title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¾Ð±Ð°ÑÑÐ½ÑÑ (Ð¼Ð¸Ð½Ð¸Ð¼Ð°ÐºÑÐ½ÑÑ ) Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÐºÐ»Ð°ÑÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¸ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ð´Ð»Ñ Ð¼Ð°Ð»ÑÑ Ð²ÑÐ±Ð¾ÑÐ¾Ðº Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ»ÑÑÐ°Ð¹Ð½ÑÑ Ð»ÐµÑÐ¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Imprecise Robust Classification and Regression Models for Small Samples Based on Random Forests
Creators: name: ÐÐ¾Ð²Ð°Ð»ÐµÐ², ÐÐ°ÐºÑÐ¸Ð¼
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: Ð¤ÑÐ½ÐºÑÐ¸Ð¸ (Ð¼Ð°Ñ.) ÐÐ¸ÑÐ¸Ñ Ð»Ðµ
ÐÑÐºÑÑÑÑÐ²ÐµÐ½Ð½ÑÐ¹ Ð¸Ð½ÑÐµÐ»Ð»ÐµÐºÑ
ÐºÐ»Ð°ÑÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ
ÑÐµÐ³ÑÐµÑÑÐ¸Ñ
ÑÐ»ÑÑÐ°Ð¹Ð½ÑÐ¹ Ð»ÐµÑ
Ð´ÐµÑÐµÐ²Ð¾ ÑÐµÑÐµÐ½Ð¸Ð¹
Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ
ÑÐ¾Ð±Ð°ÑÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð·Ð°ÑÐ¾ÑÐµÐ½Ð¸Ñ
Ð´Ð¾Ð²ÐµÑÐ¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ñ ÑÐ¾Ð±Ð°ÑÑÐ½ÑÐµ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ â ÑÐ»ÑÑÐ°Ð¹Ð½ÑÐ¹ Ð»ÐµÑ, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¸ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸. Ð¡Ð»ÑÑÐ°Ð¹Ð½ÑÐ¹ Ð»ÐµÑ ÑÐµÐ°Ð»Ð¸Ð·ÑÑÑÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð° Ð´ÐµÑÐµÐ²ÑÐµÐ² ÑÐµÑÐµÐ½Ð¸Ð¹ Ð¸ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð¸Ñ Ð¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð². ÐÐ»Ñ Ð²ÑÐ±Ð¾ÑÐ¾Ðº Ð¼Ð°Ð»Ð¾Ð³Ð¾ ÑÐ°Ð·Ð¼ÐµÑÐ° Ð¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ Ð½ÐµÐ»ÑÐ·Ñ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑ ÐºÐ°Ðº ÑÐ¾ÑÐ½ÑÐ¹. ÐÑÐ½Ð¾Ð²Ð½Ð°Ñ Ð¸Ð´ÐµÑ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¹ ÑÐ¾ÑÑÐ¾Ð¸Ñ Ð² Ð·Ð°Ð¼ÐµÐ½Ðµ Ð¾Ð±ÑÑÐ½Ð¾Ð³Ð¾ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð¸Ñ Ð½Ð° Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð¾Ðµ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð¸Ðµ, Ð¿ÑÐ¸ ÑÑÐ¾Ð¼ Ð²ÐµÑÐ° ÑÑÐ¸ÑÑÐ²Ð°ÑÑ, ÑÑÐ¾ Ð¾ÑÐµÐ½ÐºÐ¸ Ð´ÐµÑÐµÐ²ÑÐµÐ² ÑÐµÑÐµÐ½Ð¸Ð¹ ÑÐ²Ð»ÑÑÑÑÑ Ð½ÐµÑÐ¾ÑÐ½ÑÐ¼Ð¸. ÐÐ»Ñ ÑÑÐ¾Ð³Ð¾ ÑÐ¾ÑÐµÑÐ½ÑÐµ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ñ Ð·Ð°Ð¼ÐµÐ½ÑÑÑÑÑ Ð½Ð° Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÐµ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð¸ Ð´Ð¾Ð²ÐµÑÐ¸ÑÐµÐ»ÑÐ½ÑÑ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»Ð¾Ð². ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ñ ÑÐ¿ÐµÑÐ¸Ð°Ð»ÑÐ½ÑÐµ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ ÑÐµÐ»ÐµÐ²ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¸ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸, ÑÑÐ¾Ð±Ñ ÑÐ¿ÑÐ¾ÑÑÐ¸ÑÑ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð»Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ Ð²ÐµÑÐ¾Ð².
description: In the given work, one proposes robust modifications of the machine learning algorithm, Random Forest, which are used to solve classification and regression problems. Random Forest is implemented by constructing a set of Decision Trees and averaging their estimates. For small samples, the estimates cannot be regarded as accurate. The main idea of the modifications is replacing the usual averaging by a weighted averaging in which weights take into account that the estimates of decision trees are imprecise. For this, point forecasts are replaced by interval forecasts using Imprecise Statistical Inference Models and Confidence Intervals. Special modifications of objective functions in classification and regression problems are proposed in order to simplify optimization problems for calculating optimal weights.