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Found 7 papers, 1 papers with code
From Stability to Chaos: Analyzing Gradient Descent Dynamics in Quadratic Regression
We conduct a comprehensive investigation into the dynamics of gradient descent using large-order constant step-sizes in the context of quadratic regression models.
High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating model explicitly into consideration.
Statistical Inference for Linear Functionals of Online SGD in High-dimensional Linear Regression
In order to use the developed result in practice, we further develop an online approach for estimating the expectation and the variance terms appearing in the CLT, and establish high-probability bounds for the developed online estimator.
Randomly Initialized One-Layer Neural Networks Make Data Linearly Separable
Recently, neural networks have demonstrated remarkable capabilities in mapping two arbitrary sets to two linearly separable sets.
Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections
We illustrate the usefulness of this stability estimate by first providing rates of convergence for the natural discrete-discrete and semi-discrete estimators of optimal transport maps.
Entropic Optimal Transport: Geometry and Large Deviations
The exact rate function is determined in a general setting and linked to the Kantorovich potential of optimal transport.
Optimization and Control Functional Analysis Probability 90C25, 60F10, 49N05
Multivariate Ranks and Quantiles using Optimal Transport: Consistency, Rates, and Nonparametric Testing
Under mild structural assumptions, we provide global and local rates of convergence of the empirical quantile and rank maps.
Statistics Theory Probability Statistics Theory 62G30, 62G20, 60F15, 35J96
