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Found 11 papers, 2 papers with code
Shifted Interpolation for Differential Privacy
Notably, this leads to the first exact privacy analysis in the foundational setting of strongly convex optimization.
Faster high-accuracy log-concave sampling via algorithmic warm starts
Understanding the complexity of sampling from a strongly log-concave and log-smooth distribution $\pi$ on $\mathbb{R}^d$ to high accuracy is a fundamental problem, both from a practical and theoretical standpoint.
Concentration of the Langevin Algorithm's Stationary Distribution
This discretization leads the Langevin Algorithm to have a stationary distribution $\pi_{\eta}$ which differs from the stationary distribution $\pi$ of the Langevin Diffusion, and it is an important challenge to understand whether the well-known properties of $\pi$ extend to $\pi_{\eta}$.
Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Sampling
In this way, we disentangle the study of the mixing and bias of the Langevin Algorithm.
Privacy of Noisy Stochastic Gradient Descent: More Iterations without More Privacy Loss
A central issue in machine learning is how to train models on sensitive user data.
Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent
We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric.
Kernel approximation on algebraic varieties
Our results are presented for smooth isotropic kernels, the predominant class of kernels used in applications.
Wasserstein barycenters are NP-hard to compute
Moreover, our hardness results for computing Wasserstein barycenters extend to approximate computation, to seemingly simple cases of the problem, and to averaging probability distributions in other Optimal Transport metrics.
Hardness results for Multimarginal Optimal Transport problems
We demonstrate this toolkit by using it to establish the intractability of a number of MOT problems studied in the literature that have resisted previous algorithmic efforts.
Polynomial-time algorithms for Multimarginal Optimal Transport problems with structure
We illustrate this ease-of-use by developing poly(n, k) time algorithms for three general classes of MOT cost structures: (1) graphical structure; (2) set-optimization structure; and (3) low-rank plus sparse structure.
Wasserstein barycenters can be computed in polynomial time in fixed dimension
Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics.
