Update on 2025-09-25

背景：纷争乱世(Chaos)

统计学(Statistics)

机器学习(Machine learning)

数据科学(Data science)

人工智能(Artificial intelligence)

数据挖掘(Data mining)

模式识别(Pattern recognition)

深度学习(Deep learning)

入门：听闻天下武功(Recognise algrithms)

学习招式(A simple case)

Major League Baseball Data (263) from the 1986 and 1987 seasons.
Years Hits Salary
-Alan Ashby 14 81 475.0
-Alvin Davis 3 130 480.0
-Andre Dawson 11 141 500.0
-Andres Galarraga 2 87 91.5
-Alfredo Griffin 11 169 750.0
-Al Newman 2 37 70.0
-Argenis Salazar 3 73 100.0
-Andres Thomas 2 81 75.0

学习招式(Model selection)

学习招式(Model setup, training and evalutation)

建立模型(Model setup)

\[ \mathbf y = F_m(\mathbf X; \boldsymbol \beta)\ -> \mathbf X \boldsymbol \beta. \] 训练参数(Training)

\[ \hat{\boldsymbol \beta} = \underset{\boldsymbol \beta}{\rm argmin}\ L(\mathbf X_{train}, \mathbf y_{train}, \boldsymbol \beta)\ -> \underset{\boldsymbol \beta}{\rm argmin} || \mathbf y_{train} - \mathbf X_{train} \boldsymbol \beta||_2^2. \] 预测(Prediction)

\[ \hat{\mathbf y} = F_m(\mathbf X_{test}; \hat{\boldsymbol \beta})\ -> \mathbf X_{test} \hat{\boldsymbol \beta}. \] 评估(Evaluation)

\[ {\rm mse(Mean\ squared\ error}) = \frac{1}{n_{\rm test}} \sum_{n_{\rm test}} (\hat{ y} - y_{\rm test})^2,\\ \rm acc(Accuracy) = \frac{True\ samples}{Total\ samples}. \]

学习招式(Model evaluation)

学习招式(Model comparison)

选择武器(Programing)

选择武器(Python packages)

选择武器(R packages)

选择武器(Py & R)

Python

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import sklearn

R

library(data.table)
library(dplyr)
library(ggplot2)
library(mlr3)

武器比较(Platform and Versions)

## Platform:  macOS-15.7-arm64-arm-64bit
## Platform:  Apple M4 Pro

Python

print("Python version:", platform.python_version())
## Python version: 3.12.10

R

print(R.version$version.string)
## [1] "R version 4.5.1 (2025-06-13)"

武器比较(Matrix multiplication)

Python

import time
a = np.random.standard_normal([5000, 5000])
start = time.time()
b = a @ a.T
end = time.time()
time_ela = end - start
print(time_ela)
## 0.19492793083190918

R

a <- matrix(rnorm(5000 * 5000), 5000)
system.time( b <- tcrossprod(a))
##    user  system elapsed 
##   0.350   0.014   0.204

高级武器比较(The extension of python)

Python

import torch

a = torch.randn([5000, 5000], device = torch.device('mps'))
t1 = time.time()
b_t = a @ a.T
print('torch @:', time.time() - t1)
## torch @: 0.0041158199310302734
import mlx.core as mx

a = mx.random.normal([5000, 5000], stream = mx.gpu)
t1 = time.time()
b_m = a @ a.T
mx.eval(b_m)
print('mlx @:', time.time() - t1)
## mlx @: 0.06186795234680176

武器比较(Inverse matrix)

Python

start = time.time()
inv = np.linalg.inv(b)
end = time.time()
time_ela = end - start
print(time_ela)
## 0.797569990158081

R

system.time(inv <- solve(b))
##    user  system elapsed 
##   1.655   0.041   1.039

武器比较(Eigen decomposition)

Python

start = time.time()
uv = np.linalg.eigh(b)
end = time.time()
time_ela = end - start
print(time_ela)
## 7.239617109298706

R

system.time(uv <- eigen(b))
##    user  system elapsed 
##  10.713   0.128   9.472

多般兵器, 样样精通(Combine R and Python)

Python

from nycflights13 import flights
## /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/reticulate/python/rpytools/loader.py:120: UserWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html. The pkg_resources package is slated for removal as early as 2025-11-30. Refrain from using this package or pin to Setuptools<81.
##   return _find_and_load(name, import_)
pd.set_option('display.max_columns', 20)
print(flights.iloc[0:7, 0:10])
##    year  month  day  dep_time  sched_dep_time  dep_delay  arr_time  \
## 0  2013      1    1     517.0             515        2.0     830.0   
## 1  2013      1    1     533.0             529        4.0     850.0   
## 2  2013      1    1     542.0             540        2.0     923.0   
## 3  2013      1    1     544.0             545       -1.0    1004.0   
## 4  2013      1    1     554.0             600       -6.0     812.0   
## 5  2013      1    1     554.0             558       -4.0     740.0   
## 6  2013      1    1     555.0             600       -5.0     913.0   
## 
##    sched_arr_time  arr_delay carrier  
## 0             819       11.0      UA  
## 1             830       20.0      UA  
## 2             850       33.0      AA  
## 3            1022      -18.0      B6  
## 4             837      -25.0      DL  
## 5             728       12.0      UA  
## 6             854       19.0      B6

多般兵器, 样样精通(Combine R and Python)

R

kable(head(py$flights[, 1 : 10], 7), align = "c")
year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time arr_delay carrier
2013 1 1 517 515 2 830 819 11 UA
2013 1 1 533 529 4 850 830 20 UA
2013 1 1 542 540 2 923 850 33 AA
2013 1 1 544 545 -1 1004 1022 -18 B6
2013 1 1 554 600 -6 812 837 -25 DL
2013 1 1 554 558 -4 740 728 12 UA
2013 1 1 555 600 -5 913 854 19 B6

修炼内功(Books)

行走江湖，接受挑战(Kaggle)