Negative Sampling

How Negative Sampling Works

Negative Sampling works by selecting a few samples from a large pool of data that the model should classify as “negative.” When training a machine learning model, it uses these negative samples along with positive examples. This process ensures that the model can differentiate between relevant and irrelevant data effectively. It is especially useful in cases where there are far more negative samples than positive ones, reducing the overall training time and computational resources needed.

📉 Negative Sampling: Core Formulas and Concepts

1. Original Softmax Objective

Given a target word w_o and context word w_c, the original softmax objective is:

P(w_o | w_c) = exp(v'_w_o · v_w_c) / ∑_{w ∈ V} exp(v'_w · v_w_c)

This requires summing over the entire vocabulary V, which is computationally expensive.

2. Negative Sampling Objective

To avoid the full softmax, negative sampling replaces the multi-class classification with multiple binary classifications:

L = log σ(v'_w_o · v_w_c) + ∑_{i=1}^k E_{w_i ~ P_n(w)} [log σ(−v'_{w_i} · v_w_c)]

Where:

σ(x) = 1 / (1 + exp(−x))  (the sigmoid function)
k = number of negative samples
P_n(w) = noise distribution
v'_w = output vector of word w
v_w = input vector of word w

4. Noise Distribution

Commonly used noise distribution is the unigram distribution raised to the 3/4 power:

P_n(w) ∝ U(w)^{3/4}

Types of Negative Sampling

• Random Negative Sampling. This method randomly selects negative samples from the dataset without any criteria. It is simple but may not always be effective in training, as it can include irrelevant examples.
• Hard Negative Sampling. In this approach, the algorithm focuses on selecting negative samples that are similar to positive ones. It helps the model learn better by challenging it with more difficult negative examples.
• Dynamic Negative Sampling. This technique involves updating the selection of negative samples during training. It adapts to how the model improves over time, ensuring that the samples remain relevant and challenging.
• Uniform Negative Sampling. Here, the negative samples are selected uniformly across the entire dataset. It helps to ensure diversity in the samples but may not focus on the most informative ones.
• Adaptive Negative Sampling. This method adjusts the selection criteria based on the model’s learning progress. By focusing on the hardest examples that the model struggles with, it helps improve the overall accuracy and performance.

Algorithms Used in Negative Sampling

• Skip-Gram Model. This algorithm is part of Word2Vec and trains a neural network to predict surrounding words given a target word. Negative Sampling is used to speed up this training by simplifying the loss function.
• Hierarchical Softmax. This technique uses a binary tree structure to represent the output layer, making it efficient for predicting words in large vocabularies. It leverages Negative Sampling to enhance performance.
• Batch Negative Sampling. This approach collects negative samples in batches during training. It is effective for speeding up learning processes in large datasets, helping to manage computational costs.
• Factorization Machines. These are generalized linear models that can use Negative Sampling to improve prediction accuracy in scenarios involving high-dimensional sparse data.
• Graph Neural Networks. In recommendation systems, these networks can utilize Negative Sampling techniques to enhance the quality of predictions when dealing with large and complex datasets.

Industries Using Negative Sampling

• E-commerce. Negative Sampling optimizes recommendation systems, helping businesses personalize product suggestions by accurately predicting customer preferences.
• Healthcare. In medical diagnosis, it assists in building models that differentiate between positive and negative cases, improving diagnostic accuracy.
• Finance. Financial institutions use Negative Sampling for fraud detection, allowing them to focus on rare instances of fraudulent activity against a backdrop of many legitimate transactions.
• Social Media. Negative Sampling is employed in content recommendation algorithms to enhance user engagement by predicting likes and shares more effectively.
• Gaming. Gaming companies utilize Negative Sampling in player behavior modeling to improve game design and enhance user experience based on player choices.

Practical Use Cases for Businesses Using Negative Sampling

• Recommendation Systems. Businesses employ Negative Sampling to improve the accuracy of recommendations made to users, thus enhancing sales conversion rates.
• Spam Detection. Email providers use Negative Sampling to train algorithms that effectively identify and filter out spam messages from legitimate ones.
• Image Recognition. Companies in tech leverage Negative Sampling to optimize their image classifiers, allowing for better identification of relevant objects within images.
• Sentiment Analysis. Businesses analyze customer feedback by sampling negative sentiments to train models that better understand customer opinions and feelings.
• Fraud Detection. Financial services use Negative Sampling to identify suspicious transactions by focusing on hard-to-detect fraudulent patterns in massive datasets.

🧪 Negative Sampling: Practical Examples

Example 1: Word2Vec Skip-Gram with One Negative Sample

Target word: cat, Context word: sat

Positive pair: (cat, sat)

Sample one negative word: car

Compute loss:

L = log σ(v'_sat · v_cat) + log σ(−v'_car · v_cat)

This pushes sat closer to cat in embedding space and car away.

Example 3: Noise Distribution Sampling

Vocabulary frequencies:

the: 10000
cat: 500
moon: 200

Noise distribution with 3/4 smoothing:

P_n(the) ∝ 10000^(3/4)
P_n(cat) ∝ 500^(3/4)
P_n(moon) ∝ 200^(3/4)

This sampling favors frequent but not overwhelmingly common words, improving training efficiency.

Software and Services Using Negative Sampling Technology

Future Development of Negative Sampling Technology

The future of Negative Sampling technology in artificial intelligence looks promising. As models become more complex and the amount of data increases, efficient techniques like Negative Sampling will be crucial for enhancing model training speeds and accuracy. Its adaptability across various industries suggests a growing adoption that could revolutionize systems and processes, making them smarter and more efficient.

Conclusion

Negative Sampling plays a vital role in the enhancement and efficiency of machine learning models, making it easier to train on large datasets while focusing on relevant examples. As industries leverage this technique, the potential for improved performance and accuracy in AI applications continues to grow.

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