[[["āĻ¸āĻšāĻā§ āĻŦā§āĻāĻž āĻ¯āĻžā§","easyToUnderstand","thumb-up"],["āĻāĻŽāĻžāĻ° āĻ¸āĻŽāĻ¸ā§āĻ¯āĻžāĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻšā§ā§āĻā§","solvedMyProblem","thumb-up"],["āĻ āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯","otherUp","thumb-up"]],[["āĻāĻ¤ā§ āĻāĻŽāĻžāĻ° āĻĒā§āĻ°ā§ā§āĻāĻ¨ā§ā§ āĻ¤āĻĨā§āĻ¯ āĻ¨ā§āĻ","missingTheInformationINeed","thumb-down"],["āĻā§āĻŦ āĻāĻāĻŋāĻ˛ / āĻ āĻ¨ā§āĻ āĻ§āĻžāĻĒ","tooComplicatedTooManySteps","thumb-down"],["āĻĒā§āĻ°āĻ¨ā§","outOfDate","thumb-down"],["āĻ āĻ¨ā§āĻŦāĻžāĻĻ āĻ¸āĻāĻā§āĻ°āĻžāĻ¨ā§āĻ¤ āĻ¸āĻŽāĻ¸ā§āĻ¯āĻž","translationIssue","thumb-down"],["āĻ¨āĻŽā§āĻ¨āĻž / āĻā§āĻĄ āĻ¸āĻāĻā§āĻ°āĻžāĻ¨ā§āĻ¤ āĻ¸āĻŽāĻ¸ā§āĻ¯āĻž","samplesCodeIssue","thumb-down"],["āĻ āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯","otherDown","thumb-down"]],["2025-07-29 UTC-āĻ¤ā§ āĻļā§āĻˇāĻŦāĻžāĻ° āĻāĻĒāĻĄā§āĻ āĻāĻ°āĻž āĻšā§ā§āĻā§āĨ¤"],[[["\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."]]
