models.
Point Cloud Classification via Deep Set Linearized Optimal Transport
Our approach is motivated by the observation that $L^2-$distances between optimal transport maps for distinct point clouds, originating from a shared fixed reference distribution, provide an approximation of the Wasserstein-2 distance between these point clouds, under certain assumptions.
Semi-Supervised Laplacian Learning on Stiefel Manifolds
Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem} (TRS).
Effective resistance in metric spaces
One attractive application of ER is to point clouds, i. e. graphs whose vertices correspond to IID samples from a distribution over a metric space.
Linearized Wasserstein dimensionality reduction with approximation guarantees
We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space.
Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors
Probabilistic generative models provide a flexible and systematic framework for learning the underlying geometry of data.
Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders
Our numerical experiments on synthetic and real-world data verify that the proposed model can effectively manage data with multi-class nearby but disjoint manifolds of different classes, overlapping manifolds, and manifolds with non-trivial topology.
Supervised learning of sheared distributions using linearized optimal transport
In this paper we study supervised learning tasks on the space of probability measures.
Kernel distance measures for time series, random fields and other structured data
Applications are demonstrated for clustering of synthetic and real-life time series and image data, and the performance of kdiff is compared to competing distance measures for clustering.
StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm
With a novel sub-sampling scheme, StreaMRAK reduces memory and computational complexities by creating a sketch of the original data, where the sub-sampling density is adapted to the bandwidth of the kernel and the local dimensionality of the data.
Sigma-Delta and Distributed Noise-Shaping Quantization Methods for Random Fourier Features
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels.
LDLE: Low Distortion Local Eigenmaps
We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding.
Natural Graph Wavelet Packet Dictionaries
We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering.
Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations
The transform is defined by computing the optimal transport of each distribution to a fixed reference distribution, and has a number of benefits when it comes to speed of computation and to determining classification boundaries.
A deep network construction that adapts to intrinsic dimensionality beyond the domain
We study the approximation of two-layer compositions $f(x) = g(\phi(x))$ via deep networks with ReLU activation, where $\phi$ is a geometrically intuitive, dimensionality reducing feature map.
Cautious Active Clustering
Our approach is to consider the unknown probability measure as a convex combination of the conditional probabilities for each class.
PT-MMD: A Novel Statistical Framework for the Evaluation of Generative Systems
Stochastic-sampling-based Generative Neural Networks, such as Restricted Boltzmann Machines and Generative Adversarial Networks, are now used for applications such as denoising, image occlusion removal, pattern completion, and motion synthesis.
Classification Logit Two-sample Testing by Neural Networks
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem.
Coresets for Estimating Means and Mean Square Error with Limited Greedy Samples
In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data.
Variational Diffusion Autoencoders with Random Walk Sampling
Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and the sampling space.
Bounding the Error From Reference Set Kernel Maximum Mean Discrepancy
In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy.
On the Dual Geometry of Laplacian Eigenfunctions
We discuss the geometry of Laplacian eigenfunctions $-\Delta \phi = \lambda \phi$ on compact manifolds $(M, g)$ and combinatorial graphs $G=(V, E)$.
Two-sample Statistics Based on Anisotropic Kernels
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples.
People Mover's Distance: Class level geometry using fast pairwise data adaptive transportation costs
We address the problem of defining a network graph on a large collection of classes.
Function Driven Diffusion for Personalized Counterfactual Inference
We consider the problem of constructing diffusion operators high dimensional data $X$ to address counterfactual functions $F$, such as individualized treatment effectiveness.
Spectral Echolocation via the Wave Embedding
Spectral embedding uses eigenfunctions of the discrete Laplacian on a weighted graph to obtain coordinates for an embedding of an abstract data set into Euclidean space.
DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network
We introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient's covariates and treatment effectiveness in order to provide personalized treatment recommendations.
Provable approximation properties for deep neural networks
We discuss approximation of functions using deep neural nets.
Bigeometric Organization of Deep Nets
In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of the features being irrelevant to modeling functions of interest.
Diffusion Nets
In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space.
