SCIENTIA SINICA Informationis, Volume 51 , Issue 1 : 1(2021) https://doi.org/10.1360/SSI-2020-0170

## Learning from distribution-changing data streams via decision tree model reuse

• ReceivedJun 9, 2020
• AcceptedAug 5, 2020
• PublishedDec 25, 2020
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### References

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• Figure 1

(Color online) Illustration of the CondorForest algorithm

• Figure 2

(Color online) Illustration of the decision tree model reuse mechanism. (a) shows the concept and decision tree model of the source domain; (b) demonstrates those of the target domain

• Figure 3

(Color online) Robustness analysis

• Figure 4

(Color online) Parameter sensitivity analysis on different datasets: (a) Update period $p$; (b) model pool size $K$; (c) step size $\eta$

• Table 1   Basic statistics of datasets involved in the experiments
 Dataset # instance Dim # class Dataset # instance Dim # class textsfCIR500G 60000 3 2 textsfGasSensor 4450 129 6 textsfSINE500G 60000 2 2 textsfPowersupply 29928 2 2 textsfLuxembourg 1900 32 2 textsfElectricity 45312 8 2 textsfWeather 18159 8 2 textsfCovertype 581012 54 2
•

Algorithm 1 CondorForest

Require:Data stream $\{(\x_1,y_1),\ldots,(\x_T,y_T)\}$. Update period $p$; model pool size $K$; step size $\eta$; distribution change detector $\mathfrak{D}$.

Output:Predictive label $\hat{y}_{t}$, $t=~1,\ldots,T$.

Use the initial data to initialize a decision-tree model $\Tree_1$;

Initialize the model pool $\mathcal{M}~=~\{~\Tree_1\}$ and weight $w_1~=~1$;

for $t=1$ series to $T$

Receive the feature $\x_t$;

Each model of $\mathcal{M}$ makes the prediction: $\Tree_k(\x_t)$, where $k=1,\ldots,|\mathcal{M}|$;

Make the prediction $\hat{y}_t~=~\sum_{k=1}^{|\mathcal{M}|}~w_t^k~\Tree_k(\x_t)$;

Receive the ground-truth label $y_t$, and each model suffers $\ell(\Tree_k(\x_t),~y_t)$;

Update the model weight according to 1;

if $(t~\Mod~p)~=~0$ or $\mathfrak{D}$ detects the distribution change then

Sample a decision tree model $\tilde{\Tree}$ according to the weight distribution;

Learn a new model $\Tree_{\mathrm{new}}$ via the decision tree model reuse, and then add it into the model pool $\mathcal{M}$;

Update the weight as the uniform distribution;

end if

end for

• Table 2   Performance comparisons on two non-linear synthetic datasets and six real-world datasets
 Dataset DWM DTEL TIX CondorSVM CondorForest textsfCIR500G 77.09 $\pm$ 0.71 $\bullet$ 79.03 $\pm$ 0.34 $\bullet$ 66.38 $\pm$ 0.85 $\bullet$ 68.41 $\pm$ 0.87 79.60 $\pm$ 1.11 textsfSIN500G 66.99 $\pm$ 0.10 $\bullet$ 74.93 $\pm$ 0.34 $\circ$ 62.73 $\pm$ 0.14 $\bullet$ 65.68 $\pm$ 0.12 73.98 $\pm$ 0.90 textsfLuxembourg 90.42 $\pm$ 0.55 $\bullet$ 100.0 $\pm$ 0.00 $~$ 90.99 $\pm$ 0.97 $\bullet$ 99.98 $\pm$ 0.03 100.0 $\pm$ 0.00 textsfWeather 70.83 $\pm$ 0.49 $\bullet$ 68.92 $\pm$ 0.27 $\bullet$ 70.21 $\pm$ 0.33 $\bullet$ 79.37 $\pm$ 0.26 73.65 $\pm$ 0.66 textsfGasSensor 76.61 $\pm$ 0.36 $\bullet$ 63.82 $\pm$ 3.64 $\bullet$ 43.40 $\pm$ 2.88 $\bullet$ 81.57 $\pm$ 3.77 76.25 $\pm$ 4.38 textsfPowersupply 72.09 $\pm$ 0.29 $\bullet$ 69.90 $\pm$ 0.38 $\bullet$ 68.34 $\pm$ 0.16 $\bullet$ 72.82 $\pm$ 0.29 73.23 $\pm$ 0.91 textsfElectricity 78.03 $\pm$ 0.17 $\bullet$ 81.05 $\pm$ 0.35 $\bullet$ 58.44 $\pm$ 0.71 $\bullet$ 84.73 $\pm$ 0.33 87.88 $\pm$ 1.04 textsfCovertype 74.17 $\pm$ 0.87 $\bullet$ 69.43 $\pm$ 1.30 $\bullet$ 64.60 $\pm$ 0.89 $\bullet$ 89.58 $\pm$ 0.14 91.35 $\pm$ 0.24

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