Algorithm 2.
Inter-site posterior update in asynchronous EXPLORER
1: |
Global initialization: Initialize all the messages mB→h<sub>j</sub>(β) and mh<sub>j</sub>→B (β) between server variable node B and clients factor nodes hj, where the subscriptions B → hj and hj → B indicate the message directions. |
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2: | Local initialization for all the online sites: | |
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3: | Initialize messages mB<sub>j</sub>→h<sub>j</sub> (β) and each approximate likelihood function with i = mj−1 + 1, · · ·, mj. | |
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4: | Repeat: | |
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5: | for all the online sites (parallel update) | |
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6: | Update intra-site message: mh<sub>j</sub>→ B<sub>j</sub>(βj)= ∫ δ(β, βj) mB→h<sub>j</sub> (β) dβ | |
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7: | Set approximate posterior: | |
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8: | Update approximate posterior qj(βj) according to Algorithm 1. | |
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9: | Update intra-site messages at variable node Bj :
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10: | Upload message at factor node hj :
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11: | end for | |
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12: | Send out message at server node B:
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13: | Until parameters converge | |
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14: | Get the final approximate posterior distribution by multiply- ing all the incoming messages at the server node B. |