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Found 9 papers, 1 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.
Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD
In particular, we show how specific DPPs and a string of controlled approximations can lead to gradient estimators with a variance that decays faster with the batchsize than under uniform sampling.
Gaussian Determinantal Processes: a new model for directionality in data
Determinantal point processes (a. k. a.
Sparse Multi-Reference Alignment : Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem
Our techniques have implications for the problem of crystallographic phase retrieval, indicating a certain local uniqueness for the recovery of sparse signals from their power spectrum.
Disordered complex networks: energy optimal lattices and persistent homology
We demonstrate that the PTL network at this disorder strength can be taken to be an effective substitute for the RMT network model, while at the same time offering the advantages of greater tractability.
Maximum Likelihood under constraints: Degeneracies and Random Critical Points
In the Bayesian setting, we rigorously establish the posterior consistency of procedures based on these ideas, where instead of a parametric likelihood, an empirical likelihood is used to define the posterior distribution.
An easy-to-use empirical likelihood ABC method
Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models analytically.
