Soft Quantization Using Entropic Regularization
The quantization problem aims to find the best possible approximation of probability measures on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi>...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/10/1435 |
| _version_ | 1797573881078218752 |
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| author | Rajmadan Lakshmanan Alois Pichler |
| author_facet | Rajmadan Lakshmanan Alois Pichler |
| author_sort | Rajmadan Lakshmanan |
| collection | DOAJ |
| description | The quantization problem aims to find the best possible approximation of probability measures on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula> using finite and discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation. This contribution investigates the properties and robustness of the entropy-regularized quantization problem, which relaxes the standard quantization problem. The proposed approximation technique naturally adopts the softmin function, which is well known for its robustness from both theoretical and practicability standpoints. Moreover, we use the entropy-regularized Wasserstein distance to evaluate the quality of the soft quantization problem’s approximation, and we implement a stochastic gradient approach to achieve the optimal solutions. The control parameter in our proposed method allows for the adjustment of the optimization problem’s difficulty level, providing significant advantages when dealing with exceptionally challenging problems of interest. As well, this contribution empirically illustrates the performance of the method in various expositions. |
| first_indexed | 2024-03-10T21:16:21Z |
| format | Article |
| id | doaj.art-18c24c316652472da9e9cb58351895ec |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T21:16:21Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-18c24c316652472da9e9cb58351895ec2023-11-19T16:24:51ZengMDPI AGEntropy1099-43002023-10-012510143510.3390/e25101435Soft Quantization Using Entropic RegularizationRajmadan Lakshmanan0Alois Pichler1Faculty of Mathematics, Technische Universität Chemnitz, D-09111 Chemnitz, GermanyFaculty of Mathematics, Technische Universität Chemnitz, D-09111 Chemnitz, GermanyThe quantization problem aims to find the best possible approximation of probability measures on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula> using finite and discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation. This contribution investigates the properties and robustness of the entropy-regularized quantization problem, which relaxes the standard quantization problem. The proposed approximation technique naturally adopts the softmin function, which is well known for its robustness from both theoretical and practicability standpoints. Moreover, we use the entropy-regularized Wasserstein distance to evaluate the quality of the soft quantization problem’s approximation, and we implement a stochastic gradient approach to achieve the optimal solutions. The control parameter in our proposed method allows for the adjustment of the optimization problem’s difficulty level, providing significant advantages when dealing with exceptionally challenging problems of interest. As well, this contribution empirically illustrates the performance of the method in various expositions.https://www.mdpi.com/1099-4300/25/10/1435quantizationapproximation of measuresentropic regularization |
| spellingShingle | Rajmadan Lakshmanan Alois Pichler Soft Quantization Using Entropic Regularization Entropy quantization approximation of measures entropic regularization |
| title | Soft Quantization Using Entropic Regularization |
| title_full | Soft Quantization Using Entropic Regularization |
| title_fullStr | Soft Quantization Using Entropic Regularization |
| title_full_unstemmed | Soft Quantization Using Entropic Regularization |
| title_short | Soft Quantization Using Entropic Regularization |
| title_sort | soft quantization using entropic regularization |
| topic | quantization approximation of measures entropic regularization |
| url | https://www.mdpi.com/1099-4300/25/10/1435 |
| work_keys_str_mv | AT rajmadanlakshmanan softquantizationusingentropicregularization AT aloispichler softquantizationusingentropicregularization |