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06/29/2023
Private Covariance Approximation and Eigenvalue-Gap Bounds for Complex Gaussian Perturbations
We consider the problem of approximating a d × d covariance matrix M wit...
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11/11/2022
Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motion
Given a symmetric matrix M and a vector λ, we present new bounds on the ...
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07/06/2022
Private Matrix Approximation and Geometry of Unitary Orbits
Consider the following optimization problem: Given n × n matrices A and ...
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06/19/2022
Faster Sampling from Log-Concave Distributions over Polytopes via a Soft-Threshold Dikin Walk
We consider the problem of sampling from a d-dimensional log-concave dis...
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11/07/2021
Sampling from Log-Concave Distributions with Infinity-Distance Guarantees and Applications to Differentially Private Optimization
For a d-dimensional log-concave distribution π(θ)∝ e^-f(θ) on a polytope...
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04/16/2021
Sync-Switch: Hybrid Parameter Synchronization for Distributed Deep Learning
Stochastic Gradient Descent (SGD) has become the de facto way to train d...
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06/22/2020
A Provably Convergent and Practical Algorithm for Min-max Optimization with Applications to GANs
We present a new algorithm for optimizing min-max loss functions that ar...
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06/22/2020
A Second-order Equilibrium in Nonconvex-Nonconcave Min-max Optimization: Existence and Algorithm
Min-max optimization, with a nonconvex-nonconcave objective function f: ...
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05/05/2019
Faster algorithms for polytope rounding, sampling, and volume computation via a sublinear "Ball Walk"
We study the problem of "isotropically rounding" a polytope K⊆R^n, that ...
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02/22/2019
Nonconvex sampling with the Metropolis-adjusted Langevin algorithm
The Langevin Markov chain algorithms are widely deployed methods to samp...
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02/21/2019
Online Sampling from Log-Concave Distributions
Given a sequence of convex functions f_0, f_1, ..., f_T, we study the pr...
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08/09/2018
Simple Conditions for Metastability of Continuous Markov Chains
A family {Q_β}_β≥ 0 of Markov chains is said to exhibit metastable mixin...
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08/09/2018
Does Hamiltonian Monte Carlo mix faster than a random walk on multimodal densities?
Hamiltonian Monte Carlo (HMC) is a very popular and generic collection o...
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02/24/2018
Dimensionally Tight Bounds for Second-Order Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from...
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02/24/2018
Dimensionally Tight Running Time Bounds for Second-Order Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from...
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11/07/2017
Convex Optimization with Nonconvex Oracles
In machine learning and optimization, one often wants to minimize a conv...
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08/23/2017