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Found 37 papers, 17 papers with code
Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling
In this work, we investigate this normalization in a setting where points are sampled from an unknown density on a low-dimensional manifold embedded in high-dimensional space and corrupted by possibly strong, non-identically distributed, sub-Gaussian noise.
Neural Stein critics with staged $L^2$-regularization
Theoretically, we relate the training dynamic with large regularization weight to the kernel regression optimization of "lazy training" regime in early training times.
Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise
This paper proves the convergence of the bi-stochastically normalized graph Laplacian to manifold (weighted-)Laplacian with rates when $n$ data points are i. i. d.
SpecNet2: Orthogonalization-free spectral embedding by neural networks
The current paper introduces a new neural network approach, named SpecNet2, to compute spectral embedding which optimizes an equivalent objective of the eigen-problem and removes the orthogonalization layer in SpecNet1.
Invertible Neural Networks for Graph Prediction
In this work, we address conditional generation using deep invertible neural networks.
An alternative approach to train neural networks using monotone variational inequality
Despite the vast empirical success of neural networks, theoretical understanding of the training procedures remains limited, especially in providing performance guarantees of testing performance due to the non-convex nature of the optimization problem.
Police Text Analysis: Topic Modeling and Spatial Relative Density Estimation
We analyze a large corpus of police incident narrative documents in understanding the spatial distribution of the topics.
Spatiotemporal Joint Filter Decomposition in 3D Convolutional Neural Networks
In this paper, we introduce spatiotemporal joint filter decomposition to decouple spatial and temporal learning, while preserving spatiotemporal dependency in a video.
A Joint Subspace View to Convolutional Neural Networks
In other words, a CNN is now reduced to layers of filter atoms, typically a few hundred of parameters per layer, with a common block of subspace coefficients shared across layers.
Neural Spectral Marked Point Processes
In this paper, we introduce a novel and general neural network-based non-stationary influence kernel with high expressiveness for handling complex discrete events data while providing theoretical performance guarantees.
Neural Tangent Kernel Maximum Mean Discrepancy
We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a new connection between neural tangent kernel (NTK) and MMD.
Kernel Two-Sample Tests for Manifold Data
Specifically, we show that when data densities are supported on a $d$-dimensional sub-manifold $\mathcal{M}$ embedded in an $m$-dimensional space, the kernel two-sample test for data sampled from a pair of distributions $(p, q)$ that are H\"older with order $\beta$ is consistent and powerful when the number of samples $n$ is greater than $\delta_2(p, q)^{-2-d/\beta}$ up to certain constant, where $\delta_2$ is the squared $\ell_2$-divergence between two distributions on manifold.
Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples
The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization.
Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
The result holds for un-normalized and random-walk graph Laplacians when data are uniformly sampled on the manifold, as well as the density-corrected graph Laplacian (where the affinity matrix is normalized by the degree matrix from both sides) with non-uniformly sampled data.
Convergence of Graph Laplacian with kNN Self-tuned Kernels
This paper proves the convergence of graph Laplacian operator $L_N$ to manifold (weighted-)Laplacian for a new family of kNN self-tuned kernels $W^{(\alpha)}_{ij} = k_0( \frac{ \| x_i - x_j \|^2}{ \epsilon \hat{\rho}(x_i) \hat{\rho}(x_j)})/\hat{\rho}(x_i)^\alpha \hat{\rho}(x_j)^\alpha$, where $\hat{\rho}$ is the estimated bandwidth function {by kNN}, and the limiting operator is also parametrized by $\alpha$.
ACDC: Weight Sharing in Atom-Coefficient Decomposed Convolution
We then explicitly regularize CNN kernels by enforcing decomposed coefficients to be shared across sub-structures, while leaving each sub-structure only its own dictionary atoms, a few hundreds of parameters typically, which leads to dramatic model reductions.
Graph Convolution with Low-rank Learnable Local Filters
Recent deep models using graph convolutions provide an appropriate framework to handle such non-Euclidean data, but many of them, particularly those based on global graph Laplacians, lack expressiveness to capture local features required for representation of signals lying on the non-Euclidean grid.
Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization
Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing.
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.
Domain-invariant Learning using Adaptive Filter Decomposition
Domain shifts are frequently encountered in real-world scenarios.
Scale-Equivariant Neural Networks with Decomposed Convolutional Filters
Encoding the input scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many vision tasks especially when dealing with multiscale input signals.
Stochastic Conditional Generative Networks with Basis Decomposition
One of these questions is how to efficiently achieve proper diversity and sampling of the multi-mode data space.
A Dictionary Approach to Domain-Invariant Learning in Deep Networks
In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN).
Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs.
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.
Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian
The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance.
Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks
Theoretical analysis of the approximation power of Butterfly-Net to the Fourier representation of input data shows that the error decays exponentially as the depth increases.
RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks
Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks.
Defending against Adversarial Images using Basis Functions Transformations
We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images.
DCFNet: Deep Neural Network with Decomposed Convolutional Filters
In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data.
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.
The Geometry of Nodal Sets and Outlier Detection
Let $(M, g)$ be a compact manifold and let $-\Delta \phi_k = \lambda_k \phi_k$ be the sequence of Laplacian eigenfunctions.
Provable Estimation of the Number of Blocks in Block Models
Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications.
On the Diffusion Geometry of Graph Laplacians and Applications
We study directed, weighted graphs $G=(V, E)$ and consider the (not necessarily symmetric) averaging operator $$ (\mathcal{L}u)(i) = -\sum_{j \sim_{} i}{p_{ij} (u(j) - u(i))},$$ where $p_{ij}$ are normalized edge weights.
A Deep Learning Approach to Unsupervised Ensemble Learning
We show how deep learning methods can be applied in the context of crowdsourcing and unsupervised ensemble learning.
Deep Haar Scattering Networks
An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients.
Unsupervised Deep Haar Scattering on Graphs
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown.
