測驗題：參考博文

筆記：W2.自然語言處理與詞嵌入

作業1：

• 加載預訓練的 單詞向量，用 c o s ( θ ) cos(\theta) cos(θ) 余弦夾角 測量相似度
• 使用詞嵌入解決類比問題
• 修改詞嵌入降低性比歧視

import numpy as np
from w2v_utils import *

這個作業使用 50-維的 GloVe vectors 表示單詞

words, word_to_vec_map = read_glove_vecs('data/glove.6B.50d.txt')

1. 余弦相似度

CosineSimilarity(u, v) = u . v ∣ ∣ u ∣ ∣ 2 ∣ ∣ v ∣ ∣ 2 = c o s ( θ ) \text{CosineSimilarity(u, v)} = \frac {u . v} {||u||_2 ||v||_2} = cos(\theta) CosineSimilarity(u, v)=∣∣u∣∣2?∣∣v∣∣2?u.v?=cos(θ)

其中 ∣ ∣ u ∣ ∣ 2 = ∑ i = 1 n u i 2 ||u||_2 = \sqrt{\sum_{i=1}^{n} u_i^2} ∣∣u∣∣2?=∑i=1n?ui2? ?

# GRADED FUNCTION: cosine_similarity

def cosine_similarity(u, v):
    """
    Cosine similarity reflects the degree of similariy between u and v
        
    Arguments:
        u -- a word vector of shape (n,)          
        v -- a word vector of shape (n,)

    Returns:
        cosine_similarity -- the cosine similarity between u and v defined by the formula above.
    """
    
    distance = 0.0
    
    ### START CODE HERE ###
    # Compute the dot product between u and v (≈1 line)
    dot = np.dot(u, v)
    # Compute the L2 norm of u (≈1 line)
    norm_u = np.linalg.norm(u)
    
    # Compute the L2 norm of v (≈1 line)
    norm_v = np.linalg.norm(v)
    # Compute the cosine similarity defined by formula (1) (≈1 line)
    cosine_similarity = dot/(norm_u*norm_v)
    ### END CODE HERE ###
    
    return cosine_similarity

2. 單詞類比

例如：男人：女人 --> 國王：王后

# GRADED FUNCTION: complete_analogy

def complete_analogy(word_a, word_b, word_c, word_to_vec_map):
    """
    Performs the word analogy task as explained above: a is to b as c is to ____. 
    
    Arguments:
    word_a -- a word, string
    word_b -- a word, string
    word_c -- a word, string
    word_to_vec_map -- dictionary that maps words to their corresponding vectors. 
    
    Returns:
    best_word --  the word such that v_b - v_a is close to v_best_word - v_c, as measured by cosine similarity
    """
    
    # convert words to lower case
    word_a, word_b, word_c = word_a.lower(), word_b.lower(), word_c.lower()
    
    ### START CODE HERE ###
    # Get the word embeddings v_a, v_b and v_c (≈1-3 lines)
    e_a, e_b, e_c = word_to_vec_map[word_a],word_to_vec_map[word_b],word_to_vec_map[word_c]
    ### END CODE HERE ###
    
    words = word_to_vec_map.keys()
    max_cosine_sim = -100              # Initialize max_cosine_sim to a large negative number
    best_word = None                   # Initialize best_word with None, it will help keep track of the word to output

    # loop over the whole word vector set
    for w in words:        
        # to avoid best_word being one of the input words, pass on them.
        if w in [word_a, word_b, word_c] :
            continue
        
        ### START CODE HERE ###
        # Compute cosine similarity between the vector (e_b - e_a) and the vector ((w's vector representation) - e_c)  (≈1 line)
        cosine_sim = cosine_similarity(e_b-e_a, word_to_vec_map[w]-e_c)
        
        # If the cosine_sim is more than the max_cosine_sim seen so far,
            # then: set the new max_cosine_sim to the current cosine_sim and the best_word to the current word (≈3 lines)
        if cosine_sim > max_cosine_sim:
            max_cosine_sim = cosine_sim
            best_word = w
        ### END CODE HERE ###
        
    return best_word

測驗：

triads_to_try = [('italy', 'italian', 'spain'), ('india', 'delhi', 'japan'), ('man', 'woman', 'boy'), ('small', 'smaller', 'large')]
for triad in triads_to_try:
    print ('{} -> {} :: {} -> {}'.format( *triad, complete_analogy(*triad,word_to_vec_map)))

輸出：

italy -> italian :: spain -> spanish
india -> delhi :: japan -> tokyo
man -> woman :: boy -> girl
small -> smaller :: large -> larger

額外測驗：

good -> ok :: bad -> oops（糟糕）
father -> dad :: mother -> mom

3. 詞向量糾偏

研究反映在單詞嵌入中的性別偏見，并探索減少這種偏見的演算法

g = word_to_vec_map['woman'] - word_to_vec_map['man']
print(g)

輸出：向量（50維）

[-0.087144    0.2182     -0.40986    -0.03922    -0.1032      0.94165
 -0.06042     0.32988     0.46144    -0.35962     0.31102    -0.86824
  0.96006     0.01073     0.24337     0.08193    -1.02722    -0.21122
  0.695044   -0.00222     0.29106     0.5053     -0.099454    0.40445
  0.30181     0.1355     -0.0606     -0.07131    -0.19245    -0.06115
 -0.3204      0.07165    -0.13337    -0.25068714 -0.14293    -0.224957
 -0.149       0.048882    0.12191    -0.27362    -0.165476   -0.20426
  0.54376    -0.271425   -0.10245    -0.32108     0.2516     -0.33455
 -0.04371     0.01258   ]

print ('List of names and their similarities with constructed vector:')

# girls and boys name
name_list = ['john', 'marie', 'sophie', 'ronaldo', 'priya', 'rahul', 'danielle', 'reza', 'katy', 'yasmin']

for w in name_list:
    print (w, cosine_similarity(word_to_vec_map[w], g))

輸出：

List of names and their similarities with constructed vector:
john -0.23163356145973724
marie 0.315597935396073
sophie 0.31868789859418784
ronaldo -0.31244796850329437
priya 0.17632041839009402
rahul -0.16915471039231716
danielle 0.24393299216283895
reza -0.07930429672199553
katy 0.2831068659572615
yasmin 0.2331385776792876

可以看出，

• 女性的名字往往與向量 𝑔 有正的余弦相似性，
• 而男性的名字往往有負的余弦相似性，結果似乎可以接受，

試試其他的詞語

print('Other words and their similarities:')
word_list = ['lipstick', 'guns', 'science', 'arts', 'literature', 'warrior','doctor', 'tree', 'receptionist', 
             'technology',  'fashion', 'teacher', 'engineer', 'pilot', 'computer', 'singer']
for w in word_list:
    print (w, cosine_similarity(word_to_vec_map[w], g))

輸出：

Other words and their similarities:
lipstick 0.2769191625638267
guns -0.1888485567898898
science -0.06082906540929701
arts 0.008189312385880337
literature 0.06472504433459932
warrior -0.20920164641125288
doctor 0.11895289410935041
tree -0.07089399175478091
receptionist 0.3307794175059374
technology -0.13193732447554302
fashion 0.03563894625772699
teacher 0.17920923431825664
engineer -0.0803928049452407
pilot 0.0010764498991916937
computer -0.10330358873850498
singer 0.1850051813649629

這些結果反映了某些性別歧視，例如，“computer 計算機”更接近“man 男人”，“literature 文學”更接近“woman 女人”，

下面看到如何使用Boliukbasi等人2016年提出的演算法來減少這些向量的偏差，

請注意，有些詞對，如“演員”/“女演員”或“祖母”/“祖父”應保持性別特異性，而其他詞如“接待員”或“技術”應保持中立，即與性別無關，糾偏時，你必須區別對待這兩種型別的單詞

3.1 消除對非性別詞語的偏見

e b i a s _ c o m p o n e n t = e ? g ∣ ∣ g ∣ ∣ 2 2 ? g e^{bias\_component} = \frac{e \cdot g}{||g||_2^2} * g ebias_component=∣∣g∣∣22?e?g??g

e d e b i a s e d = e ? e b i a s _ c o m p o n e n t e^{debiased} = e - e^{bias\_component} edebiased=e?ebias_component

def neutralize(word, g, word_to_vec_map):
    """
    Removes the bias of "word" by projecting it on the space orthogonal to the bias axis. 
    This function ensures that gender neutral words are zero in the gender subspace.
    
    Arguments:
        word -- string indicating the word to debias
        g -- numpy-array of shape (50,), corresponding to the bias axis (such as gender)
        word_to_vec_map -- dictionary mapping words to their corresponding vectors.
    
    Returns:
        e_debiased -- neutralized word vector representation of the input "word"
    """
    
    ### START CODE HERE ###
    # Select word vector representation of "word". Use word_to_vec_map. (≈ 1 line)
    e = word_to_vec_map[word]
    
    # Compute e_biascomponent using the formula give above. (≈ 1 line)
    e_biascomponent = np.dot(e, g)/np.linalg.norm(g)**2*g
 
    # Neutralize e by substracting e_biascomponent from it 
    # e_debiased should be equal to its orthogonal projection. (≈ 1 line)
    e_debiased = e - e_biascomponent
    ### END CODE HERE ###
    
    return e_debiased

測驗：

e = "receptionist"
print("cosine similarity between " + e + " and g, before neutralizing: ", cosine_similarity(word_to_vec_map["receptionist"], g))

e_debiased = neutralize("receptionist", g, word_to_vec_map)
print("cosine similarity between " + e + " and g, after neutralizing: ", cosine_similarity(e_debiased, g))

輸出：

cosine similarity between receptionist and g, 
	before neutralizing:  0.3307794175059374
cosine similarity between receptionist and g, 
	after neutralizing:  -2.099120994400013e-17

糾偏以后，receptionist（接待員）與性別的相似度接近于 0，既不偏向男人，也不偏向女人

3.2 性別詞的均衡演算法

如何將糾偏應用于單詞對，例如“女演員”和“演員”，
均衡化應用：只希望通過性別屬性而有所不同的單詞對，
作為一個具體的例子，假設“女演員”比“演員”更接近“保姆”，通過對“保姆”進行中性化，我們可以減少與保姆相關的性別刻板印象，但這仍然不能保證“演員”和“女演員”與“保姆”的距離相等，均衡演算法可以處理這一點，

μ = e w 1 + e w 2 2 \mu = \frac{e_{w1} + e_{w2}}{2} μ=2ew1?+ew2??

μ B = μ ? bias_axis ∣ ∣ bias_axis ∣ ∣ 2 2 ? bias_axis \mu_{B} = \frac {\mu \cdot \text{bias\_axis}}{||\text{bias\_axis}||_2^2} *\text{bias\_axis} μB?=∣∣bias_axis∣∣22?μ?bias_axis??bias_axis

μ ⊥ = μ ? μ B \mu_{\perp} = \mu - \mu_{B} μ⊥?=μ?μB?

e w 1 B = e w 1 ? bias_axis ∣ ∣ bias_axis ∣ ∣ 2 2 ? bias_axis e_{w1B} = \frac {e_{w1} \cdot \text{bias\_axis}}{||\text{bias\_axis}||_2^2} *\text{bias\_axis} ew1B?=∣∣bias_axis∣∣22?ew1??bias_axis??bias_axis

e w 2 B = e w 2 ? bias_axis ∣ ∣ bias_axis ∣ ∣ 2 2 ? bias_axis e_{w2B} = \frac {e_{w2} \cdot \text{bias\_axis}}{||\text{bias\_axis}||_2^2} *\text{bias\_axis} ew2B?=∣∣bias_axis∣∣22?ew2??bias_axis??bias_axis

e w 1 B c o r r e c t e d = ∣ 1 ? ∣ ∣ μ ⊥ ∣ ∣ 2 2 ∣ ? e w1B ? μ B ∣ ( e w 1 ? μ ⊥ ) ? μ B ) ∣ e_{w1B}^{corrected} = \sqrt{ |{1 - ||\mu_{\perp} ||^2_2} |} * \frac{e_{\text{w1B}} - \mu_B} {|(e_{w1} - \mu_{\perp}) - \mu_B)|} ew1Bcorrected?=∣1?∣∣μ⊥?∣∣22?∣ ??∣(ew1??μ⊥?)?μB?)∣ew1B??μB??

e w 2 B c o r r e c t e d = ∣ 1 ? ∣ ∣ μ ⊥ ∣ ∣ 2 2 ∣ ? e w2B ? μ B ∣ ( e w 2 ? μ ⊥ ) ? μ B ) ∣ e_{w2B}^{corrected} = \sqrt{ |{1 - ||\mu_{\perp} ||^2_2} |} * \frac{e_{\text{w2B}} - \mu_B} {|(e_{w2} - \mu_{\perp}) - \mu_B)|} ew2Bcorrected?=∣1?∣∣μ⊥?∣∣22?∣ ??∣(ew2??μ⊥?)?μB?)∣ew2B??μB??

e 1 = e w 1 B c o r r e c t e d + μ ⊥ e_1 = e_{w1B}^{corrected} + \mu_{\perp} e1?=ew1Bcorrected?+μ⊥?

e 2 = e w 2 B c o r r e c t e d + μ ⊥ e_2 = e_{w2B}^{corrected} + \mu_{\perp} e2?=ew2Bcorrected?+μ⊥?

def equalize(pair, bias_axis, word_to_vec_map):
    """
    Debias gender specific words by following the equalize method described in the figure above.
    
    Arguments:
    pair -- pair of strings of gender specific words to debias, e.g. ("actress", "actor") 
    bias_axis -- numpy-array of shape (50,), vector corresponding to the bias axis, e.g. gender
    word_to_vec_map -- dictionary mapping words to their corresponding vectors
    
    Returns
    e_1 -- word vector corresponding to the first word
    e_2 -- word vector corresponding to the second word
    """
    
    ### START CODE HERE ###
    # Step 1: Select word vector representation of "word". Use word_to_vec_map. (≈ 2 lines)
    w1, w2 = pair[0], pair[1]
    e_w1, e_w2 = word_to_vec_map[w1], word_to_vec_map[w2]
    
    # Step 2: Compute the mean of e_w1 and e_w2 (≈ 1 line)
    mu = (e_w1+e_w2)/2

    # Step 3: Compute the projections of mu over the bias axis and the orthogonal axis (≈ 2 lines)
    mu_B = np.dot(mu, bias_axis)/np.linalg.norm(bias_axis)**2*bias_axis
    mu_orth = mu-mu_B

    # Step 4: Use equations (7) and (8) to compute e_w1B and e_w2B (≈2 lines)
    e_w1B = np.dot(e_w1,bias_axis)/np.linalg.norm(bias_axis)**2*bias_axis
    e_w2B = np.dot(e_w2,bias_axis)/np.linalg.norm(bias_axis)**2*bias_axis
        
    # Step 5: Adjust the Bias part of e_w1B and e_w2B using the formulas (9) and (10) given above (≈2 lines)
    corrected_e_w1B = np.sqrt(np.abs(1-np.linalg.norm(mu_orth)**2))*np.divide((e_w1B-mu_B),np.abs(e_w1-mu_orth-mu_B))
    corrected_e_w2B = np.sqrt(np.abs(1-np.linalg.norm(mu_orth)**2))*np.divide((e_w2B-mu_B),np.abs(e_w2-mu_orth-mu_B))

    # Step 6: Debias by equalizing e1 and e2 to the sum of their corrected projections (≈2 lines)
    e1 = corrected_e_w1B+mu_orth
    e2 = corrected_e_w2B+mu_orth
                                                                
    ### END CODE HERE ###
    
    return e1, e2

測驗：

print("cosine similarities before equalizing:")
print("cosine_similarity(word_to_vec_map[\"man\"], gender) = ", cosine_similarity(word_to_vec_map["man"], g))
print("cosine_similarity(word_to_vec_map[\"woman\"], gender) = ", cosine_similarity(word_to_vec_map["woman"], g))
print()
e1, e2 = equalize(("man", "woman"), g, word_to_vec_map)
print("cosine similarities after equalizing:")
print("cosine_similarity(e1, gender) = ", cosine_similarity(e1, g))
print("cosine_similarity(e2, gender) = ", cosine_similarity(e2, g))

輸出：

cosine similarities before equalizing:
cosine_similarity(word_to_vec_map["man"], gender) =  -0.11711095765336832
cosine_similarity(word_to_vec_map["woman"], gender) =  0.35666618846270376

cosine similarities after equalizing:
cosine_similarity(e1, gender) =  -0.7165727525843935
cosine_similarity(e2, gender) =  0.7396596474928909

平衡以后，相似度符號相反，數值接近

作業2：Emojify表情生成

使用 word vector representations 建立 Emojifier

讓你的訊息更有表現力😁，使用單詞向量的話，可以是你的單詞沒有在該表情的關聯里面，也能學習到可以使用該表情，

• 匯入一些包

import numpy as np
from emo_utils import *
import emoji
import matplotlib.pyplot as plt

%matplotlib inline

1. Baseline model: Emojifier-V1

1.1 資料集

X：127個句子（字串）
Y：整型 標簽 0 - 4 ，是相關的句子的表情

• 加載資料集，訓練集（127個樣本），測驗集（56個樣本）

X_train, Y_train = read_csv('data/train_emoji.csv')
X_test, Y_test = read_csv('data/tesss.csv')

maxLen = len(max(X_train, key=len).split())
print(max(X_train, key=len).split())

輸出：

['I', 'am', 'so', 'impressed', 'by', 'your', 'dedication', 'to', 'this', 'project']

最長的句子是10個單詞

• 查看資料集

index = 3
print(X_train[index], label_to_emoji(Y_train[index]))

輸出：
Miss you so much ??

1.2 模型預覽

為了方便，把 Y 的形狀從 ( m , 1 ) (m,1) (m,1) 改成 one-hot 表示 ( m , 5 ) (m,5) (m,5)

Y_oh_train = convert_to_one_hot(Y_train, C = 5)
Y_oh_test = convert_to_one_hot(Y_test, C = 5)

index = 52
print(Y_train[index], "is converted into one hot", Y_oh_train[index])

輸出：

3 is converted into one hot [0. 0. 0. 1. 0.]

1.3 實作 Emojifier-V1

使用預訓練的 50-dimensional GloVe embeddings

word_to_index, index_to_word, word_to_vec_map = read_glove_vecs('data/glove.6B.50d.txt')

• 檢查下是否正確

word = "cucumber"
index = 289846
print("the index of", word, "in the vocabulary is", word_to_index[word])
print("the", str(index) + "th word in the vocabulary is", index_to_word[index])

輸出：

the index of cucumber in the vocabulary is 113317
the 289846th word in the vocabulary is potatos

實作 sentence_to_avg()：

• 轉換每個句子為小寫，并切分成單詞
• 每個句子的單詞，使用 GloVe 向量表示，然后求句子的平均

# GRADED FUNCTION: sentence_to_avg

def sentence_to_avg(sentence, word_to_vec_map):
    """
    Converts a sentence (string) into a list of words (strings). Extracts the GloVe representation of each word
    and averages its value into a single vector encoding the meaning of the sentence.
    
    Arguments:
    sentence -- string, one training example from X
    word_to_vec_map -- dictionary mapping every word in a vocabulary into its 50-dimensional vector representation
    
    Returns:
    avg -- average vector encoding information about the sentence, numpy-array of shape (50,)
    """
    
    ### START CODE HERE ###
    # Step 1: Split sentence into list of lower case words (≈ 1 line)
    words = sentence.lower().split()

    # Initialize the average word vector, should have the same shape as your word vectors.
    avg = np.zeros(word_to_vec_map[words[0]].shape)
    
    # Step 2: average the word vectors. You can loop over the words in the list "words".
    for w in words:
        avg += word_to_vec_map[w]
    avg /= len(words)
    
    ### END CODE HERE ###
    
    return avg

測驗：

avg = sentence_to_avg("Morrocan couscous is my favorite dish", word_to_vec_map)
print("avg = ", avg)

輸出：

avg =  [-0.008005    0.56370833 -0.50427333  0.258865    0.55131103  0.03104983
 -0.21013718  0.16893933 -0.09590267  0.141784   -0.15708967  0.18525867
  0.6495785   0.38371117  0.21102167  0.11301667  0.02613967  0.26037767
  0.05820667 -0.01578167 -0.12078833 -0.02471267  0.4128455   0.5152061
  0.38756167 -0.898661   -0.535145    0.33501167  0.68806933 -0.2156265
  1.797155    0.10476933 -0.36775333  0.750785    0.10282583  0.348925
 -0.27262833  0.66768    -0.10706167 -0.283635    0.59580117  0.28747333
 -0.3366635   0.23393817  0.34349183  0.178405    0.1166155  -0.076433
  0.1445417   0.09808667]

模型

用sentence_to_avg() 處理完以后，進行前向傳播、計算損失、后向傳播更新引數

z ( i ) = W . a v g ( i ) + b z^{(i)} = W . avg^{(i)} + b z(i)=W.avg(i)+b

a ( i ) = s o f t m a x ( z ( i ) ) a^{(i)} = softmax(z^{(i)}) a(i)=softmax(z(i))

L ( i ) = ? ∑ k = 0 n y ? 1 Y o h k ( i ) ? l o g ( a k ( i ) ) \mathcal{L}^{(i)} = - \sum_{k = 0}^{n_y - 1} Yoh^{(i)}_k * log(a^{(i)}_k) L(i)=?k=0∑ny??1?Yohk(i)??log(ak(i)?)

# GRADED FUNCTION: model

def model(X, Y, word_to_vec_map, learning_rate = 0.01, num_iterations = 400):
    """
    Model to train word vector representations in numpy.
    
    Arguments:
    X -- input data, numpy array of sentences as strings, of shape (m, 1)
    Y -- labels, numpy array of integers between 0 and 7, numpy-array of shape (m, 1)
    word_to_vec_map -- dictionary mapping every word in a vocabulary into its 50-dimensional vector representation
    learning_rate -- learning_rate for the stochastic gradient descent algorithm
    num_iterations -- number of iterations
    
    Returns:
    pred -- vector of predictions, numpy-array of shape (m, 1)
    W -- weight matrix of the softmax layer, of shape (n_y, n_h)
    b -- bias of the softmax layer, of shape (n_y,)
    """
    
    np.random.seed(1)

    # Define number of training examples
    m = Y.shape[0]                          # number of training examples
    n_y = 5                                 # number of classes  
    n_h = 50                                # dimensions of the GloVe vectors 
    
    # Initialize parameters using Xavier initialization
    W = np.random.randn(n_y, n_h) / np.sqrt(n_h)
    b = np.zeros((n_y,))
    
    # Convert Y to Y_onehot with n_y classes
    Y_oh = convert_to_one_hot(Y, C = n_y) 
    
    # Optimization loop
    for t in range(num_iterations):                       # Loop over the number of iterations
        for i in range(m):                                # Loop over the training examples
            
            ### START CODE HERE ### (≈ 4 lines of code)
            # Average the word vectors of the words from the i'th training example
            avg = sentence_to_avg(X[i], word_to_vec_map)

            # Forward propagate the avg through the softmax layer
            z = np.dot(W, avg)+b
            a = softmax(z)

            # Compute cost using the i'th training label's one hot representation and "A" (the output of the softmax)
            cost = - sum(Y_oh[i]*np.log(a))
            ### END CODE HERE ###
            
            # Compute gradients 
            dz = a - Y_oh[i]
            dW = np.dot(dz.reshape(n_y,1), avg.reshape(1, n_h))
            db = dz

            # Update parameters with Stochastic Gradient Descent
            W = W - learning_rate * dW
            b = b - learning_rate * db
        
        if t % 100 == 0:
            print("Epoch: " + str(t) + " --- cost = " + str(cost))
            pred = predict(X, Y, W, b, word_to_vec_map)

    return pred, W, b

1.4 在訓練集上測驗

print("Training set:")
pred_train = predict(X_train, Y_train, W, b, word_to_vec_map)
print('Test set:')
pred_test = predict(X_test, Y_test, W, b, word_to_vec_map)

輸出：

Training set:
Accuracy: 0.9772727272727273
Test set:
Accuracy: 0.8571428571428571

隨機猜測的話，平均概率是 20%（1/5），模型的效果很不錯，在只有127個訓練樣本的情況下

讓我們來測驗：

• 我們在訓練集里看到了 I love you 有標簽 ??
• 我們來檢查下使用 adore（愛慕） （該詞沒有在訓練集出現過）

X_my_sentences = np.array(["i adore you", "i love you", "funny lol", "lets play with a ball", "food is ready", "not feeling happy"])
Y_my_labels = np.array([[0], [0], [2], [1], [4],[3]])

pred = predict(X_my_sentences, Y_my_labels , W, b, word_to_vec_map)
print_predictions(X_my_sentences, pred)

輸出：

Accuracy: 0.8333333333333334（5/6，最后一個錯了）

i adore you ??（adore 跟 love 有相似的 embedding ）
i love you ??
funny lol 😄
lets play with a ball ?
food is ready 🍴
not feeling happy 😄（識別錯誤，不能發現 not 這類組合詞）

檢查錯誤：
列印混淆矩陣可以幫助了解哪些樣本模型預測不準，
一個混淆矩陣顯示了一個標簽是一個類（真實標簽）的例子被演算法用不同的類（預測錯誤）錯誤標記的頻率

print(Y_test.shape)
print('           '+ label_to_emoji(0)+ '    ' + label_to_emoji(1) + '    ' +  label_to_emoji(2)+ '    ' + label_to_emoji(3)+'   ' + label_to_emoji(4))
print(pd.crosstab(Y_test, pred_test.reshape(56,), rownames=['Actual'], colnames=['Predicted'], margins=True))
plot_confusion_matrix(Y_test, pred_test)

2. Emojifier-V2: Using LSTMs in Keras

讓我們構建一個LSTM模型，它將單詞序列作為輸入，這個模型將能夠考慮單詞順序，
Emojifier-V2 將繼續使用預先訓練過的 word embeddings 來表示單詞，將把它們輸入LSTM，LSTM的任務是預測最合適的表情符號，

• 匯入一些包

import numpy as np
np.random.seed(0)
from keras.models import Model
from keras.layers import Dense, Input, Dropout, LSTM, Activation
from keras.layers.embeddings import Embedding
from keras.preprocessing import sequence
from keras.initializers import glorot_uniform
np.random.seed(1)

2.1 模型預覽

2.2 Keras and mini-batching

為了使樣本能夠批量訓練，我們必須處理句子，使他們的長度都一樣長，長度不夠最大長度的，后面補上一些 0 向量 ( e i , e l o v e , e y o u , 0 ? , 0 ? , … , 0 ? ) (e_{i}, e_{love}, e_{you}, \vec{0}, \vec{0}, \ldots, \vec{0}) (ei?,elove?,eyou?,0 ,0 ,…,0 )

2.3 Embedding 層

https://keras.io/zh/layers/embeddings/

• 先把所有句子的單詞對應的 idx 填好

# GRADED FUNCTION: sentences_to_indices

def sentences_to_indices(X, word_to_index, max_len):
    """
    Converts an array of sentences (strings) into an array of indices corresponding to words in the sentences.
    The output shape should be such that it can be given to `Embedding()` (described in Figure 4). 
    
    Arguments:
    X -- array of sentences (strings), of shape (m, 1)
    word_to_index -- a dictionary containing the each word mapped to its index
    max_len -- maximum number of words in a sentence. You can assume every sentence in X is no longer than this. 
    
    Returns:
    X_indices -- array of indices corresponding to words in the sentences from X, of shape (m, max_len)
    """
    
    m = X.shape[0]                                   # number of training examples
    
    ### START CODE HERE ###
    # Initialize X_indices as a numpy matrix of zeros and the correct shape (≈ 1 line)
    X_indices = np.zeros((m, max_len))
    
    for i in range(m):                               # loop over training examples
        
        # Convert the ith training sentence in lower case and split is into words. You should get a list of words.
        sentence_words = X[i].lower().split()
        
        # Initialize j to 0
        j = 0
        
        # Loop over the words of sentence_words
        for w in sentence_words:
            # Set the (i,j)th entry of X_indices to the index of the correct word.
            X_indices[i, j] = word_to_index[w]
            # Increment j to j + 1
            j = j+1
            
    ### END CODE HERE ###
    
    return X_indices

實作 pretrained_embedding_layer()

• 初始化 詞嵌入矩陣，注意 shape
• 填充 詞嵌入矩陣，從word_to_vec_map里抽取
• 定義 Keras embedding 層，注意設定trainable = False，使之不可被訓練，如果為True，則允許演算法修改詞嵌入的值
• 將 嵌入權重 設定為與 嵌入矩陣 相等

# GRADED FUNCTION: pretrained_embedding_layer

def pretrained_embedding_layer(word_to_vec_map, word_to_index):
    """
    Creates a Keras Embedding() layer and loads in pre-trained GloVe 50-dimensional vectors.
    
    Arguments:
    word_to_vec_map -- dictionary mapping words to their GloVe vector representation.
    word_to_index -- dictionary mapping from words to their indices in the vocabulary (400,001 words)

    Returns:
    embedding_layer -- pretrained layer Keras instance
    """
    
    vocab_len = len(word_to_index) + 1                  # adding 1 to fit Keras embedding (requirement)
    emb_dim = word_to_vec_map["cucumber"].shape[0]      # define dimensionality of your GloVe word vectors (= 50)
    
    ### START CODE HERE ###
    # Initialize the embedding matrix as a numpy array of zeros of shape (vocab_len, dimensions of word vectors = emb_dim)
    emb_matrix = np.zeros((vocab_len, emb_dim))
    
    # Set each row "index" of the embedding matrix to be the word vector representation of the "index"th word of the vocabulary
    for word, index in word_to_index.items():
        emb_matrix[index, :] = word_to_vec_map[word]

    # Define Keras embedding layer with the correct output/input sizes, make it trainable. Use Embedding(...). Make sure to set trainable=False. 
    embedding_layer = Embedding(vocab_len, emb_dim, trainable=False)
    ### END CODE HERE ###

    # Build the embedding layer, it is required before setting the weights of the embedding layer. Do not modify the "None".
    embedding_layer.build((None,))
    
    # Set the weights of the embedding layer to the embedding matrix. Your layer is now pretrained.
    embedding_layer.set_weights([emb_matrix])
    
    return embedding_layer

2.3 建立 Emojifier-V2

https://keras.io/zh/layers/core/#input
https://keras.io/zh/layers/embeddings/#embedding
https://keras.io/zh/layers/recurrent/#lstm
https://keras.io/zh/layers/core/#dropout
https://keras.io/zh/layers/core/#dense
https://keras.io/zh/activations/
https://keras.io/zh/models/about-keras-models/#model

# GRADED FUNCTION: Emojify_V2

def Emojify_V2(input_shape, word_to_vec_map, word_to_index):
    """
    Function creating the Emojify-v2 model's graph.
    
    Arguments:
    input_shape -- shape of the input, usually (max_len,)
    word_to_vec_map -- dictionary mapping every word in a vocabulary into its 50-dimensional vector representation
    word_to_index -- dictionary mapping from words to their indices in the vocabulary (400,001 words)

    Returns:
    model -- a model instance in Keras
    """
    
    ### START CODE HERE ###
    # Define sentence_indices as the input of the graph, it should be of shape input_shape and dtype 'int32' (as it contains indices).
    sentence_indices = Input(input_shape, dtype='int32')
    
    # Create the embedding layer pretrained with GloVe Vectors (≈1 line)
    embedding_layer = pretrained_embedding_layer(word_to_vec_map, word_to_index)
    
    # Propagate sentence_indices through your embedding layer, you get back the embeddings
    embeddings = embedding_layer(sentence_indices)
    
    # Propagate the embeddings through an LSTM layer with 128-dimensional hidden state
    # Be careful, the returned output should be a batch of sequences.
    X = LSTM(128,return_sequences=True)(embeddings)
    # Add dropout with a probability of 0.5
    X = Dropout(rate=0.5)(X)
    # Propagate X trough another LSTM layer with 128-dimensional hidden state
    # Be careful, the returned output should be a single hidden state, not a batch of sequences.
    X = LSTM(128, return_sequences=False)(X)
    # Add dropout with a probability of 0.5
    X = Dropout(rate=0.5)(X)
    # Propagate X through a Dense layer with softmax activation to get back a batch of 5-dimensional vectors.
    X = Dense(5)(X)
    # Add a softmax activation
    X = Activation('softmax')(X)
    
    # Create Model instance which converts sentence_indices into X.
    model = Model(inputs=sentence_indices, outputs=X)
    
    ### END CODE HERE ###
    
    return model

• 創建模型

model = Emojify_V2((maxLen,), word_to_vec_map, word_to_index)
model.summary()

輸出：

Model: "model_1"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_3 (InputLayer)         (None, 10)                0         
_________________________________________________________________
embedding_4 (Embedding)      (None, 10, 50)            20000050  
_________________________________________________________________
lstm_3 (LSTM)                (None, 10, 128)           91648     
_________________________________________________________________
dropout_1 (Dropout)          (None, 10, 128)           0         
_________________________________________________________________
lstm_4 (LSTM)                (None, 128)               131584    
_________________________________________________________________
dropout_2 (Dropout)          (None, 128)               0         
_________________________________________________________________
dense_1 (Dense)              (None, 5)                 645       
_________________________________________________________________
activation_1 (Activation)    (None, 5)                 0         
=================================================================
Total params: 20,223,927
Trainable params: 223,877
Non-trainable params: 20,000,050  注：（400,001個單詞*50詞向量維度）
_________________________________________________________________

• 配置模型

model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

• 訓練模型

轉換 X，Y 的格式

X_train_indices = sentences_to_indices(X_train, word_to_index, maxLen)
Y_train_oh = convert_to_one_hot(Y_train, C = 5)

訓練

model.fit(X_train_indices, Y_train_oh, epochs = 50, batch_size = 32, shuffle=True)

輸出：

WARNING:tensorflow:From c:\program files\python37\lib\site-packages\keras\backend\tensorflow_backend.py:422: The name tf.global_variables is deprecated. Please use tf.compat.v1.global_variables instead.

Epoch 1/50
132/132 [==============================] - 1s 5ms/step - loss: 1.6088 - accuracy: 0.1970
Epoch 2/50
132/132 [==============================] - 0s 582us/step - loss: 1.5221 - accuracy: 0.3636
Epoch 3/50
132/132 [==============================] - 0s 574us/step - loss: 1.4762 - accuracy: 0.3939
(省略)
Epoch 49/50
132/132 [==============================] - 0s 597us/step - loss: 0.0115 - accuracy: 1.0000
Epoch 50/50
132/132 [==============================] - 0s 582us/step - loss: 0.0182 - accuracy: 0.9924

在訓練集上的準確率幾乎 100%

• 在測驗集上測驗

X_test_indices = sentences_to_indices(X_test, word_to_index, max_len = maxLen)
Y_test_oh = convert_to_one_hot(Y_test, C = 5)
loss, acc = model.evaluate(X_test_indices, Y_test_oh)
print()
print("Test accuracy = ", acc)

輸出：

56/56 [==============================] - 0s 2ms/step

Test accuracy =  0.875

測驗集上準確率為 87.5%

• 查看預測錯誤的樣本

# This code allows you to see the mislabelled examples
C = 5
y_test_oh = np.eye(C)[Y_test.reshape(-1)]
X_test_indices = sentences_to_indices(X_test, word_to_index, maxLen)
pred = model.predict(X_test_indices)
for i in range(len(X_test)):
    x = X_test_indices
    num = np.argmax(pred[i])
    if(num != Y_test[i]):
        print('Expected emoji:'+ label_to_emoji(Y_test[i]) + ' prediction: '+ X_test[i] + label_to_emoji(num).strip())

輸出：

Expected emoji:😞 prediction: work is hard 😄
Expected emoji:😞 prediction: This girl is messing with me ??
Expected emoji:😞 prediction: work is horrible 😄
Expected emoji:🍴 prediction: any suggestions for dinner 😄
Expected emoji:😄 prediction: you brighten my day ??
Expected emoji:😞 prediction: go away ?
Expected emoji:🍴 prediction: I did not have breakfast ??

• 用自己的例子測驗

# Change the sentence below to see your prediction. Make sure all the words are in the Glove embeddings.  
x_test = np.array(['not feeling happy'])
X_test_indices = sentences_to_indices(x_test, word_to_index, maxLen)
print(x_test[0] +' '+  label_to_emoji(np.argmax(model.predict(X_test_indices))))

not feeling happy 😞 （這次 LSTM 可以預測 not 這類的組合詞了）
not very happy 😞
very happy 😄
i really love my wife ??

總結：

• 如果你有一個訓練集很小的NLP任務，使用單詞嵌入可以顯著地幫助你的演算法，單詞嵌入允許模型處理測驗集中沒有出現在訓練集中的單詞
• 在Keras（和大多數其他深度學習框架中）中訓練序列模型需要一些重要的細節：

1. 要使用 mini-batches，需要填充序列，以便 mini-batches 中的所有樣本具有相同的長度
2. “Embedding()” 層可以用預先訓練的值初始化，這些值可以是固定的，也可以在資料集中進一步訓練，如果資料集很小就不要接著訓練了（效果不大）
3. LSTM() 有一個名為“return_sequences”的標志，用于決定是回傳每個隱藏狀態還是只回傳最后一個隱藏狀態
4. 可以在LSTM() 之后使用Dropout()來正則化網路

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