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Found 16 papers, 3 papers with code
Implicit Regularization via Spectral Neural Networks and Non-linear Matrix Sensing
In this paper, we explore this problem in the context of more realistic neural networks with a general class of non-linear activation functions, and rigorously demonstrate the implicit regularization phenomenon for such networks in the setting of matrix sensing problems, together with rigorous rate guarantees that ensure exponentially fast convergence of gradient descent. In this vein, we contribute a network architecture called Spectral Neural Networks (abbrv.
Minimax-optimal estimation for sparse multi-reference alignment with collision-free signals
We demonstrate that the minimax optimal rate of estimation in for the sparse MRA problem in this setting is $\sigma^2/\sqrt{n}$, where $n$ is the sample size.
Learning Networks from Gaussian Graphical Models and Gaussian Free Fields
In this work, we propose a novel estimator for the weighted network (equivalently, its Laplacian) from repeated measurements of a GFF on the network, based on the Fourier analytic properties of the Gaussian distribution.
Consistent model selection in the spiked Wigner model via AIC-type criteria
Consider the spiked Wigner model \[ X = \sum_{i = 1}^k \lambda_i u_i u_i^\top + \sigma G, \] where $G$ is an $N \times N$ GOE random matrix, and the eigenvalues $\lambda_i$ are all spiked, i. e. above the Baik-Ben Arous-P\'ech\'e (BBP) threshold $\sigma$.
Wasserstein Projection Pursuit of Non-Gaussian Signals
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features.
Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis
Network-valued time series are currently a common form of network data.
Learning with latent group sparsity via heat flow dynamics on networks
Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike.
Changepoint Analysis of Topic Proportions in Temporal Text Data
Changepoint analysis deals with unsupervised detection and/or estimation of time-points in time-series data, when the distribution generating the data changes.
Distribution of Eigenvalues of Matrix Ensembles arising from Wigner and Palindromic Toeplitz Blocks
For definiteness we concentrate on the ensemble of palindromic real symmetric Toeplitz (PST) matrices and the ensemble of real symmetric matrices, whose limiting spectral measures are the Gaussian and semi-circular distributions, respectively; these were chosen as they are the two extreme cases in terms of moment calculations.
Probability 15A52 (primary), 60F99, 62H10 (secondary)
Some characterization results on classical and free Poisson thinning
We also prove a free probability analogue of Craig's theorem, another well-known result in multivariate statistics on the independence of quadratic functions of Gaussian random matrices.
Point Processes
Probability
Operator Algebras
Statistics Theory
Statistics Theory
46L54, 60E05, 62E10
Exact Tests for Offline Changepoint Detection in Multichannel Binary and Count Data with Application to Networks
We consider offline detection of a single changepoint in binary and count time-series.
Graphon Estimation from Partially Observed Network Data
We consider estimating the edge-probability matrix of a network generated from a graphon model when the full network is not observed---only some overlapping subgraphs are.
Morphological Network: How Far Can We Go with Morphological Neurons?
A few works have tried to utilize morphological neurons as a part of classification (and regression) networks when the input is a feature vector.
Ranked #1 on
Representation Learning
on Circle Data
(using extra training data)
Mean Field for the Stochastic Blockmodel: Optimization Landscape and Convergence Issues
Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures.
Two provably consistent divide and conquer clustering algorithms for large networks
In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks.
On clustering network-valued data
Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community.
