Recommender System Study Notes - Nomination(3/6)

• Two Tower Model - Architecture + Training

  • Pointwise Training
    • View nomination as binary classification
    • Sample: cos(a,b) -> +1, negative sample: cos(a, b) -> -1
    • Positive : negative = 1:2 / 1:3
  • Pairwise Training
    • Intuntion: cos(a, b+) > cos(a, b-)
    • Triplet hinge loss = max(0, cos(a, b-) + m - cos(a, b+))
    • Triplet logistic loss = log(1 + exp(σ) * cos(a, b-) - cos(a, b+))
  • Listwise Training
    • CrossEntropyLoss

• Two Tower Model - Positive Samples + Negative Samples

  • Positive Sample:
    • Impressed and clicked
  • Negative Sample:
  • Easy negative sample:
    • All items
    • In-batch items
  • Hard negative sample:
    • Nominated, but discarded by ranking
  • Mix easy and hard for training dataset
  • Wrong sampling:
    • Impressed, but not clicked (can be used for training ranking but not nomination)

Two Tower Model(DSSM) - Architecture and Training

Two Tower Model Architecture

Neural Network
    └── Concatenate
        ├── Embedding Layer (User ID)
        │      └── Embedding (Vector Representation)
        ├── Embedding Layers (User Discrete Feature)
        │      └── Embedding (Vector Representation)
        └── Normalization, Binning, etc. (normalize to 1, put into buckets)
               └── User Continuous Features (Vector Representation)

$\cos(a, b) = \frac{a \cdot b}{\|a\|_2 \cdot \|b\|_2}$

                            Cosine Similarity:
                                  /    \
                                /        \
                             a            b
                          /                 \
              Neural Network              Neural Network
                /                                \
         Feature Transformation           Feature Transformation
         /                                          \
User ID, Discrete Features,                 Product ID, Discrete Features,
Continuous Features                         Continuous Features

Two Tower Model Training

• Pointwise (binary classification)
• Pairwise
• Listwise

Pointwise Training

• Intuition: View nomination as binary classification
• positive sample: cos(a,b) -> +1, negative sample: cos(a, b) -> -1
• positive : negative = 1:2 / 1:3

Pairwise Training

                    cos(a, b⁺)          cos(a, b⁻)
                    /      \            /      \
                   /        \          /        \
                b⁺               a                  b⁻
        (Positive Sample)       (User)           (Negative Sample)
                |                  |                    |
        Neural Network      Neural Network     Neural Network
                |                  |                    |
Feature Transformation   Feature Transformation Feature Transformation
                |                  |                    |
    Positive Item Feature     User Features          Negative Item Feature

• Intuntion: cos(a, b+) > cos(a, b-)
• triplet hinge loss = max(0, cos(a, b-) + m - cos(a, b+))
• triplet logistic loss = log(1 + exp(σ) * cos(a, b-) - cos(a, b+))

Listwise Training

CrossEntropyLoss(y, s) = -log(s⁺)

                       +-----------------------+
                       |    CrossEntropyLoss   |
                       +-----------------------+
                                 |
                                 |
                          +-------------------------------+
                          |  Softmax Activation Function  |
                          +-------------------------------+
                                 |
      +------------+------------+-------------+ ... +------------+
      |            |            |             |     |            |
     s⁺         s⁻_1       s⁻_2         ...   s⁻_n
 (Positive)    (Negative)  (Negative)        (Negative)

    |             |             |                     |
    |             |             |                     |
 cos(a, b⁺)   cos(a, b⁻_1)  cos(a, b⁻_2)   ...  cos(a, b⁻_n)

   |              |             |                     |
(Positive)    (Negative)   (Negative)         (Negative)
 Sample         Sample        Sample            Sample

Two Tower Model(DSSM) - Positive Samples + Negative Samples

Positive Samples

• impressed and clicked
• problem: 20% item takes 80% click
• solution:
  • up-sampling: one sample appear multiple times
  • down-sampling: discard samples

Negative Samples

Simple Negative Sampling: All Items

Uniform Sampling: Unfair to unpopular items

• Most positive samples are popular items.
• If uniform sampling produces negative samples, most of the negative samples are unpopular items.
• positive sample: popular items, negative sample: unpopular items, this is unfair.

Non-uniform Sampling: The goal is to suppress popular items

• The probability of negative sampling is positively correlated with popularity (clicks).
• Sampling probability ∝ (clicks) ^ 0.75

Simple Negative Sampling: Negative Sample within a batch

user1 - item1
user2 - item2
user3 - item3

...

user_n - item_n

• one batch has n positive samples

• one batch has n(n - 1) negative samples

• The probablity that an item appear in a batch is propotional to the number of times it clicked.

• We aim to get it propotional to clicks^0.75.

• offline training cos(a, bi) - log(pi), pi ∝ clicks

• online inference cos(a, bi)

Hard Negative Sampling

Hard negative samples:

• Items that are ranked and close to the target (relatively hard).
• Items that are ranked far behind the target (extremely hard).

Binary classification for positive and negative samples:

• All items (simple): High classification accuracy.
• Items that are ranked and close to the target (relatively hard): Easy to misclassify.
• Items that are ranked far behind the target (extremely hard): Even easier to misclassify.

Datasets

• Mix negative samples
• 50% easy negative sample
• 50% hard negative sample