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This is an Ox.
Figure 19. An ox.
In 1906, a weight judging competition was held in
England.
787 participants guessed the weight of an ox. The median error of individual
guesses was 37 lb (an error of 3.1%). However, the overall median of the
guesses was only 9 lb away from the real weight of the ox (1198 lb), which was
an error of only 0.7%.
Figure 20. Histogram of individual weight guesses.
This anecdote illustrates the
Wisdom of the crowd: In
certain situations, collective opinion provides very good judgment.
Mathematically, the wisdom of the crowd can be modeled with the
Central limit theorem:
Informally, the squared error between a value and the average of N noisy
estimates of this value tends to zero with a 1/N factor.
However, if the variables are not independent, the variance is greater.
In machine learning, an
ensemble is a collection of models
whose predictions are averaged (or aggregated in some way). If the ensemble
models are different enough without being too bad individually, the quality of
the ensemble is generally better than the quality of each of the individual
models. An ensemble requires more training and inference time than a single
model. After all, you have to perform training and inference on multiple models
instead of a single model.
Informally, for an ensemble to work best, the individual models should be
independent. As an illustration, an ensemble composed of 10 of the exact same
models (that is, not independent at all) won't be better than the individual
model. On the other hand, forcing models to be independent could mean making
them worse. Effective ensembling requires finding the balance between model
independence and the quality of its sub-models.
[[["Easy to understand","easyToUnderstand","thumb-up"],["Solved my problem","solvedMyProblem","thumb-up"],["Other","otherUp","thumb-up"]],[["Missing the information I need","missingTheInformationINeed","thumb-down"],["Too complicated / too many steps","tooComplicatedTooManySteps","thumb-down"],["Out of date","outOfDate","thumb-down"],["Samples / code issue","samplesCodeIssue","thumb-down"],["Other","otherDown","thumb-down"]],["Last updated 2025-08-25 UTC."],[[["\u003cp\u003eThe "wisdom of the crowd" suggests that collective opinions can provide surprisingly accurate judgments, as demonstrated by a 1906 ox weight-guessing competition where the collective guess was remarkably close to the true weight.\u003c/p\u003e\n"],["\u003cp\u003eThis phenomenon can be explained by the Central Limit Theorem, which states that the average of multiple independent estimates tends to converge towards the true value.\u003c/p\u003e\n"],["\u003cp\u003eIn machine learning, ensembles leverage this principle by combining predictions from multiple models, improving overall accuracy when individual models are sufficiently diverse and reasonably accurate.\u003c/p\u003e\n"],["\u003cp\u003eWhile ensembles require more computational resources, their enhanced predictive performance often outweighs the added cost, especially when individual models are carefully selected and combined.\u003c/p\u003e\n"],["\u003cp\u003eAchieving optimal ensemble performance involves striking a balance between ensuring model independence to avoid redundant predictions and maintaining the individual quality of sub-models for overall accuracy.\u003c/p\u003e\n"]]],[],null,["# Random Forest\n\n\u003cbr /\u003e\n\nThis is an Ox.\n\n\n**Figure 19. An ox.**\n\n\u003cbr /\u003e\n\nIn 1906, a [weight judging competition was held in\nEngland](https://www.nature.com/articles/075450a0.pdf).\n787 participants guessed the weight of an ox. The median *error* of individual\nguesses was 37 lb (an error of 3.1%). However, the overall median of the\nguesses was only 9 lb away from the real weight of the ox (1198 lb), which was\nan error of only 0.7%.\n\n**Figure 20. Histogram of individual weight guesses.**\n\nThis anecdote illustrates the\n[Wisdom of the crowd](/machine-learning/glossary#wisdom_of_the_crowd): *In\ncertain situations, collective opinion provides very good judgment.*\n\nMathematically, the wisdom of the crowd can be modeled with the\n[Central limit theorem](https://wikipedia.org/wiki/Central_limit_theorem):\nInformally, the squared error between a value and the average of N noisy\nestimates of this value tends to zero with a 1/N factor.\nHowever, if the variables are not independent, the variance is greater.\n\nIn machine learning, an\n**[ensemble](/machine-learning/glossary#ensemble)** is a collection of models\nwhose predictions are averaged (or aggregated in some way). If the ensemble\nmodels are different enough without being too bad individually, the quality of\nthe ensemble is generally better than the quality of each of the individual\nmodels. An ensemble requires more training and inference time than a single\nmodel. After all, you have to perform training and inference on multiple models\ninstead of a single model.\n\nInformally, for an ensemble to work best, the individual models should be\nindependent. As an illustration, an ensemble composed of 10 of the exact same\nmodels (that is, not independent at all) won't be better than the individual\nmodel. On the other hand, forcing models to be independent could mean making\nthem worse. Effective ensembling requires finding the balance between model\nindependence and the quality of its sub-models."]]