Rejection sampling
Rejection sampling is a method that generates candidate samples and accepts those meeting a specified criterion while discarding the others.
Fabulous Adventures in Data Structures and Algorithms
The rejection algorithm samples candidate outcomes and discards candidates that fail a probabilistic acceptance test.
- How it is used
- Uses easy-to-sample helper distributions to generate categorical or continuous samples that follow desired weights or densities.
- How deep it goes
- Works through dartboard intuition, acceptance code, helper scaling, clamping, and unbounded retry costs.
- Examples
- Demonstrates weighted integer categories, a two-humped continuous density, and a normal distribution clamped to [0.0, 1.0].
- What you can do after
- Build it from scratch in C# using uniform samplers, a helper distribution, a target weight function, and an acceptance loop.
Read how Fabulous Adventures in Data Structures and Algorithms explains rejection sampling →
Reinforcement Learning from Human Feedback
Rejection sampling is a sampling method that accepts or filters candidate outputs according to a specified criterion or scoring procedure.
- How it is used
- Deploys reward-model filtering as a simple alternative to reinforcement learning for preference fine-tuning.
- How deep it goes
- Explains four pipeline stages and selection strategies, but defers prompt, reward-model, sequencing, and deduplication choices to experimentation.
- Examples
- Uses WebGPT, Helpful and Harmless, process reward models, Llama 2 Chat, and DeepSeek R1 as pipeline examples.
- What you can do after
- Operate/configure a generate-rank-fine-tune pipeline and choose between per-prompt and global completion selection.
Read how Reinforcement Learning from Human Feedback explains rejection sampling →
Building LLM Applications with DSPy
Rejection sampling is a method that accepts candidate samples meeting a criterion and rejects those that do not.
- How it is used
- Uses rejection sampling during DSPy bootstrapping to select safe training examples as demonstrations.
- How deep it goes
- Describes metric-based acceptance, training-set order, and repeated rounds without formalizing the sampling method.
- Examples
- Uses exact-match intent labels to accept correct predictions and reject incorrect ones.
- What you can do after
- Apply rejection sampling with DSPy's BootstrapFewShot to compile a program using accepted training examples as demonstrations.
Read how Building LLM Applications with DSPy explains rejection sampling →
Related concepts
- reward modeluses · A reward model is a learned model that assigns scores to outputs, actions, or outcomes to represent their desirability according to preferences or evaluation criteria.
- reinforcement learningalternative to · Reinforcement learning is a machine-learning paradigm in which an agent learns actions or a policy through interaction with an environment and evaluative feedback, such as rewards.
- pipelinepart of · A pipeline is an ordered or coordinated sequence of connected processing stages or tasks that passes data, work, or results toward an outcome.
- data curationkind of · Data curation is the systematic selection, review, cleaning, organization, and maintenance of data for a particular purpose.
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