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Sampling Strategies - Random, Stratified, Reservoir, Weighted

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Random Sampling

A random sample of size n is selected from the population of size N. This ensures each member of the population has an equal chance of being selected.

🎯 Understand how randomness ensures unbiased representation.
import random
population = list(range(100))
sample = random.sample(population, 10)
Stratified Sampling

Population is divided into strata; samples are drawn from each stratum proportionally to their size in the population.

🎯 Recognize the importance of maintaining proportional representation.
from sklearn.model_selection import train_test_split
strata = {'A': list(range(50)), 'B': list(range(50, 100))}
sample = {k: random.sample(v, 5) for k, v in strata.items()}
Reservoir Sampling

A fixed-size sample is maintained from a potentially infinite stream. This is done by replacing elements in the reservoir with new elements from the stream with decreasing probability.

🎯 Explain how reservoir sampling handles large data streams efficiently.
import random
def reservoir_sample(stream, k):
    reservoir = []
    for i, item in enumerate(stream):
        if i < k:
            reservoir.append(item)
        else:
            j = random.randint(0, i)
            if j < k:
                reservoir[j] = item
    return reservoir
Weighted Sampling

Samples are drawn based on weights assigned to each element, allowing for elements with higher weights to have a higher chance of being selected.

🎯 Discuss how weighted sampling can prioritize certain elements.
import random
population = ['a', 'b', 'c', 'd']
weights = [0.1, 0.2, 0.3, 0.4]
sample = random.choices(population, weights, k=2)
📊
Diagram
Diagram
┌───────────────────────────────────────────────────────────────┐
│                        Sampling Strategies                     │
├───────────────────────────────────────────────────────────────┤
│ Random Sampling:                                              │
│ ┌───────────────┐                                             │
│ │ Population    │                                             │
│ └──────┬────────┘                                             │
│        │                                                      │
│        ▼                                                      │
│    Random Sample                                             │
│                                                               │
│ Stratified Sampling:                                          │
│ ┌───────────────┐                                             │
│ │ Population    │                                             │
│ └──────┬────────┘                                             │
│        │                                                      │
│        ▼                                                      │
│    Stratified Groups                                         │
│        │                                                      │
│        ▼                                                      │
│    Stratified Sample                                         │
│                                                               │
│ Reservoir Sampling:                                           │
│ ┌───────────────┐                                             │
│ │ Stream Data   │                                             │
│ └──────┬────────┘                                             │
│        │                                                      │
│        ▼                                                      │
│    Reservoir Sample                                          │
│                                                               │
│ Weighted Sampling:                                            │
│ ┌───────────────┐                                             │
│ │ Population    │                                             │
│ └──────┬────────┘                                             │
│        │                                                      │
│        ▼                                                      │
│    Weighted Sample                                           │
└───────────────────────────────────────────────────────────────┘
Labels
  • Random Sampling: Selects samples randomly from the population.
  • Stratified Sampling: Divides population into strata and samples from each.
  • Reservoir Sampling: Maintains a sample from a data stream.
  • Weighted Sampling: Samples based on assigned weights to elements.
🔑
Key Moments
▲
Q: Why is stratified sampling beneficial when dealing with heterogeneous populations?
A: Stratified sampling ensures that each subgroup is adequately represented, reducing sampling bias and improving the accuracy of the results.
Q: How does reservoir sampling maintain a representative sample from a data stream?
A: Reservoir sampling uses a probabilistic approach to replace elements in the sample, ensuring each element in the stream has an equal chance of being included.
Q: What is the advantage of using weighted sampling over random sampling?
A: Weighted sampling allows for the prioritization of certain elements based on their importance or frequency, which can be useful in scenarios where some elements are more significant than others.
Trace Summary

This document explores four sampling strategies: Random, Stratified, Reservoir, and Weighted. Random sampling selects elements purely by chance, ensuring an unbiased sample. Stratified sampling divides the population into strata and samples from each, maintaining proportional representation. Reservoir sampling is ideal for data streams, maintaining a fixed-size sample efficiently. Weighted sampling allows for prioritization based on element importance. Understanding these strategies is crucial for selecting the appropriate method based on data characteristics and analysis goals.

Primary Focus

✓ Sampling strategies and their mechanisms

Practice

(1/5)
1. In the context of data leakage, which of the following scenarios is most likely to cause leakage during model training?
easy
A. Including future data points in the training set that are not available at prediction time.
B. Using a validation set that is randomly sampled from the training data.
C. Normalizing features using statistics from the entire dataset before splitting.
D. Using a large number of features in the model.

Solution

  1. Step 1: Identify potential leakage sources

    Data leakage occurs when information from outside the training dataset is used to create the model.

  2. Step 2: Eliminate wrong options

    Using a validation set that is randomly sampled from the training data. is common practice, Normalizing features using statistics from the entire dataset before splitting. is a preprocessing mistake but not leakage, Using a large number of features in the model. is about complexity, not leakage.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Future data in training = leakage risk [OK]
Hint: Future data in training = leakage risk [OK]
Common Mistakes:
2. In the context of transfer learning, why is it beneficial to pretrain a model on a large dataset before fine-tuning it on a smaller, task-specific dataset?
easy
A. Pretraining helps the model learn general features that can be adapted to specific tasks.
B. Pretraining is only useful for models with a large number of parameters.
C. Pretraining reduces the need for any further training on the task-specific dataset.
D. Pretraining ensures the model learns task-specific features from the start.

Solution

  1. Step 1: Understand the purpose of pretraining.

    Pretraining allows the model to learn general features from a large dataset.

  2. Step 2: Eliminate wrong options.

    Pretraining ensures the model learns task-specific features from the start. is incorrect because pretraining focuses on general, not task-specific, features. Pretraining reduces the need for any further training on the task-specific dataset. is incorrect because fine-tuning is still necessary. Pretraining is only useful for models with a large number of parameters. is incorrect because pretraining is beneficial regardless of model size.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Pretrain for general features, fine-tune for specific tasks. [check]
Hint: Pretrain for general features, fine-tune for specific tasks. [check]
Common Mistakes:
3. For a system with highly volatile data, which approach is more suitable and why?
medium
A. Continual learning, because it adapts quickly to changes.
B. Periodic retraining, because it prevents overfitting to noise.
C. Continual learning, because it is computationally cheaper.
D. Periodic retraining, because it ensures model stability.

Solution

  1. Step 1: Consider the nature of volatile data.

    Volatile data can introduce noise, which continual learning might overfit to.

  2. Step 2: Evaluate the options.

    Continual learning, because it adapts quickly to changes. is incorrect because continual learning can overfit to noise. Continual learning, because it is computationally cheaper. is incorrect because continual learning is not necessarily cheaper. Periodic retraining, because it ensures model stability. is incorrect because while periodic retraining ensures stability, it is not the primary reason for its suitability here.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Volatile data needs stability. [OK]
Hint: Volatile data needs stability. [OK]
Common Mistakes:
4. When should you prefer using Gini Impurity over Entropy in decision trees?
medium
A. When computational efficiency is a priority.
B. When you need a more interpretable model.
C. When the dataset is highly imbalanced.
D. When you need to handle continuous features.

Solution

  1. Step 1: Compare computational efficiency.

    Gini Impurity is computationally less intensive than Entropy.

  2. Step 2: Eliminate wrong options.

    Interpretability is not affected by the choice, imbalance handling is not specific to Gini, and both can handle continuous features.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Gini is faster than Entropy. [OK]
Hint: Gini is faster than Entropy. [OK]
Common Mistakes:
5. You are tasked with adapting a Transformer model for a real-time translation application on mobile devices. Which approach is most suitable?
hard
A. Use a larger model with more layers for better accuracy
B. Implement quantization to reduce model size and inference time
C. Increase the number of attention heads for better context understanding
D. Use a higher learning rate to speed up training

Solution

  1. Step 1: Consider constraints

    Real-time applications on mobile devices require efficient models with low latency and small size.

  2. Step 2: Eliminate wrong options

    Use a larger model with more layers for better accuracy is incorrect because larger models increase latency. Increase the number of attention heads for better context understanding is incorrect because more heads increase complexity. Use a higher learning rate to speed up training is incorrect because learning rate affects training, not inference.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Mobile apps need efficient, small models. [OK]
Hint: Mobile apps need efficient, small models. [OK]
Common Mistakes:
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