试图用爱德华实现贝叶斯神经网络

Question

我试图将贝叶斯神经网络用于在PyCon上的Torsten Scholak提出的用于非线性回归的一些真实世界数据，并且得到了一些奇怪的结果。合适的程度可以达到一定程度，然后可以保持平坦。关于我在做什么错的任何想法吗？我正在使用爱德华图书馆

def neural_network_with_2_layers(x, W_0, W_1, b_0, b_1):
    h = tf.nn.tanh(tf.matmul(x, W_0) + b_0)
    h = tf.matmul(h, W_1) + b_1
    return tf.reshape(h, [-1])

dim = 10  # layer dimensions
W_0 = Normal(loc=tf.zeros([D, dim]),
             scale=tf.ones([D, dim]))
W_1 = Normal(loc=tf.zeros([dim, 1]),
             scale=tf.ones([dim, 1]))
b_0 = Normal(loc=tf.zeros(dim),
             scale=tf.ones(dim))
b_1 = Normal(loc=tf.zeros(1),
             scale=tf.ones(1))

x = tf.placeholder(tf.float32, [N, D])

#Reshaping
a = neural_network_with_2_layers(x,W_0,W_1,b_0,b_1)
b = tf.reshape(a,[len(X_train),1])
y = Normal(loc=b,scale=(tf.ones([N,1])*0.1))  # constant noise


 `#BACKWARD MODEL A`

q_W_0 = Normal(loc=tf.Variable(tf.random_normal([D, dim])),
               scale=tf.nn.softplus(tf.Variable(tf.random_normal([D, dim]))))
q_W_1 = Normal(loc=tf.Variable(tf.random_normal([dim, 1])),
               scale=tf.nn.softplus(tf.Variable(tf.random_normal([dim, 1]))))
q_b_0 = Normal(loc=tf.Variable(tf.random_normal([dim])),
               scale=tf.nn.softplus(tf.Variable(tf.random_normal([dim]))))
q_b_1 = Normal(loc=tf.Variable(tf.random_normal([1])),
               scale=tf.nn.softplus(tf.Variable(tf.random_normal([1]))))


inference = ed.KLqp(latent_vars={W_0: q_W_0, b_0: q_b_0,
                                 W_1: q_W_1, b_1: q_b_1},
                    data={x: X_train, y: Y_train})

inference.run(n_samples=50, n_iter=20000)

这就是结果的样子

这是我用来绘制的代码。X_train并Y_train有大小623 X_test和Y_test具有尺寸718

plt.scatter(X_train, Y_train, s=20.0);  # blue
plt.scatter(X_test, Y_test, s=20.0,  # red
        color=sns.color_palette().as_hex()[2]);

xp = tf.placeholder(tf.float32, [1000, D])
[plt.plot(np.linspace(-1.0, 1.0, 1000),
      sess.run(neural_network_with_2_layers(xp,
                                            q_W_0, q_W_1,
                                            q_b_0, q_b_1),
               {xp: np.linspace(-1.0, 1.0, 1000)[:, np.newaxis]}),
      color='black', alpha=0.1)
 for _ in range(10)];

更新：问题是输入数据。为了使tanh函数正常工作，需要将其标准化为（-1,1）

此后的一些预测。不是最合适的，但仍在进步