What are the key differences between stochastic and deterministic sampling?

Stochastic and deterministic sampling differ primarily in their use of randomness. Deterministic sampling follows fixed rules or algorithms, ensuring the same output is produced every time for a given input. For example, selecting every 10th item from a dataset guarantees identical results across runs. In contrast, stochastic sampling incorporates randomness, meaning results can vary even with identical inputs. A simple example is rolling a die to randomly pick data points, where each execution might yield a different subset. This randomness makes stochastic methods less predictable but more flexible for exploring diverse scenarios.

The choice between these methods depends on the application. Deterministic sampling is ideal for tasks requiring reproducibility, such as unit testing or scenarios where consistent outputs are critical. For instance, stratified sampling—a deterministic technique—divides data into subgroups (e.g., age ranges) and selects a fixed number from each, ensuring balanced representation. Stochastic methods, like Monte Carlo simulations, rely on randomness to model complex systems (e.g., financial risk) by generating many possible outcomes. In machine learning, stochastic gradient descent uses random mini-batches to escape local minima during training, while dropout layers randomly deactivate neurons to prevent overfitting. These examples highlight how randomness aids in generalization and exploration.

From a developer’s perspective, deterministic methods are easier to debug and validate due to their predictability. However, they may miss patterns that require probabilistic exploration. Stochastic approaches, while powerful for modeling uncertainty, introduce variability that complicates debugging and may require averaging multiple runs (e.g., in A/B testing) or setting random seeds for reproducibility. Computational costs also differ: deterministic sampling often has lower overhead, while stochastic methods might need more resources to manage randomness (e.g., generating high-quality random numbers). Choosing between them involves balancing consistency, exploration needs, and computational constraints—key considerations for designing robust sampling logic.