DeepAI

# Convergence rate of optimal quantization grids and application to empirical measure

We study the convergence rate of optimal quantization for a probability measure sequence (μ_n)_n∈N^* on R^d which converges in the Wasserstein distance in two aspects: the first one is the convergence rate of optimal grid x^(n)∈(R^d)^K of μ_n at level K; the other one is the convergence rate of the distortion function valued at x^(n), called the `performance' of x^(n). Moreover, we will study the performance of the optimal grid of the empirical measure of a distribution μ with finite second moment but possibly unbounded support. As an application, we show that the mean performance of the empirical measure of the multidimensional normal distribution N(m, Σ) and of distributions with hyper-exponential tails behave like O(K n/√(n)).

• 4 publications
• 7 publications
07/22/2018

### On the rate of convergence of empirical measure in ∞-Wasserstein distance for unbounded density function

We consider a sequence of identically independently distributed random s...
10/29/2018

### Novel Near-Optimal Scalar Quantizers with Exponential Decay Rate and Global Convergence

Many modern distributed real-time signal sensing/monitoring systems requ...
10/16/2020

### Consistency of archetypal analysis

Archetypal analysis is an unsupervised learning method that uses a conve...
03/08/2023

### A note on L^1-Convergence of the Empiric Minimizer for unbounded functions with fast growth

For V : ℝ^d →ℝ coercive, we study the convergence rate for the L^1-dista...
02/22/2019

### Convergence Rate of Empirical Spectral Distribution of Random Matrices from Linear Codes

It is known that the empirical spectral distribution of random matrices ...
12/30/2022

### Particle method and quantization-based schemes for the simulation of the McKean-Vlasov equation

In this paper, we study three numerical schemes for the McKean-Vlasov eq...
12/13/2022

### Minimax Optimal Estimation of Stability Under Distribution Shift

The performance of decision policies and prediction models often deterio...