Derek

Thoughts, imaginations, and stories.

统计学|交互效应与混杂效应小议

1. 一些废话 前段时间在上课的时候对于两个定义的理解不是很清楚,刚好后来进一步学习了一些偏性分析,再阅读了几篇相关的文献,把一些核心的东西记录一下。 2. 交互效应 交互效应(Interaction Effect)是指当某个自变量对因变量的作用效应的大小与另一个自变量有关时,两个变量有交互作用。比如我们考虑$$\mathbb{E}[Y]=\beta_0+\beta_1X_1+\b...

实分析|序列的极限(二)

1. 上极限、下极限和极限点(二) 在上一篇我们简单介绍了上极限、下极限和极限点的概念,现在我们来给出上极限和下极限的一些基本性质. 定理 1.1    设$\lbrace a_n \rbrace$是一个实数序列,$L^+, L^-$是该序列的上极限和下极限. (1.1.1)对任意的$x>L^+,$ 存在一个$N \geq m$使$a_n<x$对所有的$n \geq N$...

实分析|序列的极限(一)

1. 收敛和极限定律 在实数的定义里我们尚未正式地定义极限,因此我们要做一些完善. 实际上,这些定义几乎与微积分课程一致. 定义 1.1(实数的柯西序列)    对任意实数$\varepsilon>0$都存在一个$N \geq m$使得$|a_n-a_{n'}| \leq \varepsilon$对所有的$n, n' \geq N$成立,那么实数序列$\lbrace a_n \r...

机器学习|Nonlinear Dimensionality Reduction

1. Introduction We have discussed about some linear dimensionality reduction methods such as PCA, LDA, CCA. Here we discuss nonlinear dimensionality reduction. There are two types: Parametric:...

机器学习|Automatic Machine Learning

1. Example Here is an example. import autosklearn.classification cls = autosklearn.classification.AutoSklearnClassifier() cls.fit(X_train, y_train) predictions = cls.predict(X_test) Automatic ...

机器学习|Feature Engineering

1. Feature Selection We could delete some existing columns by using feature importance. 2. Feature Generation/Extraction We could add some new columns. For example, generating new attributes usi...

机器学习|Model-Agnostic Interpretation Methods

1. Direct Relationship Analysis Direct relationship analysis includes partial dependence plot, individual conditional expectation, feature interaction, feature importance, and etc. 1.1 Partial De...

机器学习|Imbalanced Classes

1. Way to Handle Collect more data. Use appropriate evaluation metrics: (1) scale_pos_weight in XGBoost ($\frac{\mathrm{Number\ of\ negative\ instances}}{\mathrm{Number\ of\ positive\ instanc...

机器学习|Data

1. One-Hot Encoding As we mentioned before, we could use one-hot encoding for categorical data: pandas.get_dummies or sklearn.preprocessing.OneHotEncoder. Here is an examples. from numpy import ...

机器学习|Ensemble Learning

1. Introduction Here is the definition of ensemble learning (集成学习). Given base (weak) learners $\lbrace f_b \rbrace_{b=1}^B$ and their weights $w_b$, $$f(x)=\sum\limits_{b=1}^Bw_bf_b(x).$$ If ...