《Neural Factorization Machines for Sparse Predictive Analytics》NFM模型及python代码

1 原文

点击【原文】即可进行下载

2 NFM模型

在当今互联网工业界中，有许多预测任务需要用到大量的类别特征。要想将这些类别特征送入到模型中，就必须得将其onehot。但这样一来，就会产生大量的稀疏特征，要想从这些稀疏特征中充分学习到有用的信息，必须要考虑特征之间的相互作用。

FM算法是一种常用的解决方案，因为它充分考虑了二阶特征之间的相互作用。然而FM有一个缺点，就是它仅仅以线性的方式组合了特征，并不能考虑到特征之间的非线性关系。

本文提出了一个称为Neural Factorization Machine (NFM)的模型，来解决上述问题。NFM充分结合了FM提取的二阶线性特征与神经网络提取的高阶非线性特征。总得来说，FM可以被看作一个没有隐含层的NFM，故NFM肯定比FM更具表现力。

模型的输出结果：

上式的第1项与第2项是与FM相似的线性回归部分，第3项是NFM的核心部分，它的网络结构如下：

Embedding Layer和FM、PNN、AFM等的embedding layer是相同的，得到的vector其实就是我们在FM中要学习的隐变量v。

Bi-Interaction Layer 上层得到的输出是一个特征向量的embedding的集合，本层本质上是做一个pooling的操作，让这个embedding向量集合变为一个向量，公式如下：

其中 ⨀代表两个向量对应的元素相乘。显然，该层的输出向量为 kk 维，本层采用的pooling方式与传统的max pool和average pool一样都是线性复杂度的，上式可以变换为：

hidden layers就是多个标准的神经网络全连接层，执行过程如下：

prediction layer的输出即为$f(x)$的值：

3 python

import numpy as np
import tensorflow as tf

from time import time
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.metrics import roc_auc_score

class AFM(BaseEstimator, TransformerMixin):

    def __init__(self, feature_size, field_size,
                 embedding_size=8,
                 deep_layers=[32, 32], deep_init_size = 50,
                 dropout_deep=[0.5, 0.5, 0.5],
                 deep_layer_activation=tf.nn.relu,
                 epoch=10, batch_size=256,
                 learning_rate=0.001, optimizer="adam",
                 batch_norm=0, batch_norm_decay=0.995,
                 verbose=False, random_seed=2016,
                 loss_type="logloss", eval_metric=roc_auc_score,
                greater_is_better=True,
                 use_inner=True):
        assert loss_type in ["logloss", "mse"], \
            "loss_type can be either 'logloss' for classification task or 'mse' for regression task"

        self.feature_size = feature_size
        self.field_size = field_size
        self.embedding_size = embedding_size

        self.deep_layers = deep_layers
        self.deep_init_size = deep_init_size
        self.dropout_dep = dropout_deep
        self.deep_layers_activation = deep_layer_activation

        self.epoch = epoch
        self.batch_size = batch_size
        self.learning_rate = learning_rate
        self.optimizer_type = optimizer

        self.batch_norm = batch_norm
        self.batch_norm_decay = batch_norm_decay

        self.verbose = verbose
        self.random_seed = random_seed
        self.loss_type = loss_type
        self.eval_metric = eval_metric
        self.greater_is_better = greater_is_better
        self.train_result,self.valid_result = [],[]

        self.use_inner = use_inner

        self._init_graph()

    def _init_graph(self):
        self.graph = tf.Graph()
        with self.graph.as_default():
            tf.set_random_seed(self.random_seed)

            self.feat_index = tf.placeholder(tf.int32,
                                             shape=[None,None],
                                             name='feat_index')
            self.feat_value = tf.placeholder(tf.float32,
                                           shape=[None,None],
                                           name='feat_value')

            self.label = tf.placeholder(tf.float32,shape=[None,1],name='label')
            self.dropout_keep_deep = tf.placeholder(tf.float32,shape=[None],name='dropout_deep_deep')
            self.train_phase = tf.placeholder(tf.bool,name='train_phase')

            self.weights = self._initialize_weights()

            # Embeddings
            self.embeddings = tf.nn.embedding_lookup(self.weights['feature_embeddings'],self.feat_index) # N * F * K
            feat_value = tf.reshape(self.feat_value,shape=[-1,self.field_size,1])
            self.embeddings = tf.multiply(self.embeddings,feat_value) # N * F * K

            # first order term
            self.y_first_order = tf.nn.embedding_lookup(self.weights['feature_bias'], self.feat_index)
            self.y_first_order = tf.reduce_sum(tf.multiply(self.y_first_order, feat_value), 2)


            # second order term
            # sum-square-part
            self.summed_features_emb = tf.reduce_sum(self.embeddings, 1)  # None * k
            self.summed_features_emb_square = tf.square(self.summed_features_emb)  # None * K

            # squre-sum-part
            self.squared_features_emb = tf.square(self.embeddings)
            self.squared_sum_features_emb = tf.reduce_sum(self.squared_features_emb, 1)  # None * K

            # second order
            self.y_second_order = 0.5 * tf.subtract(self.summed_features_emb_square, self.squared_sum_features_emb)

            # Deep component
            self.y_deep = self.y_second_order
            for i in range(0, len(self.deep_layers)):
                self.y_deep = tf.add(tf.matmul(self.y_deep, self.weights["layer_%d" % i]), self.weights["bias_%d" % i])
                self.y_deep = self.deep_layers_activation(self.y_deep)
                self.y_deep = tf.nn.dropout(self.y_deep, self.dropout_keep_deep[i + 1])

            # bias
            self.y_bias = self.weights['bias'] * tf.ones_like(self.label)


            # out
            self.out = tf.add_n([tf.reduce_sum(self.y_first_order,axis=1,keep_dims=True),
                                 tf.reduce_sum(self.y_deep,axis=1,keep_dims=True),
                                 self.y_bias])

            # loss
            if self.loss_type == "logloss":
                self.out = tf.nn.sigmoid(self.out)
                self.loss = tf.losses.log_loss(self.label, self.out)
            elif self.loss_type == "mse":
                self.loss = tf.nn.l2_loss(tf.subtract(self.label, self.out))



            if self.optimizer_type == "adam":
                self.optimizer = tf.train.AdamOptimizer(learning_rate=self.learning_rate, beta1=0.9, beta2=0.999,
                                                        epsilon=1e-8).minimize(self.loss)
            elif self.optimizer_type == "adagrad":
                self.optimizer = tf.train.AdagradOptimizer(learning_rate=self.learning_rate,
                                                           initial_accumulator_value=1e-8).minimize(self.loss)
            elif self.optimizer_type == "gd":
                self.optimizer = tf.train.GradientDescentOptimizer(learning_rate=self.learning_rate).minimize(self.loss)
            elif self.optimizer_type == "momentum":
                self.optimizer = tf.train.MomentumOptimizer(learning_rate=self.learning_rate, momentum=0.95).minimize(
                    self.loss)


            #init
            self.saver = tf.train.Saver()
            init = tf.global_variables_initializer()
            self.sess = tf.Session()
            self.sess.run(init)

            # number of params
            total_parameters = 0
            for variable in self.weights.values():
                shape = variable.get_shape()
                variable_parameters = 1
                for dim in shape:
                    variable_parameters *= dim.value
                total_parameters += variable_parameters
            if self.verbose > 0:
                print("#params: %d" % total_parameters)





    def _initialize_weights(self):
        weights = dict()

        #embeddings
        weights['feature_embeddings'] = tf.Variable(
            tf.random_normal([self.feature_size,self.embedding_size],0.0,0.01),
            name='feature_embeddings')
        weights['feature_bias'] = tf.Variable(tf.random_normal([self.feature_size,1],0.0,1.0),name='feature_bias')
        weights['bias'] = tf.Variable(tf.constant(0.1),name='bias')

        #deep layers
        num_layer = len(self.deep_layers)
        input_size = self.embedding_size
        glorot = np.sqrt(2.0/(input_size + self.deep_layers[0]))

        weights['layer_0'] = tf.Variable(
            np.random.normal(loc=0,scale=glorot,size=(input_size,self.deep_layers[0])),dtype=np.float32
        )
        weights['bias_0'] = tf.Variable(
            np.random.normal(loc=0,scale=glorot,size=(1,self.deep_layers[0])),dtype=np.float32
        )


        for i in range(1,num_layer):
            glorot = np.sqrt(2.0 / (self.deep_layers[i - 1] + self.deep_layers[i]))
            weights["layer_%d" % i] = tf.Variable(
                np.random.normal(loc=0, scale=glorot, size=(self.deep_layers[i - 1], self.deep_layers[i])),
                dtype=np.float32)  # layers[i-1] * layers[i]
            weights["bias_%d" % i] = tf.Variable(
                np.random.normal(loc=0, scale=glorot, size=(1, self.deep_layers[i])),
                dtype=np.float32)  # 1 * layer[i]

        return weights


    def get_batch(self,Xi,Xv,y,batch_size,index):
        start = index * batch_size
        end = (index + 1) * batch_size
        end = end if end < len(y) else len(y)
        return Xi[start:end],Xv[start:end],[[y_] for y_ in y[start:end]]

    # shuffle three lists simutaneously
    def shuffle_in_unison_scary(self, a, b, c):
        rng_state = np.random.get_state()
        np.random.shuffle(a)
        np.random.set_state(rng_state)
        np.random.shuffle(b)
        np.random.set_state(rng_state)
        np.random.shuffle(c)

    def predict(self, Xi, Xv,y):
        """
        :param Xi: list of list of feature indices of each sample in the dataset
        :param Xv: list of list of feature values of each sample in the dataset
        :return: predicted probability of each sample
        """
        # dummy y
        feed_dict = {self.feat_index: Xi,
                     self.feat_value: Xv,
                     self.label: y,
                     self.dropout_keep_deep: [1.0] * len(self.dropout_dep),
                     self.train_phase: True}

        loss = self.sess.run([self.loss], feed_dict=feed_dict)

        return loss


    def fit_on_batch(self,Xi,Xv,y):
        feed_dict = {self.feat_index:Xi,
                     self.feat_value:Xv,
                     self.label:y,
                     self.dropout_keep_deep:self.dropout_dep,
                     self.train_phase:True}

        loss,opt = self.sess.run([self.loss,self.optimizer],feed_dict=feed_dict)

        return loss

    def fit(self, Xi_train, Xv_train, y_train,
            Xi_valid=None, Xv_valid=None, y_valid=None,
            early_stopping=False, refit=False):

        has_valid = Xv_valid is not None
        for epoch in range(self.epoch):
            t1 = time()
            self.shuffle_in_unison_scary(Xi_train, Xv_train, y_train)
            total_batch = int(len(y_train) / self.batch_size)
            for i in range(total_batch):
                Xi_batch, Xv_batch, y_batch = self.get_batch(Xi_train, Xv_train, y_train, self.batch_size, i)
                self.fit_on_batch(Xi_batch, Xv_batch, y_batch)

            if has_valid:
                y_valid = np.array(y_valid).reshape((-1,1))
                loss = self.predict(Xi_valid, Xv_valid, y_valid)
                print("epoch",epoch,"loss",loss)

参考

1、原文：http://xueshu.baidu.com/s?wd=paperuri:(698cc0e22cefdff2b65f7c24c16d5112)&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http://arxiv.org/pdf/1708.05027&ie=utf-8&sc_us=6917339300733978278
2、代码：https://github.com/princewen/tensorflow_practice/blob/master/recommendation/Basic-AFM-Demo/main.py