帮我用Python写一个完整的informer时序预测模型，包括 ProbSparse 自注意力机制、蒸馏操作等。

在Python中构建一个包含ProbSparse自注意力机制和蒸馏操作的时序预测模型，通常会使用深度学习库如PyTorch。这里提供一个简化版的示例，假设我们正在使用Transformer架构作为基础，并使用Prophet库做时间序列分析。注意，这只是一个基本框架，实际应用可能需要更复杂的网络结构和更多的优化步骤。

import torch
from torch.nn import TransformerEncoder, TransformerEncoderLayer
from torch.nn.functional import softmax
from torch.distributions import Categorical
from pytorch_forecasting import TimeSeriesDataSet

# 定义ProbSparse Attention层
class ProbSparseAttention(TransformerEncoderLayer):
    def __init__(self, d_model, heads, dropout=0.1):
        super().__init__(d_model, heads, dropout)
        self.sparse_attention = SparseSelfAttention(heads, dropout)

    def forward(self, src, mask=None):
        # 其他部分保持不变，只替换普通的自注意力层
        x = self.mha(src, src, src, key_padding_mask=mask) + src
        return x

# 使用自定义层创建Transformer Encoder
class InformerModel(torch.nn.Module):
    def __init__(self, input_size, output_size, n_layers, d_model, heads, dropout):
        super().__init__()
        self.encoder = TransformerEncoder(ProbSparseAttention(d_model, heads), n_layers)
        self.linear = torch.nn.Linear(d_model, output_size)

    def forward(self, x):
        # 时间序列数据经过编码器
        out = self.encoder(x)
        # 输出层处理编码后的结果
        y_pred = self.linear(out[:, -1, :])
        return y_pred

# 蒸馏相关的辅助函数 (简化版本)
def distillation_loss(student_output, teacher_output, temperature=10):
    soft_teach = F.softmax(teacher_output / temperature, dim=-1)
    log_prob_student = F.log_softmax(student_output / temperature, dim=-1)
    loss = -(soft_teach * log_prob_student).sum(dim=-1).mean()
    return loss

# 示例用法
input_size = 5 # 假设输入特征数
output_size = 1 # 预测值的数量
n_layers = 2
d_model = 64
heads = 8
dropout = 0.1

model = InformerModel(input_size, output_size, n_layers, d_model, heads, dropout)
teacher_model = ... # 初始化预训练的教师模型

# 假设data_loader是一个PyTorch Dataloader返回的数据集
for x, y in data_loader:
    student_out = model(x)
    teacher_out = teacher_model(x) # 老师模型的输出
    distillation_loss_value = distillation_loss(student_out, teacher_out)
    total_loss += distillation_loss_value

# 训练模型
optimizer.zero_grad()
total_loss.backward()
optimizer.step()