Roadmap

Principles

• Make complex things simple.
• Stay hungry stay foolish.
• Have fun.

Least squares

There is an overview page for the Least Squares series.

• Basic
  • Least squares derivation
  • Simple least squares applications
    • Lucas-Kanade tracking
    • Time calibration.
    • CT reconstruction.
      • Bonus: Solving Ax = b by Fourier (Radon) transform
  • Probability and least squares.
    • Gaussian MLE and least squares.
    • Covariance
      • Covariance is inverse Hessian.
      • GPS covariance.
      • Lucas-Kanade with covariance.
• Least squares variants
  • Kalman filter.
    • Least square formulation.
    • Extended Kalman filter.
  • Fixed-lagged smoothing
    • Marginalization.
    • Schur complement.
    • ISAM2.
  • Differential dynamic programming
• Constrained least squares
  • Equality constraints.
  • Inequality constraints, Primal-dual interior points method.
    • Land a rocket.
• Common techniques
  • Regularization.
  • Robust loss.
  • Sparsity.
  • Gradient checking.
• Least squares on the manifold.
  • The linear-quadratic function on SO(3)
    • Single update
  • Iterative closest point.
    • SO(3)
    • SE(3)
  • Lucas-Kanade on SE(2)
  • PCA.
    • Lie-ranking.
    • SO(N)
  • Inverse kinematics
    • Interpolation on a group
  • Differential equations on the manifold.
    • so(3) error propagation
• Interviews
  • TBD

Apply Math

• Optimization
  • Least Squares
  • The covariance for Optimization
  • Linear Programming
  • Integer Programming
  • Sum of Squares Programming
  • Global Non-Convex Optimization
  • Semidefinite Programming
  • Lyapunov Function
• Group
  • Optimization on Manifolds/Lie-groups

Applications

• Computer Vision
  • Lucus Kanade
  • Haze removal
  • Facial Landmarks Detection
• Space
  • Gimbal Lock
  • Land a Rocket
    • Problem Definition
    • Constraint Optimization
    • Exploit the Structure
• Robotics
  • Inverse Kinematics
  • Time Calibration

Software

• Inter-process communication
  • TCP/IP
  • Shared memory
• The Visitor pattern
  • Serialization
  • Configuration
• Template metaprogramming
  • Optimal matrix multiplication algorithm
  • Optimal matrix multiplication order in compile time
• Cloud Computing
  • Zookeeper & Kafka
• Computational Geometry
  • 3d tree
• Python binding
  • Sparse matrix solver

Deep learning

• Random stuff
  • Style transformation
• Shallow (deep) learning: https://github.com/yimuw/Let-Tensor-Flow (wrote long time ago, plan to update)
  • SLAM
  • investment
  • B-curve
• Interviews
  • TBD