**Input**: A user’s data set with observational data |

, user’s data number probability |

coefficient . |

**Output**: The user’s polynomial approximation function |

model , and the coefficient matrix . |

(1) Each user transforms his data into the form , |

where is the probability of in the user’s data set; |

(2) All users build their own data models with the |

polynomial approximation function algorithm in a |

distributed system; |

(3) Each user slices his data distribution model by Eq. (3) to |

obtain the coefficient matrix ; |

(4) For each user, one of the coefficient matrix rows is kept |

by himself and the remaining row pieces are sent to |

other users randomly; |

(5) Each user collects all the received matrix rows, mixes |

them and send the mixed result to the data analyst, in |

the same way, the data analyst can reconstruct the final |

model in the community by Eq. (5). |