Soft Quantization Using Entropic Regularization.

Area of Science:

• Computational Mathematics
• Probability Theory
• Optimization

Background:

• The quantization problem seeks to approximate probability measures using discrete ones.
• Wasserstein distance is commonly used to assess approximation quality.
• Standard quantization can be computationally intensive and sensitive to noise.

Purpose of the Study:

• To investigate the properties and robustness of entropy-regularized quantization.
• To introduce a novel approximation technique using the softmin function.
• To evaluate the performance of the proposed method for probability measure approximation.

Main Methods:

• Employing an entropy-regularized Wasserstein distance for approximation quality evaluation.
• Utilizing a stochastic gradient approach for optimization.
• Incorporating the softmin function for robustness in approximation.

Main Results:

• The softmin function provides theoretical and practical robustness.
• The entropy-regularized approach offers an adjustable control parameter for problem difficulty.
• Empirical results demonstrate the method's effectiveness across various scenarios.

Conclusions:

• Entropy-regularized quantization with softmin offers a robust and flexible alternative to standard methods.
• The stochastic gradient approach enables efficient optimization for complex quantization problems.
• The tunable parameter enhances applicability to challenging real-world problems.