3. Packages and applications

This part of the Scipy lecture notes is dedicated to various scientific packages useful for extended needs.

• 3.1. Statistics in Python
  • 3.1.1. Data representation and interaction
    • 3.1.1.1. Data as a table
    • 3.1.1.2. The pandas data-frame
  • 3.1.2. Hypothesis testing: comparing two groups
    • 3.1.2.1. Student’s t-test: the simplest statistical test
    • 3.1.2.2. Paired tests: repeated measurements on the same indivuals
  • 3.1.3. Linear models, multiple factors, and analysis of variance
    • 3.1.3.1. “formulas” to specify statistical models in Python
    • 3.1.3.2. Multiple Regression: including multiple factors
    • 3.1.3.3. Post-hoc hypothesis testing: analysis of variance (ANOVA)
  • 3.1.4. More visualization: seaborn for statistical exploration
    • 3.1.4.1. Pairplot: scatter matrices
    • 3.1.4.2. lmplot: plotting a univariate regression
  • 3.1.5. Testing for interactions
  • 3.1.6. Full code for the figures
  • 3.1.7. Solutions to this chapter’s exercises
• 3.2. Sympy : Symbolic Mathematics in Python
  • 3.2.1. First Steps with SymPy
    • 3.2.1.1. Using SymPy as a calculator
    • 3.2.1.2. Symbols
  • 3.2.2. Algebraic manipulations
    • 3.2.2.1. Expand
    • 3.2.2.2. Simplify
  • 3.2.3. Calculus
    • 3.2.3.1. Limits
    • 3.2.3.2. Differentiation
    • 3.2.3.3. Series expansion
    • 3.2.3.4. Integration
  • 3.2.4. Equation solving
  • 3.2.5. Linear Algebra
    • 3.2.5.1. Matrices
    • 3.2.5.2. Differential Equations
• 3.3. Scikit-image: image processing
  • 3.3.1. Introduction and concepts
    • 3.3.1.1. scikit-image and the SciPy ecosystem
    • 3.3.1.2. What’s to be found in scikit-image
  • 3.3.2. Input/output, data types and colorspaces
    • 3.3.2.1. Data types
    • 3.3.2.2. Colorspaces
  • 3.3.3. Image preprocessing / enhancement
    • 3.3.3.1. Local filters
    • 3.3.3.2. Non-local filters
    • 3.3.3.3. Mathematical morphology
  • 3.3.4. Image segmentation
    • 3.3.4.1. Binary segmentation: foreground + background
    • 3.3.4.2. Marker based methods
  • 3.3.5. Measuring regions’ properties
  • 3.3.6. Data visualization and interaction
  • 3.3.7. Feature extraction for computer vision
  • 3.3.8. Full code examples
  • 3.3.9. Examples for the scikit-image chapter
• 3.4. Traits: building interactive dialogs
  • 3.4.1. Introduction
  • 3.4.2. Example
  • 3.4.3. What are Traits
    • 3.4.3.1. Initialisation
    • 3.4.3.2. Validation
    • 3.4.3.3. Documentation
    • 3.4.3.4. Visualization: opening a dialog
    • 3.4.3.5. Deferral
    • 3.4.3.6. Notification
    • 3.4.3.7. Some more advanced traits
• 3.5. 3D plotting with Mayavi
  • 3.5.1. Mlab: the scripting interface
    • 3.5.1.1. 3D plotting functions
    • 3.5.1.2. Figures and decorations
  • 3.5.2. Interactive work
    • 3.5.2.1. The “pipeline dialog”
    • 3.5.2.2. The script recording button
  • 3.5.3. Slicing and dicing data: sources, modules and filters
    • 3.5.3.1. An example: inspecting magnetic fields
    • 3.5.3.2. Different views on data: sources and modules
  • 3.5.4. Animating the data
  • 3.5.5. Making interactive dialogs
    • 3.5.5.1. A simple dialog
    • 3.5.5.2. Making it interactive
  • 3.5.6. Putting it together
• 3.6. scikit-learn: machine learning in Python
  • 3.6.1. Introduction: problem settings
    • 3.6.1.1. What is machine learning?
    • 3.6.1.2. Data in scikit-learn
  • 3.6.2. Basic principles of machine learning with scikit-learn
    • 3.6.2.1. Introducing the scikit-learn estimator object
    • 3.6.2.2. Supervised Learning: Classification and regression
    • 3.6.2.3. A recap on Scikit-learn’s estimator interface
    • 3.6.2.4. Regularization: what it is and why it is necessary
  • 3.6.3. Supervised Learning: Classification of Handwritten Digits
    • 3.6.3.1. The nature of the data
    • 3.6.3.2. Visualizing the Data on its principal components
    • 3.6.3.3. Gaussian Naive Bayes Classification
    • 3.6.3.4. Quantitative Measurement of Performance
  • 3.6.4. Supervised Learning: Regression of Housing Data
    • 3.6.4.1. A quick look at the data
    • 3.6.4.2. Predicting Home Prices: a Simple Linear Regression
  • 3.6.5. Measuring prediction performance
    • 3.6.5.1. A quick test on the K-neighbors classifier
    • 3.6.5.2. A correct approach: Using a validation set
    • 3.6.5.3. Model Selection via Validation
    • 3.6.5.4. Cross-validation
    • 3.6.5.5. Hyperparameter optimization with cross-validation
  • 3.6.6. Unsupervised Learning: Dimensionality Reduction and Visualization
    • 3.6.6.1. Dimensionality Reduction: PCA
    • 3.6.6.2. Visualization with a non-linear embedding: tSNE
  • 3.6.7. The eigenfaces example: chaining PCA and SVMs
    • 3.6.7.1. Preprocessing: Principal Component Analysis
    • 3.6.7.2. Doing the Learning: Support Vector Machines
    • 3.6.7.3. Pipelining
  • 3.6.8. Parameter selection, Validation, and Testing
    • 3.6.8.1. Hyperparameters, Over-fitting, and Under-fitting
    • 3.6.8.2. Visualizing the Bias/Variance Tradeoff
    • 3.6.8.3. Summary on model selection
    • 3.6.8.4. A last word of caution: separate validation and test set
  • 3.6.9. Examples for the scikit-learn chapter