基于概率结构整合的世界建模

# 贝叶斯网络示例
import numpy as np
import pgmpy.models as pgm
from pgmpy.factors.discrete import TabularCPD

# 创建贝叶斯网络
model = pgm.BayesianNetwork([('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'D')])

# 定义条件概率分布
cpd_a = TabularCPD('A', 2, [[0.3], [0.7]])
cpd_b = TabularCPD('B', 2, [[0.9, 0.4], [0.1, 0.6]], evidence=['A'], evidence_card=[2])
cpd_c = TabularCPD('C', 2, [[0.2, 0.7], [0.8, 0.3]], evidence=['A'], evidence_card=[2])
cpd_d = TabularCPD('D', 2, [[0.1, 0.4, 0.3, 0.8], [0.9, 0.6, 0.7, 0.2]], 
                   evidence=['B', 'C'], evidence_card=[2, 2])

# 添加条件概率分布到模型
model.add_cpds(cpd_a, cpd_b, cpd_c, cpd_d)

# PyMC3概率编程示例
import pymc3 as pm
import numpy as np

# 生成模拟数据
np.random.seed(42)
true_intercept = 1
true_slope = 2
x = np.linspace(0, 1, 100)
y = true_intercept + true_slope * x + np.random.normal(0, 0.5, size=100)

# 定义概率模型
with pm.Model() as linear_model:
    # 定义先验分布
    intercept = pm.Normal('intercept', mu=0, sd=10)
    slope = pm.Normal('slope', mu=0, sd=10)
    sigma = pm.HalfNormal('sigma', sd=1)
    
    # 定义似然函数
    mu = intercept + slope * x
    likelihood = pm.Normal('y', mu=mu, sd=sigma, observed=y)
    
    # 进行推理
    trace = pm.sample(1000, tune=1000)

# 状态空间模型示例
class StateSpaceModel:
    def __init__(self, state_dim, obs_dim):
        self.state_dim = state_dim
        self.obs_dim = obs_dim
        
    def transition(self, state, action):
        """状态转移函数：p(s_t | s_{t-1}, a_{t-1})"""
        # 实现状态转移逻辑
        pass
    
    def emission(self, state):
        """观测函数：p(o_t | s_t)"""
        # 实现观测逻辑
        pass
    
    def inference(self, observations, actions):
        """推理：计算后验状态分布 p(s_t | o_{1:t}, a_{1:t-1})"""
        # 实现推理算法，如粒子滤波或卡尔曼滤波
        pass

# 变分自编码器示例
class VAE(nn.Module):
    def __init__(self, input_dim, hidden_dim, latent_dim):
        super(VAE, self).__init__()
        # 编码器
        self.encoder = nn.Sequential(
            nn.Linear(input_dim, hidden_dim),
            nn.ReLU(),
            nn.Linear(hidden_dim, latent_dim * 2)  # 输出均值和方差
        )
        
        # 解码器
        self.decoder = nn.Sequential(
            nn.Linear(latent_dim, hidden_dim),
            nn.ReLU(),
            nn.Linear(hidden_dim, input_dim),
            nn.Sigmoid()
        )
    
    def encode(self, x):
        h = self.encoder(x)
        mu, logvar = torch.chunk(h, 2, dim=1)
        return mu, logvar
    
    def reparameterize(self, mu, logvar):
        std = torch.exp(0.5 * logvar)
        eps = torch.randn_like(std)
        return mu + eps * std
    
    def decode(self, z):
        return self.decoder(z)
    
    def forward(self, x):
        mu, logvar = self.encode(x)
        z = self.reparameterize(mu, logvar)
        return self.decode(z), mu, logvar

# 粒子滤波示例
class ParticleFilter:
    def __init__(self, num_particles, transition_model, emission_model):
        self.num_particles = num_particles
        self.transition_model = transition_model
        self.emission_model = emission_model
        self.particles = None
        self.weights = None
    
    def init(self, initial_state):
        """初始化粒子"""
        self.particles = np.array([initial_state] * self.num_particles)
        self.weights = np.ones(self.num_particles) / self.num_particles
    
    def predict(self, action):
        """预测步骤：根据动作转移粒子"""
        for i in range(self.num_particles):
            self.particles[i] = self.transition_model(self.particles[i], action)
    
    def update(self, observation):
        """更新步骤：根据观测更新粒子权重"""
        for i in range(self.num_particles):
            self.weights[i] *= self.emission_model(self.particles[i], observation)
        
        # 归一化权重
        self.weights /= np.sum(self.weights)
    
    def resample(self):
        """重采样：根据权重重新采样粒子"""
        indices = np.random.choice(
            self.num_particles, 
            size=self.num_particles, 
            p=self.weights
        )
        self.particles = self.particles[indices]
        self.weights = np.ones(self.num_particles) / self.num_particles

# 概率循环神经网络示例
class ProbabilisticRNN(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(ProbabilisticRNN, self).__init__()
        self.hidden_size = hidden_size
        
        # 确定性RNN
        self.rnn = nn.RNN(input_size, hidden_size, batch_first=True)
        
        # 输出层：预测均值和方差
        self.fc_mean = nn.Linear(hidden_size, output_size)
        self.fc_logvar = nn.Linear(hidden_size, output_size)
    
    def forward(self, x, hidden=None):
        # 前向传播RNN
        output, hidden = self.rnn(x, hidden)
        
        # 预测分布参数
        mean = self.fc_mean(output)
        logvar = self.fc_logvar(output)
        
        return mean, logvar, hidden
    
    def init_hidden(self, batch_size):
        return torch.zeros(1, batch_size, self.hidden_size)