CTR学习笔记&代码实现6-深度ctr模型 后浪 xDeepFM/FiBiNET

xDeepFM用改良的DCN替代了DeepFM的FM部分来学习组合特征信息，而FiBiNET则是应用SENET加入了特征权重比NFM，AFM更进了一步。在看两个model前建议对DeepFM, Deep&Cross, AFM，NFM都有简单了解，不熟悉的能够看下文章最后其余model的博客连接。

如下代码针对Dense输入更容易理解模型结构，针对spare输入的代码和完整代码 👇
https://github.com/DSXiangLi/CTR

xDeepFM

模型结构

看xDeepFM的名字和DeepFM类似都拥有Deep和Linear的部分，只不过把DeepFM中用来学习二阶特征交互的FM部分替换成了CIN（Compressed Interactino Network）。而CIN是在Deep&Cross的DCN上进一步改良的获得。总体模型结构以下

咱们重点看下CIN的部分，和paper的notation保持一致，有m个特征，每一个特征Embedding是D维，第K层的CIN有\(H_k\)个unit。CIN第K层的计算分为3个部分分别对应图a-c：

1. 向量两两作element-wise product, 时间复杂度\(O(m*H_{k-1}*D)\)
   对输入层和第K-1层输出，作element-wise乘积进行两两特征交互，获得\(m*H_{k-1}\)个D维向量矩阵，若是CIN只有一层，则和FM, NFM，AFM的第一步相同。FM 直接聚合成scaler，NFM沿D进行sum_pooling，而AFM加入Attention沿D进行weighted_pooling。忽略batch的矩阵dimension变化以下

\[z^k = x^0 \odot x^{k-1} = (D * m* 1) \odot (D * 1* H_{k-1}) = D * m*H_{k-1} \]

2. Feature Map，空间复杂度\(O(H_k *H_{k-1} *m)\)，时间复杂度\(O(H_k *H_{k-1} *m*D)\)
   \(W_k \in R^{H_{k-1}*m *H_k}\) 是第K层的权重向量，能够理解为沿Embedding作CNN。每一个Filter对全部两两乘积的向量进行加权求和获得 \(1*D\)的向量 一共有\(H_k\)个channel，输出\(H_k * D\)的矩阵向量。

\[w^k \bullet z^k = (H_k *H_{k-1} *m)* (m*H_{k-1}*D) = H_k *D \]

3. Sum Pooling
   CIN对每层的输出沿Dimension进行sum pooling，获得\(H_k*1\)的输出，而后把每层输出concat之后做为CIN部分的输出。

CIN每一层的计算如上，T层CIN每一层都是上一次层的输出和第一层的输入进行交互获得更高一阶的交互信息。假设每层维度同样\(H_k=H\)， CIN 部分总体时间复杂度是\(O(TDmH^2)\)，空间复杂度来自每层的Filter权重\(O(TmH^2)\)

CIN保留DCN的任意高阶和参数共享，两个主要差异是

• DCN是bit-wise，CIN是vector-wise。DCN在作向量乘积时不区分Field，直接对全部Field拼接成的输入（m*D）进行外积。而CIN考虑Field，两两vector进行乘积
• DCN使用了ResNet由于多项式的核心只用输出最后一层，而CIN则是每层都进行pooling后输出

CIN的设计仍是很巧妙滴，不过。。。吐槽小分队上线: CIN不管是时间复杂度仍是空间复杂度都比DCN要高，感受更容易过拟合。至于说vector-wise的向量乘积要比bit-wise的向量乘积要好，这。。。至少bit-wise能够不限制embedding维度一致, 但vector-wise嘛我实在有些理解无能，明白的童鞋能够comment一下

代码实现

def cross_op(xk, x0, layer_size_prev, layer_size_curr, layer, emb_size, field_size):
    # Hamard product: ( batch * D * HK-1 * 1) * (batch * D * 1* H0) -> batch * D * HK-1 * H0
    zk = tf.matmul( tf.expand_dims(tf.transpose(xk, perm = (0, 2, 1)), 3),
                    tf.expand_dims(tf.transpose(x0, perm = (0, 2, 1)), 2))

    zk = tf.reshape(zk, [-1, emb_size, field_size * layer_size_prev]) # batch * D * HK-1 * H0 -> batch * D * (HK-1 * H0)
    add_layer_summary('zk_{}'.format(layer), zk)

    # Convolution with channel = HK: (batch * D * (HK-1*H0)) * ((HK-1*H0) * HK)-> batch * D * HK
    kernel = tf.get_variable(name = 'kernel{}'.format(layer),
                             shape = (field_size * layer_size_prev, layer_size_curr))
    xkk = tf.matmul(zk, kernel)
    xkk = tf.transpose(xkk, perm = [0,2,1]) # batch * HK * D
    add_layer_summary( 'Xk_{}'.format(layer), xkk )
    return xkk


def cin_layer(x0, cin_layer_size, emb_size, field_size):
    cin_output_list = []

    cin_layer_size.insert(0, field_size) # insert field dimension for input
    with tf.variable_scope('Cin_component'):
        xk = x0
        for layer in range(1, len(cin_layer_size)):
            with tf.variable_scope('Cin_layer{}'.format(layer)):
                # Do cross
                xk = cross_op(xk, x0, cin_layer_size[layer-1], cin_layer_size[layer],
                              layer, emb_size, field_size ) # batch * HK * D
                # sum pooling on dimension axis
                cin_output_list.append(tf.reduce_sum(xk, 2)) # batch * HK

    return tf.concat(cin_output_list, axis=1)

@tf_estimator_model
def model_fn_dense(features, labels, mode, params):
    dense_feature, sparse_feature = build_features()
    dense_input = tf.feature_column.input_layer(features, dense_feature)
    sparse_input = tf.feature_column.input_layer(features, sparse_feature)

    # Linear part
    with tf.variable_scope('Linear_component'):
        linear_output = tf.layers.dense( sparse_input, units=1 )
        add_layer_summary( 'linear_output', linear_output )

    # Deep part
    dense_output = stack_dense_layer( dense_input, params['hidden_units'],
                               params['dropout_rate'], params['batch_norm'],
                               mode, add_summary=True )
    # CIN part
    emb_size = dense_feature[0].variable_shape.as_list()[-1]
    field_size = len(dense_feature)
    embedding_matrix = tf.reshape(dense_input, [-1, field_size, emb_size]) # batch * field_size * emb_size
    add_layer_summary('embedding_matrix', embedding_matrix)

    cin_output = cin_layer(embedding_matrix, params['cin_layer_size'], emb_size, field_size)

    with tf.variable_scope('output'):
        y = tf.concat([dense_output, cin_output,linear_output], axis=1)
        y = tf.layers.dense(y, units= 1)
        add_layer_summary( 'output', y )

    return y

FiBiNET

模型结构

看FiBiNET前能够先了解下Squeeze-and-Excitation Network,感兴趣能够看下这篇博客Squeeze-and-Excitation Networks。

FiBiNET的主要创新是应用SENET学习每一个特征的重要性，加权获得新的Embedding矩阵。在FiBiNET以前，AFM，PNN，DCN和上面的xDeepFM都是在特征交互以后才用attention, 加权等方式学习特征交互的权重，而FiBiNET在保留这部分的同时，在Embedding部分就考虑特征自身的权重。模型结构以下

原始Embedding，和通过SENET调整过权重的新Embedding，在Bilinear-interaction层学习二阶交互特征，拼接后，再通过MLP进一步学习高阶特征。和paper notation保持一致（啊啊啊你们能不能统一下notation搞的我本身看本身的注释都蒙圈），f个特征，k维embedding

SENET层

SENET层学习每一个特征的权重对Embedding进行加权，分为如下3步

1. Squeeze
   把\(f*k\)的Embedding矩阵压缩成\(f*1\), 压缩方式不固定，SENET原paper用的max_pooling,做者用的sum_pooling，感受这里压缩方式应该取决于Embedding的信息表达

\[\begin{align} E &= [e_1,...,e_f] \\ Z &= [z_1,...,z_f] \\ z_i &= F_{squeeze}(e_i) = \frac{1}{k}\sum_{i=1}^K e_i \\ \end{align} \]

2. Excitation
   Excitation是一个两层的全链接层，经过先降维再升维的方式过滤一些无用特征，降维的幅度经过额外变量\(r\)来控制，第一层权重\(W_1 \in R^{f*f/r}\),第二层权重\(W_2 \in R^{f/r*f}\)。这里r越高，压缩的幅度越高，最终的权重会更集中,反之会更分散。

\[A = \sigma_2(W_2·\sigma_1(W_1·Z)) \]

3. Re-weight
   最后一步就是用Excitation获得的每一个特征的权重对Embedding进行加权获得新Embedding

\[E_{new} = F_{Reweight}(A,E) = [a_1·e_1, ...,a_f·e_f ] \]

在收入数据集上进行尝试，r=2时会有46%的embedding特征权重为0，因此SENET会在特征交互前先过滤部分对target无用的特征来增长有效特征的权重

Bilinear-Interaction层

做者提出内积和element-wise乘积都不足以捕捉特征交互信息，所以进一步引入权重W，如下面的方式进行特征交互

\[v_i · W \odot v_j \]

其中W有三种选择，能够全部特征交互共享一个权重矩阵(Field-All),或者每一个特征和其余特征的交互共享权重(Field-Each), 再或者每一个特征交互一个权重(Field-Interaction) 具体的优劣感受须要casebycase来试，不过通常仍是照着数据越少参数越少的逻辑来整。

原始Embedding和调整权重后的Embedding在Bilinear-Interaction学习交互特征后，拼接成shallow 层，再通过全链接层来学习更高阶的特征交互。后面的属于常规操做这里就再也不细说。

咱们不去吐槽FiBiNET能够加入wide&deep框架来捕捉低阶特征信息和任意高阶信息，更多把FiBiNET提供的SENET特征权重的思路放到本身的工具箱中就好。

代码实现

def Bilinear_layer(embedding_matrix, field_size, emb_size, type, name):
    # Bilinear_layer: combine inner and element-wise product
    interaction_list = []
    with tf.variable_scope('BI_interaction_{}'.format(name)):
        if type == 'field_all':
            weight = tf.get_variable( shape=(emb_size, emb_size), initializer=tf.truncated_normal_initializer(),
                                      name='Bilinear_weight_{}'.format(name) )
        for i in range(field_size):
            if type == 'field_each':
                weight = tf.get_variable( shape=(emb_size, emb_size), initializer=tf.truncated_normal_initializer(),
                                          name='Bilinear_weight_{}_{}'.format(i, name) )
            for j in range(i+1, field_size):
                if type == 'field_interaction':
                    weight = tf.get_variable( shape=(emb_size, emb_size), initializer=tf.truncated_normal_initializer(),
                                          name='Bilinear_weight_{}_{}_{}'.format(i,j, name) )
                vi = tf.gather(embedding_matrix, indices = i, axis =1, batch_dims =0, name ='v{}'.format(i)) # batch * emb_size
                vj = tf.gather(embedding_matrix, indices = j, axis =1, batch_dims =0, name ='v{}'.format(j)) # batch * emb_size
                pij = tf.matmul(tf.multiply(vi,vj), weight) # bilinear : vi * wij \odot vj
                interaction_list.append(pij)

        combination = tf.stack(interaction_list, axis =1 ) # batch * emb_size * (Field_size * (Field_size-1)/2)
        combination = tf.reshape(combination, shape = [-1, int(emb_size * (field_size * (field_size-1) /2)) ]) # batch * ~
        add_layer_summary( 'bilinear_output', combination )

    return combination


def SENET_layer(embedding_matrix, field_size, emb_size, pool_op, ratio):
    with tf.variable_scope('SENET_layer'):
        # squeeze embedding to scaler for each field
        with tf.variable_scope('pooling'):
            if pool_op == 'max':
                z = tf.reduce_max(embedding_matrix, axis=2) # batch * field_size * emb_size -> batch * field_size
            else:
                z = tf.reduce_mean(embedding_matrix, axis=2)
            add_layer_summary('pooling scaler', z)

        # excitation learn the weight of each field from above scaler
        with tf.variable_scope('excitation'):
            z1 = tf.layers.dense(z, units = field_size//ratio, activation = 'relu')
            a = tf.layers.dense(z1, units= field_size, activation = 'relu') # batch * field_size
            add_layer_summary('exciitation weight', a )

        # re-weight embedding with weight
        with tf.variable_scope('reweight'):
            senet_embedding = tf.multiply(embedding_matrix, tf.expand_dims(a, axis = -1)) # (batch * field * emb) * ( batch * field * 1)
            add_layer_summary('senet_embedding', senet_embedding) # batch * field_size * emb_size

        return senet_embedding

@tf_estimator_model
def model_fn_dense(features, labels, mode, params):
    dense_feature, sparse_feature = build_features()
    dense_input = tf.feature_column.input_layer(features, dense_feature)
    sparse_input = tf.feature_column.input_layer(features, sparse_feature)

    # Linear part
    with tf.variable_scope('Linear_component'):
        linear_output = tf.layers.dense( sparse_input, units=1 )
        add_layer_summary( 'linear_output', linear_output )

    field_size = len(dense_feature)
    emb_size = dense_feature[0].variable_shape.as_list()[-1]
    embedding_matrix = tf.reshape(dense_input, [-1, field_size, emb_size])

    # SENET_layer to get new embedding matrix
    senet_embedding_matrix = SENET_layer(embedding_matrix, field_size, emb_size,
                                         pool_op = params['pool_op'], ratio= params['senet_ratio'])

    # combination layer & BI_interaction
    BI_org = Bilinear_layer(embedding_matrix, field_size, emb_size, type = params['bilinear_type'], name = 'org')
    BI_senet = Bilinear_layer(senet_embedding_matrix, field_size, emb_size, type = params['bilinear_type'], name = 'senet')

    combination_layer = tf.concat([BI_org, BI_senet] , axis =1)

    # Deep part
    dense_output = stack_dense_layer(combination_layer, params['hidden_units'],
                               params['dropout_rate'], params['batch_norm'],
                               mode, add_summary=True )

    with tf.variable_scope('output'):
        y = dense_output + linear_output
        add_layer_summary( 'output', y )

    return y

CTR学习笔记&代码实现系列👇

https://github.com/DSXiangLi/CTR
CTR学习笔记&代码实现1-深度学习的前奏 LR->FFM
CTR学习笔记&代码实现2-深度ctr模型 MLP->Wide&Deep
CTR学习笔记&代码实现3-深度ctr模型 FNN->PNN->DeepFM
CTR学习笔记&代码实现4-深度ctr模型 NFM/AFM
CTR学习笔记&代码实现5-深度ctr模型 DeepCrossing -> Deep&Cross

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Ref

1. Jianxun Lian, 2018, xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systems
2. Tongwen Huang, 2019, FiBiNET: Combining Feature Importance and Bilinear feature Interaction for Click-Through Rate Prediction
3. Jie Hu, 2017, Squeeze-and-Excitation Networks
4. https://zhuanlan.zhihu.com/p/72931811
5. https://zhuanlan.zhihu.com/p/79659557
6. https://zhuanlan.zhihu.com/p/57162373
7. https://github.com/qiaoguan/deep-ctr-prediction