Objectives

• Differentiate supervised from unsupervised classification

• Recognize the linkage between statistical learning models and interpolation

• Define the key elements of tree-based classifiers

• Articulate the differences in statistical learning for spatial data

Explaining Spatial Patterns

Explanation So Far

• Deterministic Interpolation: best explanation for variation is distance

• Probabilistic Interpolation: best explanation is covariance (plus spatial trends)

First Order Properties

\[ \begin{equation} z(\mathbf{x}) = \mu(\mathbf{x}) + \epsilon(\mathbf{x}) \end{equation} \]

• Often we actually care about the “drivers” of \(\mu(x)\)

• Inference not prediction

Key Challenges

• Data volume

• Sampling designs

• Nonlinearity

• Autocorrelation

Statistical Learning

• “Machine Learning”

• Broad class of methods that rely on efficient, algorithmic learning

• Probabilities derived from “large” data (rather than theoretical distributions)

• Relax traditional statistical assumptions

Supervised Learning/Classification

• Goal is inference/prediction not grouping

• Training data: observations with known values used to generate model parameters

• Validation data: observations with known values used to tune hyperparameters prior to full model implementation

• Testing data: observations held out of initial model-fitting to determine accuracy

Classification Trees

Classification Trees

• Divide the predictor space (\(R\)) into \(J\) non-overlapping regions

• Every observation in \(R_j\) gets the same prediction

• Recursive binary splitting

• Maximize the information gained at each split

• Pruning and over-fitting

Benefits and drawbacks

Random Forests

Sooooo Many Trees

• How to build ensembles?

• The number of and tuning of hyperparameters

• Boosting

Key Challenges with Tree-Based Methods

• No direct way to incorporate spatial autocorrelation

• Training Set qualities vs. Inferential conditions

• Cross-validation considerations