title: [概率论]4-7:条件期望(Conditional Expectation) categories: - Mathematic - Probability keywords: - Expectation - Prediction - Law of total Probability toc: true date: 2018-03-27 10:53:24 Abstract: 本文介绍期望的条件版本,也就是条件期望 Keywords: Expectation,Prediction,La…

我知道有很多人理解不了 "条件期望" (Conditional Expectation) 这个东西,有的时候没看清把随机变量看成事件,把 \(\sigma\)-algebra 看成随机变量从而思路全错的时候,我也会觉得莫名奇妙.所以在这里用一个极其简单的例子解释一下,只要你是一只上过高中的草履虫那就能听懂. \[\] 我们来丢一枚质地均匀的硬币(意味着得到正面与反面的概率各为 \(\frac{1}{2}\)),连丢两次并记录两次结果.那么很容易可以写出全集 \(\Omega = \le…

title: [概率论]3-6:条件分布(Conditional Distributions Part I) categories: Mathematic Probability keywords: Discrete Conditional Distributions 离散条件分布 Continuous Conditional Distributions 连续条件分布 toc: true date: 2018-03-08 10:38:13 Abstract: 首先介绍随机变量的条件分布,随后介绍…

title: [概率论]3-6:条件分布(Conditional Distributions Part II) categories: Mathematic Probability keywords: Multiplication Rule for Distributions 乘法法则 Bayes' Theorem 贝叶斯理论 Law of Total Probability for Random Variables 随机变量的全概率公式 toc: true date: 2018-03-12 0…

title: [概率论]2-1:条件概率(Conditional Probability) categories: Mathematic Probability keywords: Conditional Probability 条件概率 Multiplication Rule 乘法原理 Partitions Law of total Probability 全概率公式 toc: true date: 2018-01-31 10:34:36 Abstract: 本文介绍条件概率的定义及相关知识,…

2.1. Binary Variables 1. Bernoulli distribution, p(x = 1|µ) = µ 2.Binomial distribution + 3.beta distribution(Conjugate Prior of Bernoulli distribution) The parameters a and b are often called hyperparameters because they control the distribution of…

This is the second post in Boosting algorithm. In the previous post, we go through the earliest Boosting algorithm - AdaBoost, which is actually an approximation of exponential loss via additive stage-forward modelling. What if we want to choose othe…

Problems[show] Classification Clustering Regression Anomaly detection Association rules Reinforcement learning Structured prediction Feature engineering Feature learning Online learning Semi-supervised learning Unsupervised learning Learning to rank…

Partial Dependence就是用来解释某个特征和目标值y的关系的,一般是通过画出Partial Dependence Plot(PDP)来体现. PDP是依赖于模型本身的,所以我们需要先训练模型(比如训练一个random forest模型).假设我们想研究y和特征\(X_1\)的关系,那么PDP就是一个关于\(X_1\)和模型预测值的函数.我们先拟合了一个随机森林模型RF(X),然后用\(X_k^{i}\)表示训练集中第k个样本的第i个特征,那么PDP的函数就是 \[f(X_1)=\f…

Meta Learner和之前介绍的Casual Tree直接估计模型不同,属于间接估计模型的一种.它并不直接对treatment effect进行建模,而是通过对response effect(target)进行建模,用treatment带来的target变化作为HTE的估计.主要方法有3种:T-Learner, S-Learner, X-Learner,思路相对比较传统的是在监督模型的基础上去近似因果关系. Meta-Learner的优点很明显,可以使用任意ML监督模型进行拟合不需要构建新的…