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決定木・回帰木に基づくアンサンブル学習の最近

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2018-06-07 16:00
[招待講演]決定木・回帰木に基づくアンサンブル学習の最近
スマートインフォメディアシステム研究会(SIS)

https://www.ieice.org/ken/program/index.php?tgs_regid=af34ebc128cfa2fb7204de372de4324d77c39af0fb0174779c959c116196ce9c&lang=


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決定木・回帰木に基づくアンサンブル学習の最近

  1. 1. http://art.ist.hokudai.ac.jp/~takigawa/
  2. 2. 
 
 
 
 

  3. 3. https://www.slideshare.net/itakigawa/ss-77062106
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  6. 6. 
 
 
 

  7. 7. Edward Pyro Prob Torch BayesFlow LightGBM (Microsoft) (RuleQuest)
 See5/C5.0 & Cubist (Salford Systems)
 CART® MARS® TreeNet®
 Random Forests® CatBoost (Yandex) TFBoost (Google) TenscentBoost (Tenscent) Sherwood decision forests
  8. 8. 
 ICML 2008 (Google Scholar 360 )
  9. 9.
  10. 10. First, the results confirm the experiments in (Caruana & Niculescu-Mizil, 2006) where boosted decision trees perform exceptionally well when dimensionality is low. In this study boosted trees are the method of choice for up to about 4000 dimensions. Above that, random forests have the best overall performance. (Random forests were the 2nd best performing method in the previous study.) We suspect that the reason for this is that boosting trees is prone to overfitting and this be- comes a serious problem in high dimensions. Random forests is better behaved in very high dimensions, it is easy to parallelize, scales efficiently to high dimensions and performs consistently well on all three metrics.
  11. 11. The bootstrap analysis suggests that random forests probably are the top performing method overall, with a 73% chance of ranking first, a 20% chance of ranking second, and less than a 8% chance of ranking below 2nd place. The ranks of other good methods, however, are less clear and there appears to be a three-way tie for 2nd place for boosted trees, ANNs, and SVMs.
  12. 12. 
 
 

  13. 13. CVPR 2011 (Google Scholar 2934 )
  14. 14. CVPR 2005 (Google Scholar 559 ) 

  15. 15. https://www.microsoft.com/en-us/research/project/decision-forests/ • Multiclass Decision Forest • Multiclass Decision Jungle • Multiclass Logistic Regression • Multiclass Neural Network • One-vs-All Multiclass • Two-Class Averaged Perceptron • Two-Class Bayes Point Machine • Two-Class Boosted Decision Tree • Two-Class Decision Forest • Two-Class Decision Jungle • Two-Class Locally Deep Support Vector Machine • Two-Class Logistic Regression • Two-Class Neural Network • Two-Class Support Vector Machine
  16. 16. http://xgboost.readthedocs.io/en/latest/ https://github.com/Microsoft/LightGBM 
 

  17. 17. http://blog.kaggle.com/2015/11/09/profiling-top-kagglers-gilberto-titericz-new-1-in-the-world/ Gradient Boosting Machines are the best! Before I knew of GBM, I was a big fan of neural networks. と聞いてみた It depends on the problem, but if I have to pick one, then it is GBM (its XGBoost flavor). http://blog.kaggle.com/2015/06/22/profiling-top-kagglers-owen-zhang-currently-1-in-the-world/ I like Gradient Boosting and Tree methods in general. http://blog.kaggle.com/2016/02/10/profiling-top-kagglers-kazanova-new-1-in-the-world/ http://blog.kaggle.com/2016/02/22/profiling-top-kagglers-leustagos-current-7-highest-1/ Gradient boosted trees by far!
  18. 18. https://www.kaggle.com/surveys/2017 What data science methods are used at work?
  19. 19. 
 http://proceedings.mlr.press/v64/guyon_review_2016.pdf
  20. 20. Auto Sklearn https://github.com/automl/auto-sklearn NIPS 2015 (Google Scholar 131 )
  21. 21. http://www.cs.ubc.ca/labs/beta/Projects/SMAC/ SMAC: Sequential Model-based Algorithm Configuration https://automl.github.io/SMAC3/stable/# LION(Learning & Intelligent Optimization) 2011 
 (Google Scholar 665 ) Auto Weka Auto Sklearn https://www.cs.ubc.ca/labs/beta/Projects/autoweka/ https://github.com/automl/auto-sklearn 

  22. 22. 
 

  23. 23. 
 

  24. 24. 
 
 

  25. 25. 
 
 

  26. 26. 
 
 

  27. 27. (X1, X2)<latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit><latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit><latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit><latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit>
  28. 28. 
 
 
 
 

  29. 29. 
 
 
 
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sha1_base64="o5HsOhFUXS1Pz0BG9RmwSp2KQ7I=">AAAB+nicdVDLSgMxFM34rPVVdekmWARXJSli213RjcuK9gHtUDJppg1NMkOSEcrYT3Cre3fi1p9x65eYaSto0QMXDufcy733BLHgxiL04a2srq1vbOa28ts7u3v7hYPDlokSTVmTRiLSnYAYJrhiTcutYJ1YMyIDwdrB+Crz2/dMGx6pOzuJmS/JUPGQU2KddEv7uF8oohJCCGMMM4IrF8iRWq1axlWIM8uhCBZo9AufvUFEE8mUpYIY08Uotn5KtOVUsGm+lxgWEzomQ9Z1VBHJjJ/OTp3CU6cMYBhpV8rCmfpzIiXSmIkMXKckdmSWvUz80wvk0mYbVv2UqzixTNH54jAR0EYwywEOuGbUiokjhGrubod0RDSh1qWVd6F8fw7/J61yCaMSvjkv1i8X8eTAMTgBZwCDCqiDa9AATUDBEDyCJ/DsPXgv3qv3Nm9d8RYzR+AXvPcvfACUZw==</latexit><latexit sha1_base64="o5HsOhFUXS1Pz0BG9RmwSp2KQ7I=">AAAB+nicdVDLSgMxFM34rPVVdekmWARXJSli213RjcuK9gHtUDJppg1NMkOSEcrYT3Cre3fi1p9x65eYaSto0QMXDufcy733BLHgxiL04a2srq1vbOa28ts7u3v7hYPDlokSTVmTRiLSnYAYJrhiTcutYJ1YMyIDwdrB+Crz2/dMGx6pOzuJmS/JUPGQU2KddEv7uF8oohJCCGMMM4IrF8iRWq1axlWIM8uhCBZo9AufvUFEE8mUpYIY08Uotn5KtOVUsGm+lxgWEzomQ9Z1VBHJjJ/OTp3CU6cMYBhpV8rCmfpzIiXSmIkMXKckdmSWvUz80wvk0mYbVv2UqzixTNH54jAR0EYwywEOuGbUiokjhGrubod0RDSh1qWVd6F8fw7/J61yCaMSvjkv1i8X8eTAMTgBZwCDCqiDa9AATUDBEDyCJ/DsPXgv3qv3Nm9d8RYzR+AXvPcvfACUZw==</latexit>
  30. 30. 0.5 -0.5 ここにきた サンプル の平均値 ここにきた サンプル の平均値
  31. 31. 0.5 -0.8-0.1
  32. 32. -0.8-0.10.10.8
  33. 33. -0.10.10.8 -0.5-0.9
  34. 34.
  35. 35.
  36. 36. y=0 y=0.89 + -0.36 max(0,x-0.99) + -0.88 max(0,0.99-x) y=1.23 + -0.59 max(0,x-0.99) + -1.32 max(0,0.99-x) + 1.41 max(0,x-4.96) y=0.98 + -0.23 max(0,x-0.99) + -1.0 max(0,0.99-x) + 1.69 max(0,x-4.96) + -0.51 max(0,x-2.31) y=0.95 + -0.12 max(0,x-0.99) + -0.96 max(0,0.99-x) + 0.77 max(0,x-4.96) + -0.79 max(0,x-2.31) + 0.87 max(0,x-2.31) y=0.66 + --0.29 max(0,x-0.99) y=0.94 + -0.08 max(0,x-0.99) + -0.94 max(0,0.99-x) + 0.91 max(0,x-4.96) + -0.92 max(0,x-2.31) + 0.49 max(0,x-2.31) + 0.34 max(0,x-2.31) ❶ ❶ ❷ ❸ ❹ ❺ ❻ ❷ ❸ ❹ ❺ ❻
  37. 37. + 
 

  38. 38. (X1, X2)<latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit><latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit><latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit><latexit sha1_base64="+84Bg7nc8xqYg+lRwyALxCL8Hj4=">AAACAHicbVA9SwNBFHznZ4xfUUubxSBEkHAXBC2DNpYRTHKSHMfeZi9Zsrt37O4JIaTxL9hqbye2/hNbf4mb5ApNHHgwzLzHPCZKOdPGdb+cldW19Y3NwlZxe2d3b790cNjSSaYIbZKEJ8qPsKacSdo0zHDqp4piEXHajoY3U7/9SJVmibw3o5QGAvclixnBxkoPFT/0zv2wdhaWym7VnQEtEy8nZcjRCEvf3V5CMkGlIRxr3fHc1ARjrAwjnE6K3UzTFJMh7tOOpRILqoPx7OEJOrVKD8WJsiMNmqm/L8ZYaD0Skd0U2Az0ojcV//UisZBs4qtgzGSaGSrJPDjOODIJmraBekxRYvjIEkwUs78jMsAKE2M7K9pSvMUKlkmrVvXcqnd3Ua5f5/UU4BhOoAIeXEIdbqEBTSAg4Ble4NV5ct6cd+djvrri5DdH8AfO5w81u5XI</latexit> (X1 > ✓1) ^ (X2 > ✓2) ) blue<latexit sha1_base64="tnZjQExak89pE4WaqY4lKXqUgi8=">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</latexit><latexit sha1_base64="tnZjQExak89pE4WaqY4lKXqUgi8=">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</latexit><latexit sha1_base64="tnZjQExak89pE4WaqY4lKXqUgi8=">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</latexit><latexit sha1_base64="tnZjQExak89pE4WaqY4lKXqUgi8=">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</latexit> 
 I(X1 > ✓1) · I(X2 > ✓2)<latexit sha1_base64="dfAkRKlRqLDbctNMQSeV//VJPg0=">AAACRXicbVDLSsNAFJ34Nr6qLt0MFkE3JSmCLkU3Ci4qWFswIUwmt+3g5OHMjVBCf8qf8Bd0affuxK1Oahe29cDA4dxzuWdOmEmh0XHerLn5hcWl5ZVVe219Y3Orsr1zp9NccWjyVKaqHTINUiTQRIES2pkCFocSWuHDRTlvPYHSIk1usZ+BH7NuIjqCMzRSULn2Yoa9MCyuBoftwKVeFx61ZAlSD3uALHCPbI9HKdoTxvqssX5kB5WqU3NGoLPEHZMqGaMRVIZelPI8hgS5ZFrfu06GfsEUCi5hYHu5hozxB9aFe0MTFoP2i9GvB/TAKBHtpMo8E2Ok/t0oWKx1Pw6Ns4yup2el+O8sjKcuY+fUL0SS5QgJ/z3cySXFlJaV0kgo4Cj7hjCuhMlOeY8pxtEUX5biTlcwS+7qNdepuTfH1bPzcT0rZI/sk0PikhNyRi5JgzQJJ8/klbyTofVifVif1tevdc4a7+ySCVjfP90ssPE=</latexit><latexit sha1_base64="dfAkRKlRqLDbctNMQSeV//VJPg0=">AAACRXicbVDLSsNAFJ34Nr6qLt0MFkE3JSmCLkU3Ci4qWFswIUwmt+3g5OHMjVBCf8qf8Bd0affuxK1Oahe29cDA4dxzuWdOmEmh0XHerLn5hcWl5ZVVe219Y3Orsr1zp9NccWjyVKaqHTINUiTQRIES2pkCFocSWuHDRTlvPYHSIk1usZ+BH7NuIjqCMzRSULn2Yoa9MCyuBoftwKVeFx61ZAlSD3uALHCPbI9HKdoTxvqssX5kB5WqU3NGoLPEHZMqGaMRVIZelPI8hgS5ZFrfu06GfsEUCi5hYHu5hozxB9aFe0MTFoP2i9GvB/TAKBHtpMo8E2Ok/t0oWKx1Pw6Ns4yup2el+O8sjKcuY+fUL0SS5QgJ/z3cySXFlJaV0kgo4Cj7hjCuhMlOeY8pxtEUX5biTlcwS+7qNdepuTfH1bPzcT0rZI/sk0PikhNyRi5JgzQJJ8/klbyTofVifVif1tevdc4a7+ySCVjfP90ssPE=</latexit><latexit sha1_base64="dfAkRKlRqLDbctNMQSeV//VJPg0=">AAACRXicbVDLSsNAFJ34Nr6qLt0MFkE3JSmCLkU3Ci4qWFswIUwmt+3g5OHMjVBCf8qf8Bd0affuxK1Oahe29cDA4dxzuWdOmEmh0XHerLn5hcWl5ZVVe219Y3Orsr1zp9NccWjyVKaqHTINUiTQRIES2pkCFocSWuHDRTlvPYHSIk1usZ+BH7NuIjqCMzRSULn2Yoa9MCyuBoftwKVeFx61ZAlSD3uALHCPbI9HKdoTxvqssX5kB5WqU3NGoLPEHZMqGaMRVIZelPI8hgS5ZFrfu06GfsEUCi5hYHu5hozxB9aFe0MTFoP2i9GvB/TAKBHtpMo8E2Ok/t0oWKx1Pw6Ns4yup2el+O8sjKcuY+fUL0SS5QgJ/z3cySXFlJaV0kgo4Cj7hjCuhMlOeY8pxtEUX5biTlcwS+7qNdepuTfH1bPzcT0rZI/sk0PikhNyRi5JgzQJJ8/klbyTofVifVif1tevdc4a7+ySCVjfP90ssPE=</latexit><latexit sha1_base64="dfAkRKlRqLDbctNMQSeV//VJPg0=">AAACRXicbVDLSsNAFJ34Nr6qLt0MFkE3JSmCLkU3Ci4qWFswIUwmt+3g5OHMjVBCf8qf8Bd0affuxK1Oahe29cDA4dxzuWdOmEmh0XHerLn5hcWl5ZVVe219Y3Orsr1zp9NccWjyVKaqHTINUiTQRIES2pkCFocSWuHDRTlvPYHSIk1usZ+BH7NuIjqCMzRSULn2Yoa9MCyuBoftwKVeFx61ZAlSD3uALHCPbI9HKdoTxvqssX5kB5WqU3NGoLPEHZMqGaMRVIZelPI8hgS5ZFrfu06GfsEUCi5hYHu5hozxB9aFe0MTFoP2i9GvB/TAKBHtpMo8E2Ok/t0oWKx1Pw6Ns4yup2el+O8sjKcuY+fUL0SS5QgJ/z3cySXFlJaV0kgo4Cj7hjCuhMlOeY8pxtEUX5biTlcwS+7qNdepuTfH1bPzcT0rZI/sk0PikhNyRi5JgzQJJ8/klbyTofVifVif1tevdc4a7+ySCVjfP90ssPE=</latexit>
  39. 39. `1<latexit sha1_base64="08fK0P4FbLL8ccSSHDRGsI2CLU4=">AAAB/XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jGCeUCyhNlJJxkzM7vMzAphCf6CV717E69+i1e/xEmyB00saCiquqmmokRwY33/y1tZXVvf2CxsFbd3dvf2SweHDROnmmGdxSLWrYgaFFxh3XIrsJVopDIS2IxGN1O/+Yja8Fjd23GCoaQDxfucUeukRgeF6AbdUtmv+DOQZRLkpAw5at3Sd6cXs1SiskxQY9qBn9gwo9pyJnBS7KQGE8pGdIBtRxWVaMJs9u2EnDqlR/qxdqMsmam/LzIqjRnLyG1Kaodm0ZuK/3qRXEi2/asw4ypJLSo2D+6ngtiYTKsgPa6RWTF2hDLN3e+EDammzLrCiq6UYLGCZdI4rwR+Jbi7KFev83oKcAwncAYBXEIVbqEGdWDwAM/wAq/ek/fmvXsf89UVL785gj/wPn8AiKSVhQ==</latexit><latexit 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