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Found 47 papers, 22 papers with code
Unsupervised Deep Haar Scattering on Graphs
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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 $\alpha$.
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 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.
Kernel Two-Sample Tests for Manifold Data
Specifically, when data densities $p$ and $q$ are supported on a $d$-dimensional sub-manifold ${M}$ embedded in an $m$-dimensional space and are H\"older with order $\beta$ (up to 2) on ${M}$, we prove a guarantee of the test power for finite sample size $n$ that exceeds a threshold depending on $d$, $\beta$, and $\Delta_2$ the squared $L^2$-divergence between $p$ and $q$ on the manifold, and with a properly chosen kernel bandwidth $\gamma$.
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.
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.
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.
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.
Crime Hot-Spot Modeling via Topic Modeling and Relative Density Estimation
We present a method to capture groupings of similar calls and determine their relative spatial distribution from a collection of crime record narratives.
An alternative approach to train neural networks using monotone variational inequality
We propose an alternative approach to neural network training using the monotone vector field, an idea inspired by the seminal work of Juditsky and Nemirovski [Juditsky & Nemirovsky, 2019] developed originally to solve parameter estimation problems for generalized linear models (GLM) by reducing the original non-convex problem to a convex problem of solving a monotone variational inequality (VI).
Invertible Neural Networks for Graph Prediction
The proposed model consists of an invertible sub-network that maps one-to-one from data to an intermediate encoded feature, which allows forward prediction by a linear classification sub-network as well as efficient generation from output labels via a parametric mixture model.
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.
Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise
This paper proves the convergence of bi-stochastically normalized graph Laplacian to manifold (weighted-)Laplacian with rates, when $n$ data points are i. i. d.
Neural Stein critics with staged $L^2$-regularization
In this paper, we investigate the role of $L^2$ regularization in training a neural network Stein critic so as to distinguish between data sampled from an unknown probability distribution and a nominal model distribution.
Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling
The Gaussian kernel and its traditional normalizations (e. g., row-stochastic) are popular approaches for assessing similarities between data points.
Neural network-based CUSUM for online change-point detection
Change-point detection, detecting an abrupt change in the data distribution from sequential data, is a fundamental problem in statistics and machine learning.
Spatio-temporal point processes with deep non-stationary kernels
Another popular type of deep model for point process data is based on representing the influence kernel (rather than the intensity function) by neural networks.
Normalizing flow neural networks by JKO scheme
Normalizing flow is a class of deep generative models for efficient sampling and likelihood estimation, which achieves attractive performance, particularly in high dimensions.
The G-invariant graph Laplacian
We introduce the G-invariant graph Laplacian that generalizes the graph Laplacian by accounting for the action of the group on the data set.
Computing high-dimensional optimal transport by flow neural networks
Flow-based models are widely used in generative tasks, including normalizing flow, where a neural network transports from a data distribution $P$ to a normal distribution.
Neural Differential Recurrent Neural Network with Adaptive Time Steps
We propose an RNN-based model, called RNN-ODE-Adap, that uses a neural ODE to represent the time development of the hidden states, and we adaptively select time steps based on the steepness of changes of the data over time so as to train the model more efficiently for the "spike-like" time series.
G-invariant diffusion maps
The diffusion maps embedding of data lying on a manifold have shown success in tasks ranging from dimensionality reduction and clustering, to data visualization.
Deep graph kernel point processes
Point process models are widely used for continuous asynchronous event data, where each data point includes time and additional information called "marks", which can be locations, nodes, or event types.
Convergence of flow-based generative models via proximal gradient descent in Wasserstein space
Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance.
Flow-based Distributionally Robust Optimization
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from it.
