8181:. For example, following the path that a decision tree takes to make its decision is trivial and self-explained, but following the paths of hundreds or thousands of trees is much harder. To achieve both performance and interpretability, some model compression techniques allow transforming an XGBoost into a single "born-again" decision tree that approximates the same decision function. Furthermore, its implementation may be more difficult due to the higher computational demand.
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algorithms. That is, algorithms that optimize a cost function over function space by iteratively choosing a function (weak hypothesis) that points in the negative gradient direction. This functional gradient view of boosting has led to the development of boosting algorithms in many areas of machine
8147:
The method goes by a variety of names. Friedman introduced his regression technique as a "Gradient
Boosting Machine" (GBM). Mason, Baxter et al. described the generalized abstract class of algorithms as "functional gradient boosting". Friedman et al. describe an advancement of gradient boosted
8057:
of the prediction performance improvement by evaluating predictions on those observations which were not used in the building of the next base learner. Out-of-bag estimates help avoid the need for an independent validation dataset, but often underestimate actual performance improvement and the
8082:
is to penalize model complexity of the learned model. The model complexity can be defined as the proportional number of leaves in the learned trees. The joint optimization of loss and model complexity corresponds to a post-pruning algorithm to remove branches that fail to reduce the loss by a
8134:
use variants of gradient boosting in their machine-learned ranking engines. Gradient boosting is also utilized in High Energy
Physics in data analysis. At the Large Hadron Collider (LHC), variants of gradient boosting Deep Neural Networks (DNN) were successful in reproducing the results of
7921:("bagging") method. Specifically, he proposed that at each iteration of the algorithm, a base learner should be fit on a subsample of the training set drawn at random without replacement. Friedman observed a substantial improvement in gradient boosting's accuracy with this modification.
6205:
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Gradient tree boosting implementations often also use regularization by limiting the minimum number of observations in trees' terminal nodes. It is used in the tree building process by ignoring any splits that lead to nodes containing fewer than this number of training set instances.
7165:
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calls it a "Generalized
Boosting Model", however packages expanding this work use BRT. Yet another name is TreeNet, after an early commercial implementation from Salford System's Dan Steinberg, one of researchers who pioneered the use of tree-based methods.
6821:
1010:, (in 1999 and later in 2001) simultaneously with the more general functional gradient boosting perspective of Llew Mason, Jonathan Baxter, Peter Bartlett and Marcus Frean. The latter two papers introduced the view of boosting algorithms as iterative
4097:
5176:
5141:
3727:
4908:{\displaystyle \gamma _{m}={\underset {\gamma }{\arg \min }}{\sum _{i=1}^{n}{L(y_{i},F_{m}(x_{i}))}}={\underset {\gamma }{\arg \min }}{\sum _{i=1}^{n}{L\left(y_{i},F_{m-1}(x_{i})-\gamma \nabla _{F_{m-1}}L(y_{i},F_{m-1}(x_{i}))\right)}}.}
3128:
5673:
2234:
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8164:
Gradient boosting can be used for feature importance ranking, which is usually based on aggregating importance function of the base learners. For example, if a gradient boosted trees algorithm is developed using entropy-based
5888:
2834:
6690:
2616:
8920:
Wu, Xindong; Kumar, Vipin; Ross
Quinlan, J.; Ghosh, Joydeep; Yang, Qiang; Motoda, Hiroshi; McLachlan, Geoffrey J.; Ng, Angus; Liu, Bing; Yu, Philip S.; Zhou, Zhi-Hua (2008-01-01). "Top 10 algorithms in data mining".
6038:
5430:
on the above equations. Note that this approach is a heuristic and therefore doesn't yield an exact solution to the given problem, but rather an approximation. In pseudocode, the generic gradient boosting method is:
7438:{\displaystyle F_{m}(x)=F_{m-1}(x)+\sum _{j=1}^{J_{m}}\gamma _{jm}\mathbf {1} _{R_{jm}}(x),\quad \gamma _{jm}={\underset {\gamma }{\operatorname {arg\,min} }}\sum _{x_{i}\in R_{jm}}L(y_{i},F_{m-1}(x_{i})+\gamma ).}
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that minimizes the average value of the loss function on the training set, i.e., minimizes the empirical risk. It does so by starting with a model, consisting of a constant function
7062:{\displaystyle F_{m}(x)=F_{m-1}(x)+\gamma _{m}h_{m}(x),\quad \gamma _{m}={\underset {\gamma }{\operatorname {arg\,min} }}\sum _{i=1}^{n}L(y_{i},F_{m-1}(x_{i})+\gamma h_{m}(x_{i})).}
4408:{\displaystyle O=\sum _{i=1}^{n}{L(y_{i},F_{m-1}(x_{i})+h_{m}(x_{i}))}\approx \sum _{i=1}^{n}{L(y_{i},F_{m-1}(x_{i}))+h_{m}(x_{i})\nabla _{F_{m-1}}L(y_{i},F_{m-1}(x_{i}))}+\ldots }
1962:
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6375:) of a fixed size as base learners. For this special case, Friedman proposes a modification to gradient boosting method which improves the quality of fit of each base learner.
861:
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that boosting can be interpreted as an optimization algorithm on a suitable cost function. Explicit regression gradient boosting algorithms were subsequently developed, by
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1995:
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4554:. This is the direction of steepest ascent and hence we must move in the opposite (i.e., negative) direction in order to move in the direction of steepest descent.
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2022:
1901:
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7836:
5383:{\displaystyle \gamma _{m}={\underset {\gamma }{\arg \min }}{\sum _{i=1}^{n}{L\left(y_{i},F_{m-1}(x_{i})-\gamma \nabla _{F_{m-1}}L(y_{i},F_{m-1}(x_{i}))\right)}}.}
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Like other boosting methods, gradient boosting combines weak "learners" into a single strong learner in an iterative fashion. It is easiest to explain in the
856:
707:
438:
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7472:, the number of terminal nodes in trees, is the method's parameter which can be adjusted for a data set at hand. It controls the maximum allowed level of
939:
742:
5699:
8169:, the ensemble algorithm ranks the importance of features based on entropy as well with the caveat that it is averaged out over all base learners.
2738:
6200:{\displaystyle \gamma _{m}={\underset {\gamma }{\operatorname {arg\,min} }}\sum _{i=1}^{n}L\left(y_{i},F_{m-1}(x_{i})+\gamma h_{m}(x_{i})\right).}
818:
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367:
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is a computationally infeasible optimization problem in general. Therefore, we restrict our approach to a simplified version of the problem.
8638:
8177:
While boosting can increase the accuracy of a base learner, such as a decision tree or linear regression, it sacrifices intelligibility and
8139:. Gradient boosting decision tree was also applied in earth and geological studies – for example quality evaluation of sandstone reservoir.
7677:
Another regularization parameter is the depth of the trees. The higher this value the more likely the model will overfit the training data.
7998:. The algorithm also becomes faster, because regression trees have to be fit to smaller datasets at each iteration. Friedman obtained that
876:
639:
174:
8619:
1103:
894:
8678:"An intelligent approach for reservoir quality evaluation in tight sandstone reservoir using gradient boosting decision tree algorithm"
3780:
9055:
8568:
Note that this is different from bagging, which samples with replacement because it uses samples of the same size as the training set.
6372:
727:
702:
651:
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An important part of gradient boosting method is regularization by shrinkage which consists in modifying the update rule as follows:
7816:
1664:
775:
770:
423:
433:
71:
8247:
8148:
models as
Multiple Additive Regression Trees (MART); Elith et al. describe that approach as "Boosted Regression Trees" (BRT).
6216:
4463:
2393:{\displaystyle -{\frac {\partial L_{\rm {MSE}}}{\partial F(x_{i})}}={\frac {2}{n}}(y_{i}-F(x_{i}))={\frac {2}{n}}h_{m}(x_{i})}
828:
8346:
8287:
979:. When a decision tree is the weak learner, the resulting algorithm is called gradient-boosted trees; it usually outperforms
932:
592:
413:
8417:
2843:
803:
505:
281:
3374:{\displaystyle F_{m}(x)=F_{m-1}(x)+\left({\underset {h_{m}\in {\mathcal {H}}}{\operatorname {arg\,min} }}\left\right)(x)}
7995:
7913:
Soon after the introduction of gradient boosting, Friedman proposed a minor modification to the algorithm, motivated by
7648:
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607:
585:
428:
418:
7647:
Fitting the training set too closely can lead to degradation of the model's generalization ability. Several so-called
2939:
2466:
that best approximates the output variable from the values of input variables. This is formalized by introducing some
984:
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911:
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808:
269:
91:
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798:
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871:
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of weak prediction models, i.e., models that make very few assumptions about the data, which are typically simple
925:
531:
299:
169:
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8152:
7473:
6475:
1523:
553:
473:
396:
314:
144:
106:
101:
61:
56:
3414:
9060:
988:
500:
349:
249:
76:
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7871:) yields dramatic improvements in models' generalization ability over gradient boosting without shrinking (
3492:
The basic idea behind the steepest descent is to find a local minimum of the loss function by iterating on
8215:
8166:
6368:
976:
968:
680:
656:
558:
319:
294:
254:
66:
8874:
8655:
Lalchand, Vidhi (2020). "Extracting more from boosted decision trees: A high energy physics case study".
8469:
Note: in case of usual CART trees, the trees are fitted using least-squares loss, and so the coefficient
7918:
7902:
7670:
is often selected by monitoring prediction error on a separate validation data set. Besides controlling
7666:
reduces the error on training set, but setting it too high may lead to overfitting. An optimal value of
5136:{\displaystyle F_{m}(x)=F_{m-1}(x)-\gamma _{m}\sum _{i=1}^{n}{\nabla _{F_{m-1}}L(y_{i},F_{m-1}(x_{i}))}}
1911:
634:
456:
408:
264:
179:
51:
8050:
is typically set to 0.5, meaning that one half of the training set is used to build each base learner.
8001:
8781:
8689:
6815:, chosen using line search so as to minimize the loss function, and the model is updated as follows:
1905:
1572:
1250:
1056:
563:
513:
5393:
4920:
4048:
3722:{\displaystyle F_{m}(x)=F_{m-1}(x)-\gamma \sum _{i=1}^{n}{\nabla _{F_{m-1}}L(y_{i},F_{m-1}(x_{i}))}}
2707:
8604:
7538:
2945:
2629:
2431:
2417:
1444:
1030:
666:
602:
573:
478:
304:
237:
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209:
184:
134:
86:
46:
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4420:
3734:
2035:
8956:
8902:
8750:
8656:
8635:
7898:
7848:
7105:
6791:
6532:
6009:
5149:
2076:
1098:
1007:
644:
568:
354:
149:
8725:
Friedman, Jerome (2003). "Multiple
Additive Regression Trees with Application in Epidemiology".
7159:
from the tree-fitting procedure can be then simply discarded and the model update rule becomes:
5512:
3495:
2428:, related to each other with some probabilistic distribution. The goal is to find some function
9035:
8875:"Data Analytics in Asset Management: Cost-Effective Prediction of the Pavement Condition Index"
8086:
6321:
2472:
9010:
8974:
Sagi, Omer; Rokach, Lior (2021). "Approximating XGBoost with an interpretable decision tree".
8948:
8894:
8799:
8742:
8707:
8616:
8255:
6538:
6385:
5897:
3534:. In fact, the local maximum-descent direction of the loss function is the negative gradient.
2983:
2671:
2082:
1625:
1289:
972:
737:
580:
493:
289:
259:
204:
199:
154:
96:
7970:, the algorithm is deterministic and identical to the one described above. Smaller values of
7662:(i.e. the number of trees in the model when the base learner is a decision tree). Increasing
7616:
4585:
4565:
3760:
3540:
3388:
3123:{\displaystyle F_{0}(x)={\underset {\gamma }{\arg \min }}{\sum _{i=1}^{n}{L(y_{i},\gamma )}}}
1967:
8983:
8938:
8930:
8886:
8855:"Exclusive: Interview with Dan Steinberg, President of Salford Systems, Data Mining Pioneer"
8789:
8734:
8697:
8532:
8502:
8472:
8178:
8123:
8054:
7874:
7132:
6761:
6728:
6698:
3486:
3017:
2405:
2029:
1326:
956:
765:
518:
468:
378:
362:
332:
194:
189:
139:
129:
27:
8890:
6448:
6421:
3454:
2000:
1879:
1598:
1476:
8642:
8623:
7821:
5668:{\displaystyle F_{0}(x)={\underset {\gamma }{\arg \min }}\sum _{i=1}^{n}L(y_{i},\gamma ).}
2229:{\displaystyle L_{\rm {MSE}}={\frac {1}{n}}\sum _{i=1}^{n}\left(y_{i}-F(x_{i})\right)^{2}}
793:
597:
463:
403:
7947:
7590:
7532:
the model may include effects of the interaction between up to two variables, and so on.
7509:
7479:
8785:
8693:
8453:
8435:
7805:{\displaystyle F_{m}(x)=F_{m-1}(x)+\nu \cdot \gamma _{m}h_{m}(x),\quad 0<\nu \leq 1,}
2408:
algorithm, and generalizing it entails "plugging in" a different loss and its gradient.
1358:
8676:
Ma, Longfei; Xiao, Hanmin; Tao, Jingwei; Zheng, Taiyi; Zhang, Haiqin (1 January 2022).
8529:
is equal to just the value of output variable, averaged over all training instances in
8033:
7973:
7927:
7570:
7503:
7455:
7072:
Friedman proposes to modify this algorithm so that it chooses a separate optimal value
1578:
1503:
1424:
1404:
1381:
1227:
1207:
1187:
1036:
987:
methods, but it generalizes the other methods by allowing optimization of an arbitrary
813:
344:
81:
8581:
9049:
8906:
8794:
8769:
8195:
8079:
7842:
2467:
2025:
1027:
991:
980:
732:
661:
543:
274:
159:
8754:
8265:
9030:
8960:
8353:
8294:
7658:
One natural regularization parameter is the number of gradient boosting iterations
2729:
7129:
for the whole tree. He calls the modified algorithm "TreeBoost". The coefficients
8136:
8111:
7991:
7914:
7652:
5883:{\displaystyle r_{im}=-\left_{F(x)=F_{m-1}(x)}\quad {\mbox{for }}i=1,\ldots ,n.}
5427:
1003:
538:
32:
2829:{\displaystyle {\hat {F}}(x)=\sum _{m=1}^{M}\gamma _{m}h_{m}(x)+{\mbox{const}}}
8987:
8934:
8388:
983:. A gradient-boosted trees model is built in a stage-wise fashion as in other
687:
383:
309:
8952:
8898:
8711:
8030:
leads to good results for small and moderate sized training sets. Therefore,
971:
used in traditional boosting. It gives a prediction model in the form of an
846:
627:
8803:
8746:
7567:
work well for boosting and results are fairly insensitive to the choice of
6685:{\displaystyle h_{m}(x)=\sum _{j=1}^{J_{m}}b_{jm}\mathbf {1} _{R_{jm}}(x),}
8702:
8677:
8593:
Learn
Gradient Boosting Algorithm for better predictions (with codes in R)
8135:
non-machine learning methods of analysis on datasets used to discover the
2611:{\displaystyle {\hat {F}}={\underset {F}{\arg \min }}\,\mathbb {E} _{x,y}}
8205:
8200:
8190:
9040:
1023:(This section follows the exposition of gradient boosting by Cheng Li.)
8943:
8210:
8070:
Imposing this limit helps to reduce variance in predictions at leaves.
4963:, we would update the model in accordance with the following equations
4036:{\displaystyle O=\sum _{i=1}^{n}{L(y_{i},F_{m-1}(x_{i})+h_{m}(x_{i}))}}
622:
6445:
be the number of its leaves. The tree partitions the input space into
8738:
8131:
5894:
Fit a base learner (or weak learner, e.g. tree) closed under scaling
373:
2075:
for a given model are proportional to the negative gradients of the
8661:
9005:
Boehmke, Bradley; Greenwell, Brandon (2019). "Gradient
Boosting".
8409:
Mason, L.; Baxter, J.; Bartlett, P. L.; Frean, Marcus (May 1999).
8127:
1177:{\displaystyle {\tfrac {1}{n}}\sum _{i}({\hat {y}}_{i}-y_{i})^{2}}
617:
612:
339:
3892:{\displaystyle L(y_{i},F_{m}(x_{i}))\leq L(y_{i},F_{m-1}(x_{i}))}
3489:
step to this minimization problem (functional gradient descent).
8636:
Yandex corporate blog entry about new ranking model "Snezhinsk"
8404:
8402:
8375:
8373:
6033:
by solving the following one-dimensional optimization problem:
1002:
The idea of gradient boosting originated in the observation by
8380:
Mason, L.; Baxter, J.; Bartlett, P. L.; Frean, Marcus (1999).
8078:
Another useful regularization techniques for gradient boosted
1774:{\displaystyle F_{m+1}(x_{i})=F_{m}(x_{i})+h_{m}(x_{i})=y_{i}}
1015:
learning and statistics beyond regression and classification.
8347:"Greedy Function Approximation: A Gradient Boosting Machine"
8329:. Statistics Department, University of California, Berkeley.
5399:
4926:
3433:
3233:
2713:
8411:"Boosting Algorithms as Gradient Descent in Function Space"
8053:
Also, like in bagging, subsampling allows one to define an
5930:
to pseudo-residuals, i.e. train it using the training set
7990:
introduce randomness into the algorithm and help prevent
6531:
and predicts a constant value in each region. Using the
6305:{\displaystyle F_{m}(x)=F_{m-1}(x)+\gamma _{m}h_{m}(x).}
4547:{\displaystyle \nabla _{F_{m-1}}L(y_{i},F_{m-1}(x_{i}))}
1401:
Now, let us consider a gradient boosting algorithm with
905:
List of datasets in computer vision and image processing
8873:
Piryonesi, S. Madeh; El-Diraby, Tamer E. (2020-03-01).
8582:
Generalized
Boosted Models: A guide to the gbm package.
8254:(2nd ed.). New York: Springer. pp. 337–384.
8110:
penalty on the leaf values can also be added to avoid
5850:
2923:{\displaystyle \{(x_{1},y_{1}),\dots ,(x_{n},y_{n})\}}
2820:
1108:
8535:
8505:
8475:
8089:
8036:
8004:
7976:
7950:
7930:
7877:
7851:
7824:
7694:
7619:
7593:
7573:
7541:
7512:
7506:), no interaction between variables is allowed. With
7482:
7458:
7168:
7135:
7108:
7078:
6824:
6794:
6764:
6731:
6701:
6584:
6541:
6478:
6451:
6424:
6388:
6324:
6219:
6041:
6012:
5936:
5900:
5702:
5575:
5515:
5442:
5396:
5179:
5152:
4972:
4947:
4923:
4610:
4588:
4568:
4466:
4423:
4100:
4051:
3920:
3783:
3763:
3737:
3565:
3543:
3498:
3457:
3417:
3391:
3138:
3029:
2986:
2948:
2942:
principle, the method tries to find an approximation
2846:
2741:
2710:
2674:
2632:
2522:
2475:
2434:
2245:
2124:
2085:
2038:
2003:
1970:
1914:
1882:
1793:
1667:
1628:
1601:
1581:
1526:
1506:
1479:
1473:) of gradient boosting, suppose some imperfect model
1447:
1427:
1407:
1384:
1361:
1329:
1292:
1253:
1230:
1210:
1190:
1106:
1059:
1039:
8617:
Statistical
Analysis of Bayes Optimal Subset Ranking
8393:
Advances in Neural Information Processing Systems 12
8246:
Hastie, T.; Tibshirani, R.; Friedman, J. H. (2009).
8083:
threshold. Other kinds of regularization such as an
7674:, several other regularization techniques are used.
7102:
for each of the tree's regions, instead of a single
4941:
is the set of arbitrary differentiable functions on
2622:The gradient boosting method assumes a real-valued
8819:"Boosted Regression Trees for ecological modeling"
8551:
8521:
8491:
8102:
8042:
8022:
7982:
7962:
7936:
7889:
7863:
7830:
7804:
7631:
7605:
7579:
7559:
7524:
7494:
7464:
7437:
7151:
7121:
7094:
7061:
6807:
6780:
6747:
6717:
6684:
6563:
6523:
6464:
6437:
6410:
6349:
6304:
6199:
6025:
5995:
5922:
5882:
5667:
5548:
5501:
5406:
5382:
5165:
5135:
4955:
4933:
4917:If we considered the continuous case, i.e., where
4907:
4594:
4574:
4546:
4452:
4407:
4086:
4035:
3891:
3769:
3749:
3721:
3557:such that the linear approximation remains valid:
3549:
3526:
3470:
3440:
3403:
3373:
3122:
3008:
2972:
2922:
2828:
2720:
2696:
2656:
2610:
2505:
2458:
2392:
2228:
2107:
2067:
2016:
1997:attempts to correct the errors of its predecessor
1989:
1956:
1895:
1864:
1773:
1650:
1614:
1587:
1563:
1512:
1492:
1465:
1433:
1413:
1390:
1370:
1345:
1314:
1278:
1236:
1216:
1196:
1176:
1089:
1045:
4602:value for which the loss function has a minimum:
4460:, only the derivative of the second term remains
7905:: lower learning rate requires more iterations.
7897:). However, it comes at the price of increasing
5607:
5390:In the discrete case however, i.e. when the set
5202:
4727:
4633:
4045:Doing a Taylor expansion around the fixed point
3061:
2547:
2404:So, gradient boosting could be specialized to a
8576:
8574:
8340:
8338:
8336:
8281:
8279:
8277:
8275:
7841:Empirically it has been found that using small
3913:To prove the following, consider the objective
1865:{\displaystyle h_{m}(x_{i})=y_{i}-F_{m}(x_{i})}
1622:, our algorithm should add some new estimator,
8122:Gradient boosting can be used in the field of
7655:effect by constraining the fitting procedure.
2032:, follows from the observation that residuals
1033:setting, where the goal is to "teach" a model
900:List of datasets for machine-learning research
8770:"A working guide to boosted regression trees"
933:
8:
8436:"A Gentle Introduction to Gradient Boosting"
5996:{\displaystyle \{(x_{i},r_{im})\}_{i=1}^{n}}
5973:
5937:
5502:{\displaystyle \{(x_{i},y_{i})\}_{i=1}^{n},}
5476:
5443:
5414:is finite, we choose the candidate function
3478:at each step for an arbitrary loss function
2917:
2847:
7613:is insufficient for many applications, and
963:in a functional space, where the target is
3902:
3451:Unfortunately, choosing the best function
940:
926:
18:
8942:
8793:
8701:
8660:
8540:
8534:
8510:
8504:
8480:
8474:
8382:"Boosting Algorithms as Gradient Descent"
8151:A popular open-source implementation for
8094:
8088:
8035:
8003:
7975:
7949:
7929:
7924:Subsample size is some constant fraction
7876:
7850:
7823:
7765:
7755:
7721:
7699:
7693:
7618:
7592:
7572:
7540:
7511:
7481:
7457:
7414:
7395:
7382:
7361:
7348:
7343:
7323:
7313:
7311:
7299:
7271:
7266:
7261:
7251:
7239:
7234:
7223:
7195:
7173:
7167:
7140:
7134:
7113:
7107:
7083:
7077:
7044:
7031:
7012:
6993:
6980:
6964:
6953:
6933:
6923:
6921:
6912:
6889:
6879:
6851:
6829:
6823:
6799:
6793:
6769:
6763:
6736:
6730:
6706:
6700:
6659:
6654:
6649:
6639:
6627:
6622:
6611:
6589:
6583:
6546:
6540:
6524:{\displaystyle R_{1m},\ldots ,R_{J_{m}m}}
6510:
6505:
6483:
6477:
6456:
6450:
6429:
6423:
6393:
6387:
6367:Gradient boosting is typically used with
6329:
6323:
6284:
6274:
6246:
6224:
6218:
6180:
6167:
6148:
6129:
6116:
6098:
6087:
6067:
6057:
6055:
6046:
6040:
6017:
6011:
5987:
5976:
5960:
5947:
5935:
5905:
5899:
5849:
5825:
5805:
5789:
5762:
5743:
5727:
5707:
5701:
5647:
5631:
5620:
5598:
5580:
5574:
5514:
5490:
5479:
5466:
5453:
5441:
5398:
5397:
5395:
5358:
5339:
5326:
5302:
5297:
5278:
5259:
5246:
5233:
5227:
5216:
5211:
5193:
5184:
5178:
5157:
5151:
5120:
5101:
5088:
5064:
5059:
5054:
5048:
5037:
5027:
4999:
4977:
4971:
4949:
4948:
4946:
4925:
4924:
4922:
4883:
4864:
4851:
4827:
4822:
4803:
4784:
4771:
4758:
4752:
4741:
4736:
4718:
4701:
4688:
4675:
4664:
4658:
4647:
4642:
4624:
4615:
4609:
4587:
4567:
4532:
4513:
4500:
4476:
4471:
4465:
4441:
4428:
4422:
4386:
4367:
4354:
4330:
4325:
4312:
4299:
4280:
4261:
4248:
4237:
4231:
4220:
4200:
4187:
4171:
4152:
4139:
4128:
4122:
4111:
4099:
4075:
4056:
4050:
4020:
4007:
3991:
3972:
3959:
3948:
3942:
3931:
3919:
3877:
3858:
3845:
3820:
3807:
3794:
3782:
3762:
3736:
3706:
3687:
3674:
3650:
3645:
3640:
3634:
3623:
3592:
3570:
3564:
3542:
3503:
3497:
3462:
3456:
3432:
3431:
3422:
3416:
3390:
3339:
3326:
3310:
3291:
3278:
3267:
3261:
3250:
3245:
3232:
3231:
3222:
3206:
3196:
3194:
3165:
3143:
3137:
3103:
3092:
3086:
3075:
3070:
3052:
3034:
3028:
2991:
2985:
2950:
2949:
2947:
2908:
2895:
2870:
2857:
2845:
2819:
2801:
2791:
2781:
2770:
2743:
2742:
2740:
2712:
2711:
2709:
2679:
2673:
2634:
2633:
2631:
2563:
2559:
2558:
2556:
2538:
2524:
2523:
2521:
2474:
2436:
2435:
2433:
2381:
2368:
2354:
2339:
2320:
2303:
2288:
2260:
2259:
2249:
2244:
2220:
2206:
2187:
2171:
2160:
2146:
2130:
2129:
2123:
2096:
2084:
2056:
2043:
2037:
2008:
2002:
1975:
1969:
1945:
1932:
1919:
1913:
1887:
1881:
1853:
1840:
1827:
1811:
1798:
1792:
1765:
1749:
1736:
1720:
1707:
1691:
1672:
1666:
1633:
1627:
1606:
1600:
1580:
1564:{\displaystyle {\hat {y}}_{i}={\bar {y}}}
1550:
1549:
1540:
1529:
1528:
1525:
1505:
1484:
1478:
1446:
1426:
1406:
1383:
1360:
1334:
1328:
1303:
1291:
1267:
1256:
1255:
1252:
1229:
1209:
1189:
1168:
1158:
1145:
1134:
1133:
1123:
1107:
1105:
1061:
1060:
1058:
1038:
9009:. Chapman & Hall. pp. 221–245.
8241:
8239:
8237:
8235:
8233:
8231:
5567:Initialize model with a constant value:
1224:of actual values of the output variable
8615:Cossock, David and Zhang, Tong (2008).
8227:
5426:may then be calculated with the aid of
3441:{\displaystyle h_{m}\in {\mathcal {H}}}
1204:indexes over some training set of size
26:
7944:of the size of the training set. When
3907:Proof of functional form of Derivative
1964:. As in other boosting variants, each
1876:Therefore, gradient boosting will fit
8868:
8866:
8864:
7535:Hastie et al. comment that typically
7476:between variables in the model. With
6725:is the value predicted in the region
2420:problems there is an output variable
7:
8252:The Elements of Statistical Learning
8126:. The commercial web search engines
3016:, and incrementally expands it in a
2840:We are usually given a training set
8391:and T.K. Leen and K. MĂĽller (ed.).
6382:-th step would fit a decision tree
2030:classification and ranking problems
2024:. A generalization of this idea to
895:Glossary of artificial intelligence
8891:10.1061/(ASCE)IS.1943-555X.0000512
7330:
7327:
7324:
7320:
7317:
7314:
6940:
6937:
6934:
6930:
6927:
6924:
6074:
6071:
6068:
6064:
6061:
6058:
5776:
5730:
5294:
5056:
4819:
4468:
4322:
3642:
3213:
3210:
3207:
3203:
3200:
3197:
2513:and minimizing it in expectation:
2275:
2267:
2264:
2261:
2252:
2137:
2134:
2131:
1957:{\displaystyle y_{i}-F_{m}(x_{i})}
14:
9036:Gradient Boosted Regression Trees
8923:Knowledge and Information Systems
8879:Journal of Infrastructure Systems
8345:Friedman, J. H. (February 1999).
8248:"10. Boosting and Additive Trees"
8023:{\displaystyle 0.5\leq f\leq 0.8}
6378:Generic gradient boosting at the
2664:in the form of a weighted sum of
2028:other than squared error, and to
9031:How to explain gradient boosting
9007:Hands-On Machine Learning with R
8795:10.1111/j.1365-2656.2008.01390.x
8454:"The Method of Steepest Descent"
8062:Number of observations in leaves
7262:
6650:
2424:and a vector of input variables
7838:is called the "learning rate".
7783:
7294:
6907:
5848:
5509:a differentiable loss function
5173:is the step length, defined as
2079:loss function (with respect to
1520:, this model may simply return
1279:{\displaystyle {\hat {y}}_{i}=}
1090:{\displaystyle {\hat {y}}=F(x)}
8395:. MIT Press. pp. 512–518.
8288:"Stochastic Gradient Boosting"
8286:Friedman, J. H. (March 1999).
8058:optimal number of iterations.
7777:
7771:
7739:
7733:
7711:
7705:
7429:
7420:
7407:
7375:
7288:
7282:
7213:
7207:
7185:
7179:
7053:
7050:
7037:
7018:
7005:
6973:
6901:
6895:
6869:
6863:
6841:
6835:
6676:
6670:
6601:
6595:
6558:
6552:
6405:
6399:
6341:
6335:
6296:
6290:
6264:
6258:
6236:
6230:
6186:
6173:
6154:
6141:
5969:
5940:
5917:
5911:
5843:
5837:
5815:
5809:
5795:
5782:
5771:
5768:
5755:
5736:
5659:
5640:
5592:
5586:
5540:
5537:
5531:
5519:
5472:
5446:
5407:{\displaystyle {\mathcal {H}}}
5367:
5364:
5351:
5319:
5284:
5271:
5129:
5126:
5113:
5081:
5017:
5011:
4989:
4983:
4934:{\displaystyle {\mathcal {H}}}
4892:
4889:
4876:
4844:
4809:
4796:
4710:
4707:
4694:
4668:
4541:
4538:
4525:
4493:
4447:
4434:
4395:
4392:
4379:
4347:
4318:
4305:
4289:
4286:
4273:
4241:
4209:
4206:
4193:
4177:
4164:
4132:
4087:{\displaystyle F_{m-1}(x_{i})}
4081:
4068:
4029:
4026:
4013:
3997:
3984:
3952:
3886:
3883:
3870:
3838:
3829:
3826:
3813:
3787:
3715:
3712:
3699:
3667:
3610:
3604:
3582:
3576:
3521:
3515:
3368:
3362:
3348:
3345:
3332:
3316:
3303:
3271:
3183:
3177:
3155:
3149:
3115:
3096:
3046:
3040:
3003:
2997:
2967:
2961:
2955:
2914:
2888:
2876:
2850:
2813:
2807:
2760:
2754:
2748:
2721:{\displaystyle {\mathcal {H}}}
2691:
2685:
2651:
2645:
2639:
2605:
2602:
2599:
2593:
2581:
2575:
2529:
2500:
2497:
2491:
2479:
2453:
2447:
2441:
2387:
2374:
2348:
2345:
2332:
2313:
2294:
2281:
2212:
2199:
2102:
2089:
2062:
2049:
1951:
1938:
1859:
1846:
1817:
1804:
1755:
1742:
1726:
1713:
1697:
1684:
1645:
1639:
1555:
1534:
1309:
1296:
1261:
1165:
1139:
1129:
1084:
1078:
1066:
1053:to predict values of the form
315:Relevance vector machine (RVM)
1:
8605:Introduction to Boosted Trees
7560:{\displaystyle 4\leq J\leq 8}
6788:are multiplied by some value
4562:Furthermore, we can optimize
4417:Now differentiating w.r.t to
3537:Hence, moving a small amount
2973:{\displaystyle {\hat {F}}(x)}
2657:{\displaystyle {\hat {F}}(x)}
2459:{\displaystyle {\hat {F}}(x)}
1466:{\displaystyle 1\leq m\leq M}
804:Computational learning theory
368:Expectation–maximization (EM)
7909:Stochastic gradient boosting
7639:is unlikely to be required.
7095:{\displaystyle \gamma _{jm}}
4956:{\displaystyle \mathbb {R} }
4453:{\displaystyle h_{m}(x_{i})}
3750:{\displaystyle \gamma >0}
3448:is a base learner function.
2934:and corresponding values of
2626:. It seeks an approximation
2068:{\displaystyle h_{m}(x_{i})}
761:Coefficient of determination
608:Convolutional neural network
320:Support vector machine (SVM)
8074:Penalize complexity of tree
7864:{\displaystyle \nu <0.1}
7122:{\displaystyle \gamma _{m}}
6808:{\displaystyle \gamma _{m}}
6575:can be written as the sum:
6026:{\displaystyle \gamma _{m}}
5418:closest to the gradient of
5166:{\displaystyle \gamma _{m}}
2940:empirical risk minimization
1012:functional gradient descent
912:Outline of machine learning
809:Empirical risk minimization
9082:
8452:Lambers, Jim (2011–2012).
8160:Feature importance ranking
5549:{\displaystyle L(y,F(x)),}
5422:for which the coefficient
3527:{\displaystyle F_{m-1}(x)}
2930:of known sample values of
549:Feedforward neural network
300:Artificial neural networks
16:Machine learning technique
9056:Classification algorithms
8988:10.1016/j.ins.2021.05.055
8935:10.1007/s10115-007-0114-2
8774:Journal of Animal Ecology
8318:Breiman, L. (June 1997).
8103:{\displaystyle \ell _{2}}
7901:both during training and
6418:to pseudo-residuals. Let
6350:{\displaystyle F_{M}(x).}
2938:. In accordance with the
2506:{\displaystyle L(y,F(x))}
1378:the number of samples in
532:Artificial neural network
6564:{\displaystyle h_{m}(x)}
6411:{\displaystyle h_{m}(x)}
5923:{\displaystyle h_{m}(x)}
3009:{\displaystyle F_{0}(x)}
2697:{\displaystyle h_{m}(x)}
2108:{\displaystyle F(x_{i})}
2077:mean squared error (MSE)
1651:{\displaystyle h_{m}(x)}
1315:{\displaystyle F(x_{i})}
967:rather than the typical
841:Journals and conferences
788:Mathematical foundations
698:Temporal difference (TD)
554:Recurrent neural network
474:Conditional random field
397:Dimensionality reduction
145:Dimensionality reduction
107:Quantum machine learning
102:Neuromorphic engineering
62:Self-supervised learning
57:Semi-supervised learning
8580:Ridgeway, Greg (2007).
7651:techniques reduce this
7632:{\displaystyle J>10}
4595:{\displaystyle \gamma }
4575:{\displaystyle \gamma }
3770:{\displaystyle \gamma }
3550:{\displaystyle \gamma }
3485:The idea is to apply a
3404:{\displaystyle m\geq 1}
1990:{\displaystyle F_{m+1}}
1595:). In order to improve
250:Apprenticeship learning
8727:Statistics in Medicine
8553:
8552:{\displaystyle R_{jm}}
8523:
8522:{\displaystyle R_{jm}}
8493:
8492:{\displaystyle b_{jm}}
8216:Decision tree learning
8104:
8044:
8024:
7994:, acting as a kind of
7984:
7964:
7938:
7891:
7890:{\displaystyle \nu =1}
7865:
7832:
7806:
7633:
7607:
7581:
7561:
7526:
7496:
7466:
7439:
7246:
7153:
7152:{\displaystyle b_{jm}}
7123:
7096:
7063:
6969:
6809:
6782:
6781:{\displaystyle b_{jm}}
6758:Then the coefficients
6749:
6748:{\displaystyle R_{jm}}
6719:
6718:{\displaystyle b_{jm}}
6686:
6634:
6565:
6525:
6466:
6439:
6412:
6363:Gradient tree boosting
6351:
6306:
6201:
6103:
6027:
5997:
5924:
5884:
5669:
5636:
5550:
5503:
5408:
5384:
5232:
5167:
5137:
5053:
4957:
4935:
4909:
4757:
4663:
4596:
4576:
4548:
4454:
4409:
4236:
4127:
4088:
4037:
3947:
3893:
3771:
3751:
3723:
3639:
3551:
3528:
3472:
3442:
3405:
3375:
3266:
3124:
3091:
3010:
2974:
2924:
2830:
2786:
2722:
2698:
2658:
2612:
2507:
2460:
2394:
2230:
2176:
2109:
2069:
2018:
1991:
1958:
1897:
1866:
1775:
1652:
1616:
1589:
1565:
1514:
1494:
1467:
1435:
1421:stages. At each stage
1415:
1392:
1372:
1347:
1346:{\displaystyle y_{i}=}
1316:
1280:
1238:
1218:
1198:
1178:
1091:
1047:
799:Bias–variance tradeoff
681:Reinforcement learning
657:Spiking neural network
67:Reinforcement learning
8703:10.1515/geo-2022-0354
8554:
8524:
8494:
8105:
8045:
8025:
7985:
7965:
7939:
7919:bootstrap aggregation
7892:
7866:
7833:
7807:
7634:
7608:
7582:
7562:
7527:
7497:
7467:
7440:
7219:
7154:
7124:
7097:
7064:
6949:
6810:
6783:
6750:
6720:
6687:
6607:
6566:
6526:
6467:
6465:{\displaystyle J_{m}}
6440:
6438:{\displaystyle J_{m}}
6413:
6352:
6307:
6202:
6083:
6028:
5998:
5925:
5885:
5670:
5616:
5556:number of iterations
5551:
5504:
5409:
5385:
5212:
5168:
5138:
5033:
4958:
4936:
4910:
4737:
4643:
4597:
4577:
4549:
4455:
4410:
4216:
4107:
4089:
4038:
3927:
3894:
3772:
3752:
3724:
3619:
3552:
3529:
3473:
3471:{\displaystyle h_{m}}
3443:
3406:
3376:
3246:
3125:
3071:
3011:
2975:
2925:
2831:
2766:
2723:
2699:
2659:
2613:
2508:
2461:
2395:
2231:
2156:
2110:
2070:
2019:
2017:{\displaystyle F_{m}}
1992:
1959:
1898:
1896:{\displaystyle h_{m}}
1867:
1776:
1653:
1617:
1615:{\displaystyle F_{m}}
1590:
1566:
1515:
1495:
1493:{\displaystyle F_{m}}
1468:
1436:
1416:
1393:
1373:
1348:
1317:
1281:
1239:
1219:
1199:
1179:
1092:
1048:
1019:Informal introduction
635:Neural radiance field
457:Structured prediction
180:Structured prediction
52:Unsupervised learning
8976:Information Sciences
8768:Elith, Jane (2008).
8533:
8503:
8473:
8327:Technical Report 486
8087:
8034:
8002:
7974:
7948:
7928:
7875:
7849:
7831:{\displaystyle \nu }
7822:
7692:
7617:
7591:
7571:
7539:
7510:
7480:
7456:
7166:
7133:
7106:
7076:
6822:
6792:
6762:
6729:
6699:
6582:
6539:
6476:
6449:
6422:
6386:
6322:
6217:
6039:
6010:
5934:
5898:
5700:
5573:
5513:
5440:
5436:Input: training set
5394:
5177:
5150:
4970:
4945:
4921:
4608:
4586:
4566:
4464:
4421:
4098:
4049:
3918:
3781:
3777:, this implies that
3761:
3735:
3563:
3541:
3496:
3455:
3415:
3389:
3136:
3027:
2984:
2946:
2844:
2739:
2708:
2672:
2630:
2520:
2473:
2432:
2243:
2122:
2083:
2036:
2001:
1968:
1912:
1880:
1791:
1665:
1626:
1599:
1579:
1524:
1504:
1477:
1445:
1425:
1405:
1382:
1359:
1327:
1290:
1286:the predicted value
1251:
1228:
1208:
1188:
1104:
1057:
1037:
824:Statistical learning
722:Learning with humans
514:Local outlier factor
8786:2008JAnEc..77..802E
8694:2022OGeo...14..354M
7963:{\displaystyle f=1}
7606:{\displaystyle J=2}
7525:{\displaystyle J=3}
7495:{\displaystyle J=2}
6006:Compute multiplier
5992:
5495:
2418:supervised learning
959:technique based on
667:Electrochemical RAM
574:reservoir computing
305:Logistic regression
224:Supervised learning
210:Multimodal learning
185:Feature engineering
130:Generative modeling
92:Rule-based learning
87:Curriculum learning
47:Supervised learning
22:Part of a series on
8641:2012-03-01 at the
8622:2010-08-07 at the
8549:
8519:
8489:
8100:
8040:
8020:
7980:
7960:
7934:
7899:computational time
7887:
7861:
7828:
7802:
7629:
7603:
7577:
7557:
7522:
7492:
7462:
7435:
7371:
7337:
7149:
7119:
7092:
7059:
6947:
6805:
6778:
6745:
6715:
6682:
6561:
6533:indicator notation
6521:
6462:
6435:
6408:
6347:
6302:
6211:Update the model:
6197:
6081:
6023:
5993:
5972:
5920:
5880:
5854:
5690:Compute so-called
5665:
5614:
5546:
5499:
5475:
5404:
5380:
5209:
5163:
5133:
4953:
4931:
4905:
4734:
4640:
4592:
4572:
4544:
4450:
4405:
4094:up to first order
4084:
4033:
3889:
3767:
3747:
3719:
3547:
3524:
3468:
3438:
3401:
3371:
3239:
3120:
3068:
3006:
2970:
2920:
2826:
2824:
2728:, called base (or
2718:
2694:
2654:
2608:
2554:
2503:
2456:
2390:
2226:
2105:
2065:
2014:
1987:
1954:
1893:
1862:
1784:or, equivalently,
1771:
1648:
1612:
1585:
1561:
1510:
1490:
1463:
1431:
1411:
1388:
1371:{\displaystyle n=}
1368:
1353:the observed value
1343:
1312:
1276:
1234:
1214:
1194:
1174:
1128:
1117:
1099:mean squared error
1097:by minimizing the
1087:
1043:
1008:Jerome H. Friedman
235: •
150:Density estimation
9066:Ensemble learning
9016:978-1-138-49568-5
8982:(2021): 522–542.
8320:"Arcing The Edge"
8261:978-0-387-84857-0
8043:{\displaystyle f}
7983:{\displaystyle f}
7937:{\displaystyle f}
7580:{\displaystyle J}
7465:{\displaystyle J}
7339:
7312:
6922:
6472:disjoint regions
6056:
5853:
5799:
5599:
5194:
4719:
4625:
4559:
4558:
3195:
3053:
2958:
2823:
2751:
2642:
2539:
2532:
2444:
2362:
2311:
2298:
2154:
1588:{\displaystyle y}
1558:
1537:
1513:{\displaystyle m}
1434:{\displaystyle m}
1414:{\displaystyle M}
1391:{\displaystyle y}
1264:
1237:{\displaystyle y}
1217:{\displaystyle n}
1197:{\displaystyle i}
1142:
1119:
1116:
1069:
1046:{\displaystyle F}
953:Gradient boosting
950:
949:
755:Model diagnostics
738:Human-in-the-loop
581:Boltzmann machine
494:Anomaly detection
290:Linear regression
205:Ontology learning
200:Grammar induction
175:Semantic analysis
170:Association rules
155:Anomaly detection
97:Neuro-symbolic AI
9073:
9020:
8992:
8991:
8971:
8965:
8964:
8946:
8917:
8911:
8910:
8870:
8859:
8858:
8851:
8845:
8844:
8842:
8840:
8834:
8828:. Archived from
8823:
8814:
8808:
8807:
8797:
8765:
8759:
8758:
8739:10.1002/sim.1501
8733:(9): 1365–1381.
8722:
8716:
8715:
8705:
8682:Open Geosciences
8673:
8667:
8666:
8664:
8652:
8646:
8633:
8627:
8613:
8607:
8601:
8595:
8590:
8584:
8578:
8569:
8566:
8560:
8558:
8556:
8555:
8550:
8548:
8547:
8528:
8526:
8525:
8520:
8518:
8517:
8498:
8496:
8495:
8490:
8488:
8487:
8467:
8461:
8460:
8458:
8449:
8443:
8442:
8440:
8431:
8425:
8424:
8422:
8416:. Archived from
8415:
8406:
8397:
8396:
8386:
8377:
8368:
8367:
8365:
8364:
8358:
8352:. Archived from
8351:
8342:
8331:
8330:
8324:
8315:
8309:
8308:
8306:
8305:
8299:
8293:. Archived from
8292:
8283:
8270:
8269:
8264:. Archived from
8243:
8179:interpretability
8124:learning to rank
8109:
8107:
8106:
8101:
8099:
8098:
8055:out-of-bag error
8049:
8047:
8046:
8041:
8029:
8027:
8026:
8021:
7989:
7987:
7986:
7981:
7969:
7967:
7966:
7961:
7943:
7941:
7940:
7935:
7896:
7894:
7893:
7888:
7870:
7868:
7867:
7862:
7837:
7835:
7834:
7829:
7811:
7809:
7808:
7803:
7770:
7769:
7760:
7759:
7732:
7731:
7704:
7703:
7638:
7636:
7635:
7630:
7612:
7610:
7609:
7604:
7586:
7584:
7583:
7578:
7566:
7564:
7563:
7558:
7531:
7529:
7528:
7523:
7501:
7499:
7498:
7493:
7471:
7469:
7468:
7463:
7444:
7442:
7441:
7436:
7419:
7418:
7406:
7405:
7387:
7386:
7370:
7369:
7368:
7353:
7352:
7338:
7333:
7307:
7306:
7281:
7280:
7279:
7278:
7265:
7259:
7258:
7245:
7244:
7243:
7233:
7206:
7205:
7178:
7177:
7158:
7156:
7155:
7150:
7148:
7147:
7128:
7126:
7125:
7120:
7118:
7117:
7101:
7099:
7098:
7093:
7091:
7090:
7068:
7066:
7065:
7060:
7049:
7048:
7036:
7035:
7017:
7016:
7004:
7003:
6985:
6984:
6968:
6963:
6948:
6943:
6917:
6916:
6894:
6893:
6884:
6883:
6862:
6861:
6834:
6833:
6814:
6812:
6811:
6806:
6804:
6803:
6787:
6785:
6784:
6779:
6777:
6776:
6754:
6752:
6751:
6746:
6744:
6743:
6724:
6722:
6721:
6716:
6714:
6713:
6691:
6689:
6688:
6683:
6669:
6668:
6667:
6666:
6653:
6647:
6646:
6633:
6632:
6631:
6621:
6594:
6593:
6570:
6568:
6567:
6562:
6551:
6550:
6535:, the output of
6530:
6528:
6527:
6522:
6520:
6519:
6515:
6514:
6491:
6490:
6471:
6469:
6468:
6463:
6461:
6460:
6444:
6442:
6441:
6436:
6434:
6433:
6417:
6415:
6414:
6409:
6398:
6397:
6356:
6354:
6353:
6348:
6334:
6333:
6311:
6309:
6308:
6303:
6289:
6288:
6279:
6278:
6257:
6256:
6229:
6228:
6206:
6204:
6203:
6198:
6193:
6189:
6185:
6184:
6172:
6171:
6153:
6152:
6140:
6139:
6121:
6120:
6102:
6097:
6082:
6077:
6051:
6050:
6032:
6030:
6029:
6024:
6022:
6021:
6002:
6000:
5999:
5994:
5991:
5986:
5968:
5967:
5952:
5951:
5929:
5927:
5926:
5921:
5910:
5909:
5889:
5887:
5886:
5881:
5855:
5851:
5847:
5846:
5836:
5835:
5804:
5800:
5798:
5794:
5793:
5774:
5767:
5766:
5748:
5747:
5728:
5715:
5714:
5692:pseudo-residuals
5686:
5682:
5674:
5672:
5671:
5666:
5652:
5651:
5635:
5630:
5615:
5610:
5585:
5584:
5559:
5555:
5553:
5552:
5547:
5508:
5506:
5505:
5500:
5494:
5489:
5471:
5470:
5458:
5457:
5425:
5421:
5417:
5413:
5411:
5410:
5405:
5403:
5402:
5389:
5387:
5386:
5381:
5376:
5375:
5374:
5370:
5363:
5362:
5350:
5349:
5331:
5330:
5315:
5314:
5313:
5312:
5283:
5282:
5270:
5269:
5251:
5250:
5231:
5226:
5210:
5205:
5189:
5188:
5172:
5170:
5169:
5164:
5162:
5161:
5142:
5140:
5139:
5134:
5132:
5125:
5124:
5112:
5111:
5093:
5092:
5077:
5076:
5075:
5074:
5052:
5047:
5032:
5031:
5010:
5009:
4982:
4981:
4962:
4960:
4959:
4954:
4952:
4940:
4938:
4937:
4932:
4930:
4929:
4914:
4912:
4911:
4906:
4901:
4900:
4899:
4895:
4888:
4887:
4875:
4874:
4856:
4855:
4840:
4839:
4838:
4837:
4808:
4807:
4795:
4794:
4776:
4775:
4756:
4751:
4735:
4730:
4714:
4713:
4706:
4705:
4693:
4692:
4680:
4679:
4662:
4657:
4641:
4636:
4620:
4619:
4601:
4599:
4598:
4593:
4581:
4579:
4578:
4573:
4553:
4551:
4550:
4545:
4537:
4536:
4524:
4523:
4505:
4504:
4489:
4488:
4487:
4486:
4459:
4457:
4456:
4451:
4446:
4445:
4433:
4432:
4414:
4412:
4411:
4406:
4398:
4391:
4390:
4378:
4377:
4359:
4358:
4343:
4342:
4341:
4340:
4317:
4316:
4304:
4303:
4285:
4284:
4272:
4271:
4253:
4252:
4235:
4230:
4212:
4205:
4204:
4192:
4191:
4176:
4175:
4163:
4162:
4144:
4143:
4126:
4121:
4093:
4091:
4090:
4085:
4080:
4079:
4067:
4066:
4042:
4040:
4039:
4034:
4032:
4025:
4024:
4012:
4011:
3996:
3995:
3983:
3982:
3964:
3963:
3946:
3941:
3903:
3898:
3896:
3895:
3890:
3882:
3881:
3869:
3868:
3850:
3849:
3825:
3824:
3812:
3811:
3799:
3798:
3776:
3774:
3773:
3768:
3756:
3754:
3753:
3748:
3728:
3726:
3725:
3720:
3718:
3711:
3710:
3698:
3697:
3679:
3678:
3663:
3662:
3661:
3660:
3638:
3633:
3603:
3602:
3575:
3574:
3556:
3554:
3553:
3548:
3533:
3531:
3530:
3525:
3514:
3513:
3487:steepest descent
3481:
3477:
3475:
3474:
3469:
3467:
3466:
3447:
3445:
3444:
3439:
3437:
3436:
3427:
3426:
3410:
3408:
3407:
3402:
3380:
3378:
3377:
3372:
3361:
3357:
3356:
3352:
3351:
3344:
3343:
3331:
3330:
3315:
3314:
3302:
3301:
3283:
3282:
3265:
3260:
3240:
3238:
3237:
3236:
3227:
3226:
3216:
3176:
3175:
3148:
3147:
3129:
3127:
3126:
3121:
3119:
3118:
3108:
3107:
3090:
3085:
3069:
3064:
3039:
3038:
3015:
3013:
3012:
3007:
2996:
2995:
2979:
2977:
2976:
2971:
2960:
2959:
2951:
2937:
2933:
2929:
2927:
2926:
2921:
2913:
2912:
2900:
2899:
2875:
2874:
2862:
2861:
2835:
2833:
2832:
2827:
2825:
2821:
2806:
2805:
2796:
2795:
2785:
2780:
2753:
2752:
2744:
2727:
2725:
2724:
2719:
2717:
2716:
2704:from some class
2703:
2701:
2700:
2695:
2684:
2683:
2667:
2663:
2661:
2660:
2655:
2644:
2643:
2635:
2625:
2617:
2615:
2614:
2609:
2574:
2573:
2562:
2555:
2550:
2534:
2533:
2525:
2512:
2510:
2509:
2504:
2465:
2463:
2462:
2457:
2446:
2445:
2437:
2427:
2423:
2406:gradient descent
2399:
2397:
2396:
2391:
2386:
2385:
2373:
2372:
2363:
2355:
2344:
2343:
2325:
2324:
2312:
2304:
2299:
2297:
2293:
2292:
2273:
2272:
2271:
2270:
2250:
2235:
2233:
2232:
2227:
2225:
2224:
2219:
2215:
2211:
2210:
2192:
2191:
2175:
2170:
2155:
2147:
2142:
2141:
2140:
2114:
2112:
2111:
2106:
2101:
2100:
2074:
2072:
2071:
2066:
2061:
2060:
2048:
2047:
2023:
2021:
2020:
2015:
2013:
2012:
1996:
1994:
1993:
1988:
1986:
1985:
1963:
1961:
1960:
1955:
1950:
1949:
1937:
1936:
1924:
1923:
1902:
1900:
1899:
1894:
1892:
1891:
1871:
1869:
1868:
1863:
1858:
1857:
1845:
1844:
1832:
1831:
1816:
1815:
1803:
1802:
1780:
1778:
1777:
1772:
1770:
1769:
1754:
1753:
1741:
1740:
1725:
1724:
1712:
1711:
1696:
1695:
1683:
1682:
1657:
1655:
1654:
1649:
1638:
1637:
1621:
1619:
1618:
1613:
1611:
1610:
1594:
1592:
1591:
1586:
1570:
1568:
1567:
1562:
1560:
1559:
1551:
1545:
1544:
1539:
1538:
1530:
1519:
1517:
1516:
1511:
1499:
1497:
1496:
1491:
1489:
1488:
1472:
1470:
1469:
1464:
1440:
1438:
1437:
1432:
1420:
1418:
1417:
1412:
1397:
1395:
1394:
1389:
1377:
1375:
1374:
1369:
1352:
1350:
1349:
1344:
1339:
1338:
1321:
1319:
1318:
1313:
1308:
1307:
1285:
1283:
1282:
1277:
1272:
1271:
1266:
1265:
1257:
1243:
1241:
1240:
1235:
1223:
1221:
1220:
1215:
1203:
1201:
1200:
1195:
1183:
1181:
1180:
1175:
1173:
1172:
1163:
1162:
1150:
1149:
1144:
1143:
1135:
1127:
1118:
1109:
1096:
1094:
1093:
1088:
1071:
1070:
1062:
1052:
1050:
1049:
1044:
965:pseudo-residuals
957:machine learning
942:
935:
928:
889:Related articles
766:Confusion matrix
519:Isolation forest
464:Graphical models
243:
242:
195:Learning to rank
190:Feature learning
28:Machine learning
19:
9081:
9080:
9076:
9075:
9074:
9072:
9071:
9070:
9046:
9045:
9027:
9017:
9004:
9001:
8999:Further reading
8996:
8995:
8973:
8972:
8968:
8919:
8918:
8914:
8885:(1): 04019036.
8872:
8871:
8862:
8853:
8852:
8848:
8838:
8836:
8835:on 25 July 2020
8832:
8821:
8816:
8815:
8811:
8767:
8766:
8762:
8724:
8723:
8719:
8675:
8674:
8670:
8654:
8653:
8649:
8643:Wayback Machine
8634:
8630:
8624:Wayback Machine
8614:
8610:
8602:
8598:
8591:
8587:
8579:
8572:
8567:
8563:
8536:
8531:
8530:
8506:
8501:
8500:
8499:for the region
8476:
8471:
8470:
8468:
8464:
8456:
8451:
8450:
8446:
8438:
8433:
8432:
8428:
8420:
8413:
8408:
8407:
8400:
8384:
8379:
8378:
8371:
8362:
8360:
8356:
8349:
8344:
8343:
8334:
8322:
8317:
8316:
8312:
8303:
8301:
8297:
8290:
8285:
8284:
8273:
8262:
8245:
8244:
8229:
8224:
8187:
8175:
8162:
8145:
8120:
8090:
8085:
8084:
8076:
8064:
8032:
8031:
8000:
7999:
7972:
7971:
7946:
7945:
7926:
7925:
7911:
7873:
7872:
7847:
7846:
7820:
7819:
7761:
7751:
7717:
7695:
7690:
7689:
7683:
7645:
7615:
7614:
7589:
7588:
7587:in this range,
7569:
7568:
7537:
7536:
7508:
7507:
7504:decision stumps
7478:
7477:
7454:
7453:
7451:
7410:
7391:
7378:
7357:
7344:
7295:
7267:
7260:
7247:
7235:
7191:
7169:
7164:
7163:
7136:
7131:
7130:
7109:
7104:
7103:
7079:
7074:
7073:
7040:
7027:
7008:
6989:
6976:
6908:
6885:
6875:
6847:
6825:
6820:
6819:
6795:
6790:
6789:
6765:
6760:
6759:
6732:
6727:
6726:
6702:
6697:
6696:
6655:
6648:
6635:
6623:
6585:
6580:
6579:
6542:
6537:
6536:
6506:
6501:
6479:
6474:
6473:
6452:
6447:
6446:
6425:
6420:
6419:
6389:
6384:
6383:
6365:
6360:
6359:
6325:
6320:
6319:
6280:
6270:
6242:
6220:
6215:
6214:
6176:
6163:
6144:
6125:
6112:
6111:
6107:
6042:
6037:
6036:
6013:
6008:
6007:
5956:
5943:
5932:
5931:
5901:
5896:
5895:
5821:
5785:
5775:
5758:
5739:
5729:
5723:
5722:
5703:
5698:
5697:
5684:
5680:
5643:
5600:
5576:
5571:
5570:
5557:
5511:
5510:
5462:
5449:
5438:
5437:
5423:
5419:
5415:
5392:
5391:
5354:
5335:
5322:
5298:
5293:
5274:
5255:
5242:
5241:
5237:
5195:
5180:
5175:
5174:
5153:
5148:
5147:
5116:
5097:
5084:
5060:
5055:
5023:
4995:
4973:
4968:
4967:
4943:
4942:
4919:
4918:
4879:
4860:
4847:
4823:
4818:
4799:
4780:
4767:
4766:
4762:
4720:
4697:
4684:
4671:
4626:
4611:
4606:
4605:
4584:
4583:
4582:by finding the
4564:
4563:
4560:
4528:
4509:
4496:
4472:
4467:
4462:
4461:
4437:
4424:
4419:
4418:
4382:
4363:
4350:
4326:
4321:
4308:
4295:
4276:
4257:
4244:
4196:
4183:
4167:
4148:
4135:
4096:
4095:
4071:
4052:
4047:
4046:
4016:
4003:
3987:
3968:
3955:
3916:
3915:
3908:
3873:
3854:
3841:
3816:
3803:
3790:
3779:
3778:
3759:
3758:
3733:
3732:
3702:
3683:
3670:
3646:
3641:
3588:
3566:
3561:
3560:
3539:
3538:
3499:
3494:
3493:
3479:
3458:
3453:
3452:
3418:
3413:
3412:
3387:
3386:
3335:
3322:
3306:
3287:
3274:
3241:
3218:
3217:
3193:
3189:
3161:
3139:
3134:
3133:
3099:
3054:
3030:
3025:
3024:
2987:
2982:
2981:
2944:
2943:
2935:
2931:
2904:
2891:
2866:
2853:
2842:
2841:
2797:
2787:
2737:
2736:
2706:
2705:
2675:
2670:
2669:
2665:
2628:
2627:
2623:
2557:
2540:
2518:
2517:
2471:
2470:
2430:
2429:
2425:
2421:
2414:
2377:
2364:
2335:
2316:
2284:
2274:
2255:
2251:
2241:
2240:
2202:
2183:
2182:
2178:
2177:
2125:
2120:
2119:
2092:
2081:
2080:
2052:
2039:
2034:
2033:
2004:
1999:
1998:
1971:
1966:
1965:
1941:
1928:
1915:
1910:
1909:
1883:
1878:
1877:
1849:
1836:
1823:
1807:
1794:
1789:
1788:
1761:
1745:
1732:
1716:
1703:
1687:
1668:
1663:
1662:
1629:
1624:
1623:
1602:
1597:
1596:
1577:
1576:
1575:is the mean of
1527:
1522:
1521:
1502:
1501:
1480:
1475:
1474:
1443:
1442:
1423:
1422:
1403:
1402:
1380:
1379:
1357:
1356:
1330:
1325:
1324:
1299:
1288:
1287:
1254:
1249:
1248:
1226:
1225:
1206:
1205:
1186:
1185:
1164:
1154:
1132:
1102:
1101:
1055:
1054:
1035:
1034:
1021:
1000:
946:
917:
916:
890:
882:
881:
842:
834:
833:
794:Kernel machines
789:
781:
780:
756:
748:
747:
728:Active learning
723:
715:
714:
683:
673:
672:
598:Diffusion model
534:
524:
523:
496:
486:
485:
459:
449:
448:
404:Factor analysis
399:
389:
388:
372:
335:
325:
324:
245:
244:
228:
227:
226:
215:
214:
120:
112:
111:
77:Online learning
42:
30:
17:
12:
11:
5:
9079:
9077:
9069:
9068:
9063:
9061:Decision trees
9058:
9048:
9047:
9044:
9043:
9038:
9033:
9026:
9025:External links
9023:
9022:
9021:
9015:
9000:
8997:
8994:
8993:
8966:
8912:
8860:
8846:
8809:
8780:(4): 802–813.
8760:
8717:
8688:(1): 629–645.
8668:
8647:
8628:
8608:
8596:
8585:
8570:
8561:
8546:
8543:
8539:
8516:
8513:
8509:
8486:
8483:
8479:
8462:
8444:
8426:
8423:on 2018-12-22.
8398:
8369:
8332:
8310:
8271:
8268:on 2009-11-10.
8260:
8226:
8225:
8223:
8220:
8219:
8218:
8213:
8208:
8203:
8198:
8193:
8186:
8183:
8174:
8171:
8167:decision trees
8161:
8158:
8144:
8141:
8119:
8116:
8097:
8093:
8075:
8072:
8063:
8060:
8039:
8019:
8016:
8013:
8010:
8007:
7996:regularization
7979:
7959:
7956:
7953:
7933:
7910:
7907:
7886:
7883:
7880:
7860:
7857:
7854:
7843:learning rates
7827:
7813:
7812:
7801:
7798:
7795:
7792:
7789:
7786:
7782:
7779:
7776:
7773:
7768:
7764:
7758:
7754:
7750:
7747:
7744:
7741:
7738:
7735:
7730:
7727:
7724:
7720:
7716:
7713:
7710:
7707:
7702:
7698:
7682:
7679:
7649:regularization
7644:
7643:Regularization
7641:
7628:
7625:
7622:
7602:
7599:
7596:
7576:
7556:
7553:
7550:
7547:
7544:
7521:
7518:
7515:
7491:
7488:
7485:
7461:
7450:
7447:
7446:
7445:
7434:
7431:
7428:
7425:
7422:
7417:
7413:
7409:
7404:
7401:
7398:
7394:
7390:
7385:
7381:
7377:
7374:
7367:
7364:
7360:
7356:
7351:
7347:
7342:
7336:
7332:
7329:
7326:
7322:
7319:
7316:
7310:
7305:
7302:
7298:
7293:
7290:
7287:
7284:
7277:
7274:
7270:
7264:
7257:
7254:
7250:
7242:
7238:
7232:
7229:
7226:
7222:
7218:
7215:
7212:
7209:
7204:
7201:
7198:
7194:
7190:
7187:
7184:
7181:
7176:
7172:
7146:
7143:
7139:
7116:
7112:
7089:
7086:
7082:
7070:
7069:
7058:
7055:
7052:
7047:
7043:
7039:
7034:
7030:
7026:
7023:
7020:
7015:
7011:
7007:
7002:
6999:
6996:
6992:
6988:
6983:
6979:
6975:
6972:
6967:
6962:
6959:
6956:
6952:
6946:
6942:
6939:
6936:
6932:
6929:
6926:
6920:
6915:
6911:
6906:
6903:
6900:
6897:
6892:
6888:
6882:
6878:
6874:
6871:
6868:
6865:
6860:
6857:
6854:
6850:
6846:
6843:
6840:
6837:
6832:
6828:
6802:
6798:
6775:
6772:
6768:
6742:
6739:
6735:
6712:
6709:
6705:
6693:
6692:
6681:
6678:
6675:
6672:
6665:
6662:
6658:
6652:
6645:
6642:
6638:
6630:
6626:
6620:
6617:
6614:
6610:
6606:
6603:
6600:
6597:
6592:
6588:
6560:
6557:
6554:
6549:
6545:
6518:
6513:
6509:
6504:
6500:
6497:
6494:
6489:
6486:
6482:
6459:
6455:
6432:
6428:
6407:
6404:
6401:
6396:
6392:
6369:decision trees
6364:
6361:
6358:
6357:
6346:
6343:
6340:
6337:
6332:
6328:
6316:
6315:
6314:
6313:
6312:
6301:
6298:
6295:
6292:
6287:
6283:
6277:
6273:
6269:
6266:
6263:
6260:
6255:
6252:
6249:
6245:
6241:
6238:
6235:
6232:
6227:
6223:
6209:
6208:
6207:
6196:
6192:
6188:
6183:
6179:
6175:
6170:
6166:
6162:
6159:
6156:
6151:
6147:
6143:
6138:
6135:
6132:
6128:
6124:
6119:
6115:
6110:
6106:
6101:
6096:
6093:
6090:
6086:
6080:
6076:
6073:
6070:
6066:
6063:
6060:
6054:
6049:
6045:
6020:
6016:
6004:
5990:
5985:
5982:
5979:
5975:
5971:
5966:
5963:
5959:
5955:
5950:
5946:
5942:
5939:
5919:
5916:
5913:
5908:
5904:
5892:
5891:
5890:
5879:
5876:
5873:
5870:
5867:
5864:
5861:
5858:
5845:
5842:
5839:
5834:
5831:
5828:
5824:
5820:
5817:
5814:
5811:
5808:
5803:
5797:
5792:
5788:
5784:
5781:
5778:
5773:
5770:
5765:
5761:
5757:
5754:
5751:
5746:
5742:
5738:
5735:
5732:
5726:
5721:
5718:
5713:
5710:
5706:
5677:
5676:
5675:
5664:
5661:
5658:
5655:
5650:
5646:
5642:
5639:
5634:
5629:
5626:
5623:
5619:
5613:
5609:
5606:
5603:
5597:
5594:
5591:
5588:
5583:
5579:
5545:
5542:
5539:
5536:
5533:
5530:
5527:
5524:
5521:
5518:
5498:
5493:
5488:
5485:
5482:
5478:
5474:
5469:
5465:
5461:
5456:
5452:
5448:
5445:
5434:
5433:
5401:
5379:
5373:
5369:
5366:
5361:
5357:
5353:
5348:
5345:
5342:
5338:
5334:
5329:
5325:
5321:
5318:
5311:
5308:
5305:
5301:
5296:
5292:
5289:
5286:
5281:
5277:
5273:
5268:
5265:
5262:
5258:
5254:
5249:
5245:
5240:
5236:
5230:
5225:
5222:
5219:
5215:
5208:
5204:
5201:
5198:
5192:
5187:
5183:
5160:
5156:
5144:
5143:
5131:
5128:
5123:
5119:
5115:
5110:
5107:
5104:
5100:
5096:
5091:
5087:
5083:
5080:
5073:
5070:
5067:
5063:
5058:
5051:
5046:
5043:
5040:
5036:
5030:
5026:
5022:
5019:
5016:
5013:
5008:
5005:
5002:
4998:
4994:
4991:
4988:
4985:
4980:
4976:
4951:
4928:
4904:
4898:
4894:
4891:
4886:
4882:
4878:
4873:
4870:
4867:
4863:
4859:
4854:
4850:
4846:
4843:
4836:
4833:
4830:
4826:
4821:
4817:
4814:
4811:
4806:
4802:
4798:
4793:
4790:
4787:
4783:
4779:
4774:
4770:
4765:
4761:
4755:
4750:
4747:
4744:
4740:
4733:
4729:
4726:
4723:
4717:
4712:
4709:
4704:
4700:
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4691:
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4683:
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4527:
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4508:
4503:
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4495:
4492:
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4427:
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4401:
4397:
4394:
4389:
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4376:
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4370:
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4362:
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4349:
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4339:
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4333:
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4324:
4320:
4315:
4311:
4307:
4302:
4298:
4294:
4291:
4288:
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4279:
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4267:
4264:
4260:
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4240:
4234:
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4120:
4117:
4114:
4110:
4106:
4103:
4083:
4078:
4074:
4070:
4065:
4062:
4059:
4055:
4031:
4028:
4023:
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4015:
4010:
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3994:
3990:
3986:
3981:
3978:
3975:
3971:
3967:
3962:
3958:
3954:
3951:
3945:
3940:
3937:
3934:
3930:
3926:
3923:
3910:
3909:
3906:
3901:
3888:
3885:
3880:
3876:
3872:
3867:
3864:
3861:
3857:
3853:
3848:
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3840:
3837:
3834:
3831:
3828:
3823:
3819:
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3806:
3802:
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3793:
3789:
3786:
3766:
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3709:
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3626:
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3618:
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3609:
3606:
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3509:
3506:
3502:
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3425:
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3383:
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3370:
3367:
3364:
3360:
3355:
3350:
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3338:
3334:
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3325:
3321:
3318:
3313:
3309:
3305:
3300:
3297:
3294:
3290:
3286:
3281:
3277:
3273:
3270:
3264:
3259:
3256:
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3249:
3244:
3235:
3230:
3225:
3221:
3215:
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3205:
3202:
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3192:
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3182:
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3106:
3102:
3098:
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3089:
3084:
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3078:
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3033:
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2809:
2804:
2800:
2794:
2790:
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2376:
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2128:
2104:
2099:
2095:
2091:
2088:
2064:
2059:
2055:
2051:
2046:
2042:
2026:loss functions
2011:
2007:
1984:
1981:
1978:
1974:
1953:
1948:
1944:
1940:
1935:
1931:
1927:
1922:
1918:
1890:
1886:
1874:
1873:
1861:
1856:
1852:
1848:
1843:
1839:
1835:
1830:
1826:
1822:
1819:
1814:
1810:
1806:
1801:
1797:
1782:
1781:
1768:
1764:
1760:
1757:
1752:
1748:
1744:
1739:
1735:
1731:
1728:
1723:
1719:
1715:
1710:
1706:
1702:
1699:
1694:
1690:
1686:
1681:
1678:
1675:
1671:
1647:
1644:
1641:
1636:
1632:
1609:
1605:
1584:
1557:
1554:
1548:
1543:
1536:
1533:
1509:
1487:
1483:
1462:
1459:
1456:
1453:
1450:
1430:
1410:
1399:
1398:
1387:
1367:
1364:
1354:
1342:
1337:
1333:
1322:
1311:
1306:
1302:
1298:
1295:
1275:
1270:
1263:
1260:
1233:
1213:
1193:
1171:
1167:
1161:
1157:
1153:
1148:
1141:
1138:
1131:
1126:
1122:
1115:
1112:
1086:
1083:
1080:
1077:
1074:
1068:
1065:
1042:
1020:
1017:
999:
996:
989:differentiable
977:decision trees
948:
947:
945:
944:
937:
930:
922:
919:
918:
915:
914:
909:
908:
907:
897:
891:
888:
887:
884:
883:
880:
879:
874:
869:
864:
859:
854:
849:
843:
840:
839:
836:
835:
832:
831:
826:
821:
816:
814:Occam learning
811:
806:
801:
796:
790:
787:
786:
783:
782:
779:
778:
773:
771:Learning curve
768:
763:
757:
754:
753:
750:
749:
746:
745:
740:
735:
730:
724:
721:
720:
717:
716:
713:
712:
711:
710:
700:
695:
690:
684:
679:
678:
675:
674:
671:
670:
664:
659:
654:
649:
648:
647:
637:
632:
631:
630:
625:
620:
615:
605:
600:
595:
590:
589:
588:
578:
577:
576:
571:
566:
561:
551:
546:
541:
535:
530:
529:
526:
525:
522:
521:
516:
511:
503:
497:
492:
491:
488:
487:
484:
483:
482:
481:
476:
471:
460:
455:
454:
451:
450:
447:
446:
441:
436:
431:
426:
421:
416:
411:
406:
400:
395:
394:
391:
390:
387:
386:
381:
376:
370:
365:
360:
352:
347:
342:
336:
331:
330:
327:
326:
323:
322:
317:
312:
307:
302:
297:
292:
287:
279:
278:
277:
272:
267:
257:
255:Decision trees
252:
246:
232:classification
222:
221:
220:
217:
216:
213:
212:
207:
202:
197:
192:
187:
182:
177:
172:
167:
162:
157:
152:
147:
142:
137:
132:
127:
125:Classification
121:
118:
117:
114:
113:
110:
109:
104:
99:
94:
89:
84:
82:Batch learning
79:
74:
69:
64:
59:
54:
49:
43:
40:
39:
36:
35:
24:
23:
15:
13:
10:
9:
6:
4:
3:
2:
9078:
9067:
9064:
9062:
9059:
9057:
9054:
9053:
9051:
9042:
9039:
9037:
9034:
9032:
9029:
9028:
9024:
9018:
9012:
9008:
9003:
9002:
8998:
8989:
8985:
8981:
8977:
8970:
8967:
8962:
8958:
8954:
8950:
8945:
8940:
8936:
8932:
8928:
8924:
8916:
8913:
8908:
8904:
8900:
8896:
8892:
8888:
8884:
8880:
8876:
8869:
8867:
8865:
8861:
8856:
8850:
8847:
8831:
8827:
8820:
8817:Elith, Jane.
8813:
8810:
8805:
8801:
8796:
8791:
8787:
8783:
8779:
8775:
8771:
8764:
8761:
8756:
8752:
8748:
8744:
8740:
8736:
8732:
8728:
8721:
8718:
8713:
8709:
8704:
8699:
8695:
8691:
8687:
8683:
8679:
8672:
8669:
8663:
8658:
8651:
8648:
8644:
8640:
8637:
8632:
8629:
8625:
8621:
8618:
8612:
8609:
8606:
8603:Tianqi Chen.
8600:
8597:
8594:
8589:
8586:
8583:
8577:
8575:
8571:
8565:
8562:
8544:
8541:
8537:
8514:
8511:
8507:
8484:
8481:
8477:
8466:
8463:
8455:
8448:
8445:
8437:
8430:
8427:
8419:
8412:
8405:
8403:
8399:
8394:
8390:
8383:
8376:
8374:
8370:
8359:on 2019-11-01
8355:
8348:
8341:
8339:
8337:
8333:
8328:
8321:
8314:
8311:
8300:on 2014-08-01
8296:
8289:
8282:
8280:
8278:
8276:
8272:
8267:
8263:
8257:
8253:
8249:
8242:
8240:
8238:
8236:
8234:
8232:
8228:
8221:
8217:
8214:
8212:
8209:
8207:
8204:
8202:
8199:
8197:
8196:Random forest
8194:
8192:
8189:
8188:
8184:
8182:
8180:
8173:Disadvantages
8172:
8170:
8168:
8159:
8157:
8154:
8149:
8142:
8140:
8138:
8133:
8129:
8125:
8117:
8115:
8113:
8095:
8091:
8081:
8073:
8071:
8068:
8061:
8059:
8056:
8051:
8037:
8017:
8014:
8011:
8008:
8005:
7997:
7993:
7977:
7957:
7954:
7951:
7931:
7922:
7920:
7916:
7908:
7906:
7904:
7900:
7884:
7881:
7878:
7858:
7855:
7852:
7844:
7839:
7825:
7818:
7799:
7796:
7793:
7790:
7787:
7784:
7780:
7774:
7766:
7762:
7756:
7752:
7748:
7745:
7742:
7736:
7728:
7725:
7722:
7718:
7714:
7708:
7700:
7696:
7688:
7687:
7686:
7680:
7678:
7675:
7673:
7669:
7665:
7661:
7656:
7654:
7650:
7642:
7640:
7626:
7623:
7620:
7600:
7597:
7594:
7574:
7554:
7551:
7548:
7545:
7542:
7533:
7519:
7516:
7513:
7505:
7489:
7486:
7483:
7475:
7459:
7449:Size of trees
7448:
7432:
7426:
7423:
7415:
7411:
7402:
7399:
7396:
7392:
7388:
7383:
7379:
7372:
7365:
7362:
7358:
7354:
7349:
7345:
7340:
7334:
7308:
7303:
7300:
7296:
7291:
7285:
7275:
7272:
7268:
7255:
7252:
7248:
7240:
7236:
7230:
7227:
7224:
7220:
7216:
7210:
7202:
7199:
7196:
7192:
7188:
7182:
7174:
7170:
7162:
7161:
7160:
7144:
7141:
7137:
7114:
7110:
7087:
7084:
7080:
7056:
7045:
7041:
7032:
7028:
7024:
7021:
7013:
7009:
7000:
6997:
6994:
6990:
6986:
6981:
6977:
6970:
6965:
6960:
6957:
6954:
6950:
6944:
6918:
6913:
6909:
6904:
6898:
6890:
6886:
6880:
6876:
6872:
6866:
6858:
6855:
6852:
6848:
6844:
6838:
6830:
6826:
6818:
6817:
6816:
6800:
6796:
6773:
6770:
6766:
6756:
6740:
6737:
6733:
6710:
6707:
6703:
6679:
6673:
6663:
6660:
6656:
6643:
6640:
6636:
6628:
6624:
6618:
6615:
6612:
6608:
6604:
6598:
6590:
6586:
6578:
6577:
6576:
6574:
6555:
6547:
6543:
6534:
6516:
6511:
6507:
6502:
6498:
6495:
6492:
6487:
6484:
6480:
6457:
6453:
6430:
6426:
6402:
6394:
6390:
6381:
6376:
6374:
6370:
6362:
6344:
6338:
6330:
6326:
6317:
6299:
6293:
6285:
6281:
6275:
6271:
6267:
6261:
6253:
6250:
6247:
6243:
6239:
6233:
6225:
6221:
6213:
6212:
6210:
6194:
6190:
6181:
6177:
6168:
6164:
6160:
6157:
6149:
6145:
6136:
6133:
6130:
6126:
6122:
6117:
6113:
6108:
6104:
6099:
6094:
6091:
6088:
6084:
6078:
6052:
6047:
6043:
6035:
6034:
6018:
6014:
6005:
5988:
5983:
5980:
5977:
5964:
5961:
5957:
5953:
5948:
5944:
5914:
5906:
5902:
5893:
5877:
5874:
5871:
5868:
5865:
5862:
5859:
5856:
5840:
5832:
5829:
5826:
5822:
5818:
5812:
5806:
5801:
5790:
5786:
5779:
5763:
5759:
5752:
5749:
5744:
5740:
5733:
5724:
5719:
5716:
5711:
5708:
5704:
5696:
5695:
5693:
5689:
5688:
5678:
5662:
5656:
5653:
5648:
5644:
5637:
5632:
5627:
5624:
5621:
5617:
5611:
5604:
5601:
5595:
5589:
5581:
5577:
5569:
5568:
5566:
5565:
5564:
5561:
5543:
5534:
5528:
5525:
5522:
5516:
5496:
5491:
5486:
5483:
5480:
5467:
5463:
5459:
5454:
5450:
5432:
5429:
5377:
5371:
5359:
5355:
5346:
5343:
5340:
5336:
5332:
5327:
5323:
5316:
5309:
5306:
5303:
5299:
5290:
5287:
5279:
5275:
5266:
5263:
5260:
5256:
5252:
5247:
5243:
5238:
5234:
5228:
5223:
5220:
5217:
5213:
5206:
5199:
5196:
5190:
5185:
5181:
5158:
5154:
5121:
5117:
5108:
5105:
5102:
5098:
5094:
5089:
5085:
5078:
5071:
5068:
5065:
5061:
5049:
5044:
5041:
5038:
5034:
5028:
5024:
5020:
5014:
5006:
5003:
5000:
4996:
4992:
4986:
4978:
4974:
4966:
4965:
4964:
4915:
4902:
4896:
4884:
4880:
4871:
4868:
4865:
4861:
4857:
4852:
4848:
4841:
4834:
4831:
4828:
4824:
4815:
4812:
4804:
4800:
4791:
4788:
4785:
4781:
4777:
4772:
4768:
4763:
4759:
4753:
4748:
4745:
4742:
4738:
4731:
4724:
4721:
4715:
4702:
4698:
4689:
4685:
4681:
4676:
4672:
4665:
4659:
4654:
4651:
4648:
4644:
4637:
4630:
4627:
4621:
4616:
4612:
4603:
4589:
4569:
4555:
4533:
4529:
4520:
4517:
4514:
4510:
4506:
4501:
4497:
4490:
4483:
4480:
4477:
4473:
4442:
4438:
4429:
4425:
4415:
4402:
4399:
4387:
4383:
4374:
4371:
4368:
4364:
4360:
4355:
4351:
4344:
4337:
4334:
4331:
4327:
4313:
4309:
4300:
4296:
4292:
4281:
4277:
4268:
4265:
4262:
4258:
4254:
4249:
4245:
4238:
4232:
4227:
4224:
4221:
4217:
4213:
4201:
4197:
4188:
4184:
4180:
4172:
4168:
4159:
4156:
4153:
4149:
4145:
4140:
4136:
4129:
4123:
4118:
4115:
4112:
4108:
4104:
4101:
4076:
4072:
4063:
4060:
4057:
4053:
4043:
4021:
4017:
4008:
4004:
4000:
3992:
3988:
3979:
3976:
3973:
3969:
3965:
3960:
3956:
3949:
3943:
3938:
3935:
3932:
3928:
3924:
3921:
3912:
3911:
3905:
3904:
3900:
3878:
3874:
3865:
3862:
3859:
3855:
3851:
3846:
3842:
3835:
3832:
3821:
3817:
3808:
3804:
3800:
3795:
3791:
3784:
3764:
3744:
3741:
3738:
3729:
3707:
3703:
3694:
3691:
3688:
3684:
3680:
3675:
3671:
3664:
3657:
3654:
3651:
3647:
3635:
3630:
3627:
3624:
3620:
3616:
3613:
3607:
3599:
3596:
3593:
3589:
3585:
3579:
3571:
3567:
3558:
3544:
3535:
3518:
3510:
3507:
3504:
3500:
3490:
3488:
3483:
3463:
3459:
3449:
3428:
3423:
3419:
3398:
3395:
3392:
3365:
3358:
3353:
3340:
3336:
3327:
3323:
3319:
3311:
3307:
3298:
3295:
3292:
3288:
3284:
3279:
3275:
3268:
3262:
3257:
3254:
3251:
3247:
3242:
3228:
3223:
3219:
3190:
3186:
3180:
3172:
3169:
3166:
3162:
3158:
3152:
3144:
3140:
3132:
3112:
3109:
3104:
3100:
3093:
3087:
3082:
3079:
3076:
3072:
3065:
3058:
3055:
3049:
3043:
3035:
3031:
3023:
3022:
3021:
3019:
3000:
2992:
2988:
2964:
2952:
2941:
2909:
2905:
2901:
2896:
2892:
2885:
2882:
2879:
2871:
2867:
2863:
2858:
2854:
2816:
2810:
2802:
2798:
2792:
2788:
2782:
2777:
2774:
2771:
2767:
2763:
2757:
2745:
2735:
2734:
2733:
2731:
2688:
2680:
2676:
2648:
2636:
2596:
2590:
2587:
2584:
2578:
2570:
2567:
2564:
2551:
2544:
2541:
2535:
2526:
2516:
2515:
2514:
2494:
2488:
2485:
2482:
2476:
2469:
2468:loss function
2450:
2438:
2419:
2411:
2409:
2407:
2382:
2378:
2369:
2365:
2359:
2356:
2351:
2340:
2336:
2329:
2326:
2321:
2317:
2308:
2305:
2300:
2289:
2285:
2278:
2256:
2246:
2239:
2238:
2221:
2216:
2207:
2203:
2196:
2193:
2188:
2184:
2179:
2172:
2167:
2164:
2161:
2157:
2151:
2148:
2143:
2126:
2118:
2117:
2116:
2097:
2093:
2086:
2078:
2057:
2053:
2044:
2040:
2031:
2027:
2009:
2005:
1982:
1979:
1976:
1972:
1946:
1942:
1933:
1929:
1925:
1920:
1916:
1908:
1907:
1888:
1884:
1854:
1850:
1841:
1837:
1833:
1828:
1824:
1820:
1812:
1808:
1799:
1795:
1787:
1786:
1785:
1766:
1762:
1758:
1750:
1746:
1737:
1733:
1729:
1721:
1717:
1708:
1704:
1700:
1692:
1688:
1679:
1676:
1673:
1669:
1661:
1660:
1659:
1642:
1634:
1630:
1607:
1603:
1582:
1574:
1552:
1546:
1541:
1531:
1507:
1485:
1481:
1460:
1457:
1454:
1451:
1448:
1428:
1408:
1385:
1365:
1362:
1355:
1340:
1335:
1331:
1323:
1304:
1300:
1293:
1273:
1268:
1258:
1247:
1246:
1245:
1231:
1211:
1191:
1169:
1159:
1155:
1151:
1146:
1136:
1124:
1120:
1113:
1110:
1100:
1081:
1075:
1072:
1063:
1040:
1032:
1029:
1028:least-squares
1024:
1018:
1016:
1013:
1009:
1005:
997:
995:
993:
992:loss function
990:
986:
982:
981:random forest
978:
974:
970:
966:
962:
958:
954:
943:
938:
936:
931:
929:
924:
923:
921:
920:
913:
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479:Hidden Markov
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275:Random forest
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160:Data cleaning
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8830:the original
8825:
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819:PAC learning
506:
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350:Hierarchical
282:
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8944:10983/15329
8929:(1): 1–37.
8137:Higgs boson
8112:overfitting
7992:overfitting
7653:overfitting
7474:interaction
5563:Algorithm:
5428:line search
1004:Leo Breiman
703:Multi-agent
640:Transformer
539:Autoencoder
295:Naive Bayes
33:data mining
9050:Categories
8662:2001.06033
8626:, page 14.
8434:Cheng Li.
8389:S.A. Solla
8363:2018-08-27
8304:2013-11-13
8222:References
6571:for input
2668:functions
1031:regression
688:Q-learning
586:Restricted
384:Mean shift
333:Clustering
310:Perceptron
238:regression
140:Clustering
135:Regression
8953:0219-3116
8907:213782055
8899:1943-555X
8839:31 August
8712:2391-5447
8092:ℓ
8015:≤
8009:≤
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7853:ν
7845:(such as
7826:ν
7817:parameter
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4214:≈
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4061:−
3977:−
3929:∑
3863:−
3833:≤
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3739:γ
3692:−
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3643:∇
3621:∑
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3508:−
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3396:≥
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3229:∈
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3073:∑
3066:γ
3059:
3020:fashion:
2956:^
2883:…
2789:γ
2768:∑
2749:^
2640:^
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2442:^
2412:Algorithm
2327:−
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2247:−
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1926:−
1834:−
1556:¯
1535:^
1500:(for low
1458:≤
1452:≤
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1140:^
1121:∑
1067:^
969:residuals
847:ECML PKDD
829:VC theory
776:ROC curve
708:Self-play
628:DeepDream
469:Bayes net
260:Ensembles
41:Paradigms
9041:LightGBM
8804:18397250
8755:41965832
8747:12704603
8639:Archived
8620:Archived
8206:LightGBM
8201:Catboost
8191:AdaBoost
8185:See also
7903:querying
3411:, where
2416:In many
1906:residual
1658:. Thus,
1184:, where
985:boosting
973:ensemble
961:boosting
270:Boosting
119:Problems
8961:2367747
8782:Bibcode
8690:Bibcode
8211:XGBoost
7915:Breiman
6318:Output
5683:= 1 to
1903:to the
998:History
852:NeurIPS
669:(ECRAM)
623:AlexNet
265:Bagging
9013:
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8132:Yandex
7815:where
6695:where
5424:γ
5146:where
3731:where
3018:greedy
645:Vision
501:RANSAC
379:OPTICS
374:DBSCAN
358:-means
165:AutoML
8957:S2CID
8903:S2CID
8833:(PDF)
8822:(PDF)
8751:S2CID
8657:arXiv
8457:(PDF)
8439:(PDF)
8421:(PDF)
8414:(PDF)
8387:. In
8385:(PDF)
8357:(PDF)
8350:(PDF)
8323:(PDF)
8298:(PDF)
8291:(PDF)
8143:Names
8128:Yahoo
8118:Usage
8080:trees
6373:CARTs
2822:const
955:is a
867:IJCAI
693:SARSA
652:Mamba
618:LeNet
613:U-Net
439:t-SNE
363:Fuzzy
340:BIRCH
9011:ISBN
8949:ISSN
8895:ISSN
8841:2018
8826:CRAN
8800:PMID
8743:PMID
8708:ISSN
8256:ISBN
8130:and
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7788:<
7624:>
5679:For
3742:>
3385:for
2730:weak
877:JMLR
862:ICLR
857:ICML
743:RLHF
559:LSTM
345:CURE
31:and
8984:doi
8980:572
8939:hdl
8931:doi
8887:doi
8790:doi
8735:doi
8698:doi
8018:0.8
8006:0.5
7917:'s
7859:0.1
5608:min
5602:arg
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5197:arg
4728:min
4722:arg
4634:min
4628:arg
3062:min
3056:arg
2548:min
2542:arg
2115:):
1573:RHS
603:SOM
593:GAN
569:ESN
564:GRU
509:-NN
444:SDL
434:PGD
429:PCA
424:NMF
419:LDA
414:ICA
409:CCA
285:-NN
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4113:i
4105:=
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934:t
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507:k
356:k
283:k
241:)
229:(
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