MindMap Gallery Basic regression algorithm for machine learning
It summarizes the basic regression algorithms in machine learning, such as basic linear regression, recursive regression, regularized linear regression, sparse linear regression Lasso, linear basis function regression, singular value decomposition, error decomposition of regression learning, etc.
Edited at 2023-02-15 23:14:30This is a panoramic infographic—currently sweeping across the web—illustrating the comprehensive applications of OpenClaw, a popular open-source AI agent platform. It systematically introduces this intelligent agent framework—affectionately dubbed "Lobster Farming"—helping readers quickly grasp its core value, technical features, application scenarios, and security protocols. It serves as an excellent introductory guide and practical manual.
這是一張最近風靡全網關於熱門開源AI代理平台OpenClaw的全網應用全景圖解。它系統性地介紹了這款被稱為「養龍蝦」的智慧體框架,幫助讀者快速理解其核心價值、技術特性、應用場景及安全規範,是一份極佳的入門指南與實操手冊。此圖主要針對希望利用AI建構自動化工作流程的技術從業人員、中小企業主及效率追求者,透過9大模組層層遞進,全面剖析了OpenClaw從概念到落地的整個過程。 圖中核心內容首先釐清了「養龍蝦」指涉的是OpenClawd開源智能體,並強調其本質是「AI基建」而非一般聊天機器人。隨後詳細比較其與傳統AI助理的區別,擁有記憶管理、權限控制、會話隔離和異常恢復四大基礎能力,支援跨平台存取和多模型相容(如GPT、Claude、Ollama)。同時,圖解提供了完整的部署方案(雲端/本地/Docker),並列舉了辦公室自動化、內容創作、資料收集等五大應用程式場景。此外,還展示了其火爆程度、政府與大廠佈局、安全部署建議及適合/不適合的人群分類。幫助你快速掌握OpenClaw技術架構與應用價值,指導個人或企業建構AI自動化系統,規避資料外洩與權限失控風險,是學習「執行式AI」轉型的權威參考圖譜。
本圖由萬興腦圖繪製,是針對IT研發崗位的結構化個人履歷模板,完整涵蓋求職核心資訊模組。基本資訊區包含姓名、電話、信箱、求職意願及GitHub連結;專業概要要求以2-3句提煉核心優勢;工作經驗以「公司A高級Java開發工程師」為例,以「透過(行動),達成(量化成果)」格式呈現微服務架構設計、系統效能優化、團隊技術規範制定等職責,公司B經歷則聚焦功能模組開發與Elasticsearch搜尋優化;技能專長分程式語言、後端框架、中介軟體、資料庫、容器雲等維度,清楚展示技術堆疊;專案成果以「電商平台秒殺系統」為例,說明技術棧、架構設計、個人貢獻(Redis Lua庫存原子扣減)及KPI;教育背景包含一流大學電腦專業學歷,以及AWS認證解決方案架構師、軟考中級軟體設計師證書。模板邏輯嚴謹,涵蓋IT研發求職全流程關鍵訊息,幫助求職者清晰、量化展示專業能力。
This is a panoramic infographic—currently sweeping across the web—illustrating the comprehensive applications of OpenClaw, a popular open-source AI agent platform. It systematically introduces this intelligent agent framework—affectionately dubbed "Lobster Farming"—helping readers quickly grasp its core value, technical features, application scenarios, and security protocols. It serves as an excellent introductory guide and practical manual.
這是一張最近風靡全網關於熱門開源AI代理平台OpenClaw的全網應用全景圖解。它系統性地介紹了這款被稱為「養龍蝦」的智慧體框架,幫助讀者快速理解其核心價值、技術特性、應用場景及安全規範,是一份極佳的入門指南與實操手冊。此圖主要針對希望利用AI建構自動化工作流程的技術從業人員、中小企業主及效率追求者,透過9大模組層層遞進,全面剖析了OpenClaw從概念到落地的整個過程。 圖中核心內容首先釐清了「養龍蝦」指涉的是OpenClawd開源智能體,並強調其本質是「AI基建」而非一般聊天機器人。隨後詳細比較其與傳統AI助理的區別,擁有記憶管理、權限控制、會話隔離和異常恢復四大基礎能力,支援跨平台存取和多模型相容(如GPT、Claude、Ollama)。同時,圖解提供了完整的部署方案(雲端/本地/Docker),並列舉了辦公室自動化、內容創作、資料收集等五大應用程式場景。此外,還展示了其火爆程度、政府與大廠佈局、安全部署建議及適合/不適合的人群分類。幫助你快速掌握OpenClaw技術架構與應用價值,指導個人或企業建構AI自動化系統,規避資料外洩與權限失控風險,是學習「執行式AI」轉型的權威參考圖譜。
本圖由萬興腦圖繪製,是針對IT研發崗位的結構化個人履歷模板,完整涵蓋求職核心資訊模組。基本資訊區包含姓名、電話、信箱、求職意願及GitHub連結;專業概要要求以2-3句提煉核心優勢;工作經驗以「公司A高級Java開發工程師」為例,以「透過(行動),達成(量化成果)」格式呈現微服務架構設計、系統效能優化、團隊技術規範制定等職責,公司B經歷則聚焦功能模組開發與Elasticsearch搜尋優化;技能專長分程式語言、後端框架、中介軟體、資料庫、容器雲等維度,清楚展示技術堆疊;專案成果以「電商平台秒殺系統」為例,說明技術棧、架構設計、個人貢獻(Redis Lua庫存原子扣減)及KPI;教育背景包含一流大學電腦專業學歷,以及AWS認證解決方案架構師、軟考中級軟體設計師證書。模板邏輯嚴謹,涵蓋IT研發求職全流程關鍵訊息,幫助求職者清晰、量化展示專業能力。
machine learning Basic regression algorithm
regression learning
Features
supervised learning
Data set with label y
learning process
The process of determining model parameters w
predict or extrapolate
The process of calculating regression output by substituting new inputs
linear regression
basic linear regression
target linear function
Error Gaussian distribution assumption
There is a discrepancy between the output value and the labeled value
Assuming that the model output is the expected value, the probability function of the random variable (labeled value) yi is
Since the samples are independently and identically distributed, the joint probability density function of all labeled values is
Likelihood function to find optimal parameters (least squares LS solution)
log likelihood function
error sum of squares
maximum likelihood solution
Mean square error test formula
Recursive learning for linear regression
Targeted issues
The scale of the problem is too large and it is difficult to solve the matrix
gradient descent algorithm
Take all samples to calculate the average gradient
average gradient
Recursion formula
Stochastic gradient descent SGD algorithm (LMS)
Take random samples to calculate the gradient
stochastic gradient
Recursion formula
Mini-batch SGD algorithm
Take a small batch of samples to calculate the average gradient
average gradient
Recursion formula
regularized linear regression
Targeted issues
The condition number of the matrix is very large and the numerical stability is not good.
The nature of the large condition number of the problem
Some column vectors of a matrix are proportional or approximately proportional
There are redundant weight coefficients and overfitting occurs.
Solution
Should "reduce the number of model parameters" or "regularize the model parameters"
Regularized objective function
Error sum of squares J(w) hyperparameter λ constraining parameter vector w
form
Regularized least squares LS solution
Regularized Linear Regression Probability Interpretation
The prior distribution of the weight coefficient vector w is the Bayesian "maximum posterior probability estimate" MAP under the Gaussian distribution
Gradient recursion algorithm (small batch stochastic gradient descent method SGD as an example)
Multiple output (output vector y) linear regression
Targeted issues
The output is a vector y instead of a scalar y
Error sum of squares objective function J(W)
Least squares LS solution
Sparse Linear Regression Lasso
norm of the regularization term
Norm p>1
None of the solution coordinates are 0, and the solution is not sparse.
Norm p=1
Most of the solution coordinates are 0, the solutions are sparse, and the processing is relatively easy.
Norm p<1
Most of the solution coordinates are 0, the solutions are sparse, and the processing is difficult.
Lasso problem
content
For the problem of minimizing the error sum of squares function, a constraint ||w||1<t is imposed
regularization expression
Lasso’s cyclic coordinate descent algorithm
preprocessing
Zero-mean the data matrix X columns and normalize them to Z
Lasso's solution in single variable case
Lasso solution
Generalization of Lasso solution in multi-variable cases
Cyclic coordinate descent method CCD
First determine one of the parameters wj
Calculate the parameters that minimize the sum of squared errors
At this time, other parameters w are not optimal values, so the calculation result of wj is only an estimate.
Loop calculation
The same idea is used to calculate other parameters in a loop until the parameter estimates converge.
Part of the residual value ri(j) replaces yi
Mathematically consistent with univariate
parameter estimates
Lasso’s LAR algorithm
Be applicable
Solve the sparse regression problem under 1-norm constraints
Corresponding to the regularized regression problem
Classification
λ=0
Standard least squares problem
The larger λ
The sparser the model parameter solution w vector is, the sparser it is
linear basis function regression
basis function
regression model
data matrix
regression coefficient solution
singular value decomposition
pseudoinverse
SVD decomposition
Regression coefficient model solution
Error decomposition for regression learning
error function
error expectation
Model
theoretical best model
Learning model
error decomposition
Model complexity and error decomposition
The model is simple
Large deviation, small variance
The model is complex
Small deviation, large variance
Appropriate model complexity needs to be chosen