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Model Selection Guide — Cross-Topic Synthesis

Which model to try, in what order, and how to compare candidates without fooling yourself. See INDEX.md for the full curriculum index.

Overview

Model selection is three decisions in a fixed order: evaluation design (how you will measure), candidate set (which families are plausible), and comparison protocol (how you record and decide). Evaluation design comes first because it is the only step whose mistakes are irreversible — a leaked test set cannot be un-leaked.

Step 1 — Evaluation Design First

Choose the split strategy and metric before comparing models. Model selection performed on the test set leaks information; the test set is used once, after the complete pipeline has been selected.

Data situation Validation design
Independent, identically distributed observations Random train/validation/test split or shuffled k-fold CV
Time-ordered observations Forward or rolling validation; never shuffle the future into training
Multiple rows per person/device/group Group-aware split (all rows of a group on one side)
Rare classes Stratified split plus class-appropriate metrics (PR-AUC, per-class recall)
Small data and tuning Nested CV when an unbiased comparison matters

Leakage pitfalls (each produces a "too good to be true" score):

  • Fitting scalers, PCA, or feature selection on the full dataset before splitting — preprocessing must be fit on each fold's training portion only.
  • Tuning hyperparameters, or monitoring early stopping, on the test set.
  • Shuffled CV on temporal data — the model "predicts" the past from the future.
  • Duplicates or grouped rows landing on both sides of a split.
  • Target-derived features (target encoding, imputation using \(y\)) computed on all rows.

Step 2 — Problem Type → Candidate Families

Problem Trivial baseline First real model Main candidates Escalate to
Tabular regression Predict the mean Linear/Ridge Random Forest, Boosting NN (rarely wins on tabular)
Tabular classification Majority class Logistic Regression Trees, Ensembles, SVM, KNN Boosting, tuned
High-dim sparse (text counts) Majority class Naive Bayes Linear SVM, Logistic Transformer, pretrained
Images — Small CNN CNN + augmentation Pretrained backbone
Sequences Last-value / n-gram RNN/LSTM Transformer Pretrained LLM (21)
Graph-structured data Logistic on node features GNN GCN/GAT variants —
Unlabeled grouping Single cluster K-Means GMM, DBSCAN, hierarchical —
Dimensionality reduction Keep raw features PCA t-SNE/UMAP (visualization only) Autoencoder
Density / generation Histogram / GMM GMM VAE, GAN, diffusion —
Sequential decisions Random / greedy policy Tabular Q-learning Deep RL —

Step 3 — Trade-off Table

Family Small \(n\) Large \(n\) High \(d\) Interpretability Train cost Inference cost
Linear / Logistic Good Good Good with \(\ell_1/\ell_2\) High (coefficients) Low Very low
Naive Bayes Very good OK Very good (sparse) Medium Very low Very low
KNN Good Memory-bound Poor (distance concentration) Medium (neighbors) None High: \(O(nd)\) per query
Decision Tree Overfits fast OK OK High (small trees) Low Very low
Random Forest Good Good Good Low–medium (importances) Medium Medium
Gradient Boosting Good if tuned Very good Good Low–medium Medium Low–medium
Kernel SVM Good Poor: \(O(n^2)\)–\(O(n^3)\) Good (margin) Low High Medium (\(\propto\) support vectors)
Neural Networks Poor without transfer Very good Good (learned features) Low High Medium

Step 4 — Hyperparameter Sensitivity by Family

Family Critical hyperparameters Sensitivity Practical note
Ridge / Lasso \(\lambda\) Moderate Log-spaced grid; loss is smooth in \(\log\lambda\)
Logistic Regression Regularization strength Low–moderate Rarely the bottleneck
KNN \(k\), metric, feature scaling High Unscaled features silently break distances
Decision Tree Depth, min samples per leaf High Unpruned trees interpolate noise
Random Forest Number of trees, features per split Low More trees never hurts accuracy, only time
Gradient Boosting Learning rate \(\times\) rounds, depth High Small learning rate + early stopping
Kernel SVM \(C\), \(\gamma\) Very high Joint 2-D log grid; wrong \(\gamma\) means all points are support vectors
K-Means \(k\), initialization High Multiple restarts; elbow/silhouette for \(k\)
DBSCAN \(\varepsilon\), min points Very high Small \(\varepsilon\) changes flip cluster count
Neural Networks Learning rate first; then width/depth, batch size Very high Learning rate dominates every other choice — see Optimization Methods

When From-Scratch Understanding Says "Don't Use the Fancy Model"

Implementing these models from first principles yields concrete stop signs:

  • \(n \lesssim d\) or \(n\) small: variance dominates; a regularized linear model beats a deep net because the bias–variance trade-off is against you.
  • KNN in high dimensions: pairwise distances concentrate, nearest and farthest neighbors become indistinguishable — see Geometry of ML.
  • Boosting on noisy labels: boosting keeps reweighting the mislabeled points it can never fit; random forests degrade more gracefully.
  • K-Means on non-convex or unequal-density clusters: the objective is distortion to centroids, so it will return \(k\) convex cells whether or not they exist in the data.
  • Deep nets on small tabular data: tree ensembles usually win at a fraction of the tuning cost.
  • The tie-break rule: if the simple model is within one standard deviation (across folds/seeds) of the complex one, select the simple model — lower variance, cheaper inference, easier audits.

Required Comparison Record

For every selected model record the baseline, split, preprocessing fitted on training data only, hyperparameter search space, primary and secondary metrics, uncertainty across folds/seeds, runtime, error slices, and final limitations.

Connections