Examples of model leakage and model protection, showing model matrices, where columns correspond to tasks and rows correspond to features. The 10-th task is an anomaly task that requires privacy protection. In (a), the matrix denoted by W (0) is firstly generated from i.i.d. uniform distribution U (0, 1). Then the last column is multiplied by 100. We then run Algorithm 2, taking m = 10, d = 5, T = 1, η = 1, 1 = = 0.1, δ = 0, K = 100 √ 5 and λ = 50. The noise matrix E is not added in (b) but added in (c). (a) shows W (0) ; (b) and (c) show W (1) under their respective settings. Columns shown have been divided by their respective 2 norms. In (b), the 10-th task results in significantly influences on the parameters of other models, especially on the first and the last features. In (c), the influences from the 10-th task are not significant. Meanwhile, the second and the fifth features are shared by most tasks as should be.

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... provide a running example for model leakage and model protection under different settings of Algorithm 2, as shown in Fig. 2. We generate models for m = 10 tasks, in which the data dimension is d = 5. The 10th task (the rightmost one), is an anomaly task that requires privacy protection. In Fig. 2 (a), the matrix denoted by W (0) is first generated from an i.i.d. uniform distribution U(0, 1). Then, the rightmost column is multiplied by 100. For MTL with ...

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... provide a running example for model leakage and model protection under different settings of Algorithm 2, as shown in Fig. 2. We generate models for m = 10 tasks, in which the data dimension is d = 5. The 10th task (the rightmost one), is an anomaly task that requires privacy protection. In Fig. 2 (a), the matrix denoted by W (0) is first generated from an i.i.d. uniform distribution U(0, 1). Then, the rightmost column is multiplied by 100. For MTL with model leakage, we execute Algorithm 2, setting T = 1, η = 1, , 1 = = 1e40, δ = 0, K = 100 √ 5 and λ = 50. It can be regarded that the noise matrix E is not added, since 1. The output ...

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... by W (0) is first generated from an i.i.d. uniform distribution U(0, 1). Then, the rightmost column is multiplied by 100. For MTL with model leakage, we execute Algorithm 2, setting T = 1, η = 1, , 1 = = 1e40, δ = 0, K = 100 √ 5 and λ = 50. It can be regarded that the noise matrix E is not added, since 1. The output model matrix W (1) is shown in Fig. 2 (b), in which the 10th task results in significantly influences on the parameters of other models: other models' parameters are similar to those of the 10th task, e.g., for each task, the first feature is the biggest, and the fifth feature is the smallest. For MTL with model protection, we execute Algorithm 2 with the same setting as above ...

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... which the 10th task results in significantly influences on the parameters of other models: other models' parameters are similar to those of the 10th task, e.g., for each task, the first feature is the biggest, and the fifth feature is the smallest. For MTL with model protection, we execute Algorithm 2 with the same setting as above except that we Fig. 2 (c), in which the influences from the 10th task are not significant: other models' parameters are not similar to those of the 10th task. Meanwhile, for W (0) , shown in Fig. 2 (a), for tasks 1-9, the 2 norms of the second and the fifth rows are the two largest ones; these are clearly shown in Fig. 2 (c). This result means the shared ...

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... the first feature is the biggest, and the fifth feature is the smallest. For MTL with model protection, we execute Algorithm 2 with the same setting as above except that we Fig. 2 (c), in which the influences from the 10th task are not significant: other models' parameters are not similar to those of the 10th task. Meanwhile, for W (0) , shown in Fig. 2 (a), for tasks 1-9, the 2 norms of the second and the fifth rows are the two largest ones; these are clearly shown in Fig. 2 (c). This result means the shared information between tasks is to use the second and the fifth features, which is successfully extracted by the MTL method with model ...

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... 2 with the same setting as above except that we Fig. 2 (c), in which the influences from the 10th task are not significant: other models' parameters are not similar to those of the 10th task. Meanwhile, for W (0) , shown in Fig. 2 (a), for tasks 1-9, the 2 norms of the second and the fifth rows are the two largest ones; these are clearly shown in Fig. 2 (c). This result means the shared information between tasks is to use the second and the fifth features, which is successfully extracted by the MTL method with model ...

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... we present the results mostly for our low-rank algorithm (denoted by MP-MTL-LR) because it always outperforms our group-sparse algorithm (MP-MTL-GS) in the above experiments. The results corresponding to School Data are shown in Fig. 11; the results corresponding to LSOA II Data are shown in Fig. 12. From those plots, we observe that on both real-world datasets, our MP-MTL method behaves similarly at different training-data percentages and outperforms DP-MTRL and DP-AGGR, especially when is ...