コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題 from Udemy

What's inside

Syllabus

はじめに

レクシャースライドPDFです．ファイルは***slide.pdfです（映像撮影時の古いものも残してありますが，新しいほうは誤植などを修正してあります）．
演習問題の解答例のファイルは***answer.pdfです．
演習用のコードはリンクのgithubを参照してください．

論文例

ギリシャ文字

ギリシャ文字２

記号いろいろ

カッコ・演算子

太字・細字・斜体・立体

行列・ベクトルの記法

添字と総和

線形代数：行列とベクトル

集合

集合の書き方

部分集合

和集合，積集合

直積

集合の要素数

区間の最大最小・上界下界

ベクトルの記法

行列の記法，行列の和

ベクトル空間（線形空間）

内積：ベクトル同士の積

内積＝射影

ノルムと距離

ノルムいろいろ

行列ノルム

行列と列ベクトルの積

行列と行ベクトルの積

行列同士の積

行列とベクトルの積：計算例

行列の積：総和での表現

行列／ベクトルの積：次元の確認

行列／ベクトルの積：列の和，行の和

対角行列

Axの解釈：列ベクトルの線形和

Axの解釈：行への射影

線形結合，線形独立

行列のランク

Ax=bの解釈：投影した座標

零空間

Axの解釈：列の線形和

行列積を総和で実装：pythonで列の線形和を計算

行列積を総和で実装：pythonのunittestで確認

行列積を総和で実装：pythonコードと数式証明

連立方程式Ax=bの解釈

連立方程式Ax=bの解

一般化逆行列による解の解釈

学習画像Aの線形和で目標画像bを近似するpython実装

ニューラルネットワーク＝行列ベクトル積＋非線形

numpyの行列積だけ2層でニューラルネットワークを実装

複数の連立方程式をまとめる行列方程式

微分：関数と導関数

関数

凸集合

凸関数

凸の重要性

関数の分類

線形関数

微分

微分と連続

微分と連続２

微分と傾き

劣微分

微分の記法

全微分：１次元

全微分：２次元

偏微分：記法

勾配＝偏微分

ベクトルでの微分

ヘッセ行列：２階微分行列

ヘッセ行列の解釈

勾配ベクトルとヘッセ行列の例

勾配ベクトルの要素の計算

勾配ベクトルの要素の計算２

勾配ベクトルの要素の計算３

ヘッセ行列の要素の計算

ヤコビ行列：ベクトル値関数の微分

ヤコビ行列：１階微分行列

ヤコビ行列と勾配ベクトル

関数合成の微分：具体例

関数合成の微分：連鎖律

関数合成の微分：連鎖律で計算

ベクトル版の連鎖律

微分の計算；数式微分，数値微分，自動微分

自動微分１

自動微分２

自動微分３

計算グラフ上の連鎖律

計算グラフ上の連鎖律：誤差逆伝播

微分の実装；数式微分，数値微分，自動微分

sympyによる数式微分１

sympyによる数式微分２

scipyによる数値微分

autogradによる自動微分

数式微分と自動微分の違い

最適化：勾配法とパラメータ推定

連続最適化

反復法（勾配法）の基本：1次元の最急降下法

最急降下法：デモ

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores mathematical formulations, concepts, and techniques used in computer vision, pattern recognition, and image processing

Provides a foundation in linear equations, differential calculus, regression analysis, and constrained optimization

Offers a practical approach with Python code demonstrations to enhance understanding

Emphasizes the interpretation of the widely encountered equation Ax=b in various contexts

Suitable for learners with a background in linear algebra and a desire to apply mathematical concepts to real-world problems

Requires familiarity with basic programming concepts and Python syntax

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題 with these activities:

Review Linear Algebra Foundations

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Brush up on the concepts of linear algebra, such as matrix operations, vector spaces, and linear transformations, to strengthen your understanding of the mathematical foundation used in this course.

Browse courses on Linear Algebra

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Review notes and textbooks from previous linear algebra courses
Complete practice problems and exercises to test your understanding
Watch online lectures or tutorials to reinforce key concepts

Join a Matrix Theory Study Group

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Engage with fellow students or classmates to discuss concepts, share insights, and work through problems collaboratively. This interactive activity will enhance your understanding and provide support.

Browse courses on Linear Algebra

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Reach out to classmates or form a study group with interested individuals
Establish a regular meeting schedule and set clear goals for each session
Take turns presenting concepts, solving problems, and facilitating discussions

Solve Practice Matrix Problems

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Engage in regular practice of solving matrix problems to improve your computational skills and deepen your understanding of matrix theory.

Browse courses on Matrix Operations

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Find online problem sets or textbooks with practice exercises
Allocate dedicated time for solving these problems on a regular basis
Review your solutions and identify areas for improvement

Three other activities

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Show all six activities

Solve Differential Calculus Practice Problems

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Sharpen your differential calculus skills by regularly practicing problem-solving. This will strengthen your understanding of the concepts and improve your ability to apply them.

Browse courses on Derivatives

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Find online problem sets or textbooks with practice exercises
Allocate dedicated time for solving these problems on a regular basis
Review your solutions and identify areas for improvement

Explore Advanced Matrix Analysis Tutorials

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Seek out specialized tutorials or online courses to expand your knowledge of advanced matrix analysis techniques and their applications in various fields.

Browse courses on Singular Value Decomposition

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Identify reputable online platforms or educators offering tutorials
Review the course content and select tutorials that align with your interests
Follow the tutorials, complete the exercises, and engage in discussions

Create Visualizations of Matrix Transformations

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Enhance your understanding of matrix transformations by creating visual representations using tools like Python or MATLAB. This hands-on activity will solidify your grasp of the geometric interpretations.

Browse courses on Linear Transformations

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Choose a matrix transformation and its corresponding geometric operation
Write a program to generate a visual representation of the transformation
Experiment with different transformation parameters and observe the resulting effects

Career center

Learners who complete コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題 will develop knowledge and skills that may be useful to these careers:

Computer Vision Engineer

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See salaries and explore the career path for Computer Vision Engineer

Data Scientist

Data Scientists use their expertise in statistical modeling, machine learning, and data analysis to extract insights from data. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can provide you with a strong foundation in the mathematical principles and techniques used in data science, including linear algebra, optimization, and numerical methods. These concepts are essential for developing and implementing data-driven solutions.

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Operations Research Analyst

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Market Researcher

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Data Analyst

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Software Engineer

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Statistician

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Business Analyst

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Data Engineer

Data Engineers design and build systems for storing, managing, and processing data. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding data structures, algorithms, and data management techniques.

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Economist

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Actuary

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Financial Analyst

Financial Analysts use financial data and models to make investment recommendations and provide financial advice. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding and implementing financial models and making informed investment decisions.

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Consultant

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Quantitative Analyst

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Machine Learning Engineer

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