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My Thesis: A Overview

These are some scratch notes for organizing my thesis.

IDEAS to Add

  • Two Views on Regression with PyMC3 and sklearn - prezi

Main Idea

  1. Spatial-Temporal, High Dimensional, Complex Data - What do we do with it?
  2. Data Inherent Features - Point Estimates, Spatial Meaning, Temporal Meaning
  3. Understaing - Similarities → Correlations → Dependencies → Causation
  4. ML Emulator Attributes - Sensitivity, Uncertainty, Scale, Error Propagation

Part I - Sensitivity Analysis

Opening up black-box models (i.e. kernel methods)

  • We look at sensitivity methods in the context of kernel methods
  • "Open the black box"
  • Non-Bayesian Context
  • (KRR, SVM, KDE, HSIC)
  • Earth Data
  • "Incomplete" Bayesian Context
  • Show examples in the context of a Bayesian Model (GPs + Emulation)

Publication

  • SAKAME

Lab Notebooks

  • GPs + GSA + Emulation - \phi-Week

Tutorials

  • Regression: KRR, OKRR, RFF
  • Classification: SVM, RFF+SGD
  • Density Estimation: KDE, OKECA
  • Dependence Estimation: HSIC, rHSIC

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ML Problems

  • Representations?
  • Sensitivity
  • Uncertainty Estimates
  • Noise Characterization

Background

  • Representations (Kernels, Random Features, Deep Networks)
  • Uncertainty
  • Noise
  • Analysis

Key Concepts

  • Representations - Kernels, Random Features, NNs|PNN|BNNs
  • Similarity Measures - Naive, HSIC, IT
  • Uncertainty - Epistemic, Aleatoric, Out-of-Distribution
  • Methods - Discriminative (Model), Density Destructors (Density Estimation)

Model-Based

  • Representations
  • Analysis - Derivative, Sensitivity
  • Uncertainty Characterization - Output-Variance (eGP, eSGP), Input-Training (eVGP, BGPLVM)
  • Applications
  • Emulation + Sensitivity
  • Multi-Output + Sensitivity

Information-Based

  • IT Measures
  • Classic Methods - single-dimension/multivariate, mean, std dev, pt est. stats
  • generative modeling - VAE, GAN, NF, DDD
  • GAUSSIANIZATION
  • Neural Networks, Deep GPs
  • Noise Characterization
  • Require Densities - Gaussian, Mixture, Histogram, KDE, Neural, RBIG
  • Applications
  • climate model + noise + MI
  • sampling

Applications

  • Climate Models
  • Spatial Representations
  • Noise Characterization
  • Information Theory Estimates
  • IASI
  • Error Propagation
  • Uncertainty Estimates
  • Multi-Output
  • Spatial-Temporal
  • ARGP - BBP Data
  • Multi-Output
  • Spatial-Temporal
  • Sensitivity
  • Uncertainty
  • Drought Variables
  • Temporal
  • Emulation
  • Sensitivity
  • Uncertainty