Machine Learning Library

Models explained from first principles — assumptions, learning, weaknesses, and market relevance.

Machine-learning models explained from first principles. The point of this section is to show that I understand model logic, not just how to call a library function — and, as in the Equation Library, to test each model honestly against real Nasdaq-100 data rather than take its reputation on trust.

Every model page answers the same nine questions:

  1. What problem does this model solve?
  2. What assumptions does it make?
  3. What data does it need?
  4. How does it learn?
  5. What are its strengths?
  6. What are its weaknesses?
  7. How could it apply to markets?
  8. What does the Python code look like?
  9. How would I explain it to a supervisor?

Published models

Added one at a time, to the standard above. The roadmap below is the plan.

Supervised Liquidity-Stress Modelling

decision systems
supervised learning

The supervised half of the liquidity specialist: a gradient-boosted classifier that forecasts whether the coming week will be a stress week, evaluated with purged walk-forward. It beats chance handsomely (average precision 0.46 against a 15% base rate, ROC-AUC 0.80) and is well calibrated (Brier 0.106) — but ranking days by a single transparent feature, today’s 20-day realised volatility, beats it (AP 0.49, ROC-AUC 0.83). Forward-stress predictability is volatility persistence; the supervised label buys a calibrated probability, not incremental timing.

9 min

Bayesian Hypothesis Reconciliation — the Consensus Engine

decision systems
consensus

The capstone of the specialist tier. Instead of averaging model outputs, it treats each specialist as evidence with a learned, state-dependent reliability and computes a posterior over competing market-state hypotheses. On a known three-state process it beats averaging and voting on both accuracy (0.78 vs 0.73 vs 0.70) and calibration (log-loss 0.55 vs 0.64 vs 0.83), because each specialist is reliable in a different state; its posterior entropy runs 31% higher at transitions — it knows when it doesn’t know; and it holds on real Nasdaq vol-states (0.74 vs 0.68).

11 min

CUSUM & Concept-Drift Detection

decision systems
change detection

The lightweight, frequentist complement to Bayesian change-point detection. A from-scratch CUSUM detects a known 1σ shift in 7 steps, and its operating characteristic makes the fundamental trade-off explicit: raising the threshold moves the in-control false-alarm interval from 18 to 3,300 steps but slows detection from 3 to 16 steps — no free lunch. On the Nasdaq it flags 69 volatility-regime onsets point-in-time, catching the COVID crash on 2020-02-25, one day after BOCPD, at a fraction of the compute.

10 min

Contextual Bandits — Conditional Reliability, Learned

decision systems
reinforcement learning

The mechanism for condition-specific expert reliability, and the RL alternative the proposal names. LinUCB, verified on a task where each expert is best in a different regime, reaches the oracle exactly (0.75 vs 0.49 context-free) and recovers the routing perfectly. But pointed at real volatility forecasters routed by regime, it does not beat a fixed best expert (0.535 vs 0.539) — the conditional structure is real but too weak to exploit. Contextual bandits are the right tool for conditional reliability; whether it pays is an empirical question, and here it is another H7 null.

11 min

Cross-Asset Dependence — DCC, Factor Structure & Networks

decision systems
dependence

The machinery of the Cross-Asset Confirmation specialist. A from-scratch dynamic conditional correlation model (DCC, a+b=0.99) shows average pairwise correlation roughly tripling from calm to crisis (0.23 in 2017 to 0.76 in the COVID crash), and the defensive staple that diversifies in normal times (PEP–tech correlation 0.31) re-couples when it counts (0.70 in 2020). Diversification fails exactly when you need it — and a real-time dependence estimate is the signal that says so.

11 min

EGARCH, GJR & HAR-RV — Asymmetric and Realized Volatility

decision systems
volatility

Extending the GARCH entry with the models a volatility specialist actually uses. On the Nasdaq, next-day realized vol is 0.95% after down days vs 0.77% after up days — a leverage effect that GJR (γ=+0.15, t 4.2) and EGARCH (γ=−0.13, t −5.7) both capture, beating symmetric GARCH decisively on BIC (9202→9143→9118). And HAR-RV, a three-line regression on a Garman-Klass realized measure, forecasts next-day volatility better out-of-sample (QLIKE 0.70) than GARCH (0.87) or a random walk (0.99) — because it is fit directly on the realized measure.

10 min

Liquidity-Stress Anomaly Detection

decision systems
anomaly detection

The liquidity specialist’s detector: unsupervised anomaly detection on microstructure-stress features. An Isolation Forest recovers injected anomalies at 0.95 precision/recall, and on the Nasdaq it flags 5% of days that concentrate 5.4× into known crises and precede sharply higher volatility (41.6% vs 17.3% forward). Crucially, 18% of its flags are ‘quiet illiquidity’ — wide intraday ranges with no big close-to-close move — exactly the stress a simple return threshold misses.

10 min

Online Expert Weighting (Prediction with Expert Advice)

decision systems
online learning

The adaptive successor to static ensembles. When several forecasters compete and the best one changes with the regime, the Hedge algorithm updates their weights online and is provably almost as good as the best expert in hindsight — no foreknowledge required. On four volatility forecasters whose ranking genuinely rotates across 2015–2026, Hedge matched the best single expert (mean loss 0.068 vs 0.064), beat equal-weighting (0.078) and drove the weak expert’s weight to zero, with cumulative regret 11.5 against a worst-case bound of 44.3 — while the fancier ‘forgetting’ variant did not help, an honest H7 null.

11 min

The Kalman Filter & State-Space Models

decision systems
filtering

The workhorse for estimating a latent state that evolves over time, in real time, with honest uncertainty. Implemented from scratch and verified against statsmodels to 2.8e-10, it recovers a known drifting β on synthetic data (95.9% coverage of its 2σ band) and tracks AAPL’s genuinely time-varying β to the Nasdaq (median 1.04, drifting 0.67–1.27). It is the linear-Gaussian cousin of the HMM forward filter — and it makes the site’s filtered-vs-smoothed look-ahead point exactly: the smoothed estimate ‘peeks’, revising the real-time one by 0.08 using the future.

12 min

The Strategy-Suitability Council

decision systems
strategy

The proposal’s strategy layer, and the test of H5. A council that routes among trend, mean-reversion and defensive strategies by regime, with a hand-designed suitability mapping, underperforms plain diversification (Sharpe 0.39 vs 0.58) — because the intuitive mapping is empirically wrong: trend beats mean-reversion even in ‘range’ regimes, and mean-reversion beats cash in ‘stress.’ Learn the mapping from data instead and the council flips to 0.66, beating static — but buy-and-hold’s 0.84 still tops all timing. Suitability must be learned, not assumed.

10 min

Ensemble Methods & Model Combination

decision systems
ensembles

The consensus baselines any fancier reconciliation layer must beat. On a genuinely forecastable target (next-day turbulence, AUC≈0.67), four base models combined four ways: Bayesian model averaging edged the best single model (Brier 0.2099 vs 0.2102), equal-weight matched it, stacking over-fit, and hard majority-vote was catastrophic — because the base models were 0.97-correlated. The lesson is the variance-reduction identity: an ensemble helps in proportion to base-model diversity, not count.

11 min

Bayesian Change-Point Detection

decision systems
reinforcement learning

The HMM labels regimes in hindsight; a live system needs to know a regime has changed as it happens, from data up to today only. Bayesian Online Change-Point Detection maintains a posterior over the time since the last change and signals when it collapses. Validated on synthetic ground truth (latency 1/8/3 steps), then run online on the Nasdaq — flagging the COVID crash and the 2022 bear onset with no look-ahead.

12 min

Market Microstructure & Execution Modelling

decision systems
reinforcement learning

A signal is worthless if execution costs eat the edge. Market microstructure is the anatomy of a traded price — spread, order flow, impact — and optimal execution is the discipline of trading a position at least cost. The Almgren–Chriss efficient frontier of execution, its closed-form trajectory verified against a numerical optimizer to machine precision, and the square-root impact law calibrated to the Nasdaq.

11 min

Markov Decision Processes & Bellman Equations

decision systems
reinforcement learning

An MDP formalises decision-making over time: states, actions, transitions, rewards, and a discount factor, tied together by the Bellman equation. Value iteration solves a regime-based position-sizing MDP built from this site’s fitted HMM — exactly, with a policy that quantifies what foresight is worth.

10 min

Markov-Switching Regression

decision systems
reinforcement learning

The HMM switches the distribution of returns; Markov-switching regression switches a relationship. Fit to a defensive stock’s beta on the Nasdaq, it finds that beta doubles in the turbulent regime — the ‘correlations converge in a crisis’ effect, made a parameter. Validated by recovering a known switching-beta model exactly, with an independent Hamilton filter reproducing the likelihood to twelve decimals.

10 min

Multi-Agent Systems & Credit Assignment

decision systems
reinforcement learning

The proposal is a team of agents that together produce one P&L; the Review & Learning Agent must say who earned it. Markov games are the formal framework, and Shapley values the fair attribution. Applied to a four-agent Nasdaq strategy, credit assignment overturns the naïve story: leave-one-out gets vol-targeting’s sign wrong, and the same agents earn opposite credit under a drawdown objective — with the efficiency axiom verified to machine precision.

11 min

Policy Gradients & Actor-Critic

decision systems
reinforcement learning

Policy-gradient methods optimise the policy itself by gradient ascent on expected reward, handling continuous actions natively. A Gaussian-policy actor-critic learns the analytically optimal exposure on the regime environment, and the baseline’s variance reduction is measured: 3,176×.

9 min

Probability Calibration & Conformal Prediction

decision systems
reinforcement learning

A next-day direction model has no skill (AUC≈0.50) — but it must still be honest about its uncertainty. Calibration turns over-confident scores into trustworthy probabilities (ECE 0.105→0.062) without touching the absent skill; conformal prediction wraps a point forecast in an interval with a distribution-free coverage guarantee, and vol-normalization makes that interval honest in every regime.

11 min

Proximal Policy Optimisation (PPO)

decision systems
reinforcement learning

PPO fixes the two failings of vanilla policy gradients — step-size fragility and no sample reuse — with a clipped surrogate objective that acts as a built-in trust region. Demonstrated on the regime environment: stable convergence to the analytic optimum, and the clip capping updates on a fixed batch.

9 min

Q-Learning & Deep Q-Networks

decision systems
reinforcement learning

Q-learning solves an MDP without knowing its transition probabilities or rewards, from sampled experience, off-policy. Demonstrated on the regime MDP whose exact Q* is known: tabular and DQN-style learners recover the optimal policy exactly — even while behaving randomly.

8 min

Risk-Sensitive & Constrained RL

decision systems
reinforcement learning

Plain RL maximises reward, which in finance means it will take catastrophic risk for marginal return. Risk-sensitive objectives trade return for risk continuously; constrained MDPs impose hard limits the policy cannot cross. A CVaR-budgeted agent that wants 6.3× leverage, capped to 1.41× — the proposal’s Risk Agent, formalised.

9 min

Activation Functions

deep learning
neural networks

Activation functions inject the nonlinearity without which a deep network collapses to a single linear map. Sigmoid, tanh, ReLU and its variants, the vanishing-gradient problem that stalled deep learning, and why ReLU fixed it.

7 min

Attention

deep learning
neural networks

Attention is a differentiable, content-based lookup: a query retrieves a similarity-weighted blend of values. Scaled dot-product attention and why the √d matters, multi-head attention, and the difference between self- and cross-attention.

8 min

Avoiding Data Leakage

quant-specific ML
validation

Data leakage is any time information from the test set, the future, or the outcome contaminates training, silently inflating results. The taxonomy of leakage, the preprocess-inside-the-split rule, and a demonstration where leakage manufactures a 0.81 AUC from pure noise.

8 min

Backpropagation as an Algorithm

deep learning
neural networks

Backpropagation is the algorithm that trains every neural network: reverse-mode autodiff that computes the gradient of the loss w.r.t. all parameters in one backward pass, exact to machine precision and at a cost independent of the parameter count. Gradient checking and the efficiency that makes deep learning possible.

9 min

Convolutional Neural Networks

deep learning
neural networks

A CNN slides small shared filters across grid-structured data to detect local, translation-invariant patterns at a fraction of a dense net’s parameters. Convolution, pooling, the inductive bias, and an honest 1D-CNN test on Nasdaq sequences.

9 min

Decision Trees

foundation models
trees

Decision trees recursively split feature space to cut impurity (Gini/entropy). Nonparametric and interpretable, they capture nonlinearities — but a single tree overfits, memorising the Nasdaq’s noise while generalising to the base rate.

6 min

Embeddings

deep learning
neural networks

An embedding maps discrete entities — words, tickers, categories — to dense learned vectors whose geometry encodes similarity, replacing sparse one-hot encoding. The lookup matrix, learning by factorization, and a real asset embedding from Nasdaq co-movement.

7 min

Feature Engineering for Returns

quant-specific ML
feature engineering

In applied quant ML the features matter more than the model. Making prices stationary, building lag/volatility/momentum features point-in-time, the stationarity–memory trade-off, and an honest test of which features predict direction versus volatility on the Nasdaq.

8 min

Gaussian Mixture Models

foundation models
clustering

A GMM models data as a mixture of Gaussians, fit by EM, giving each point a probability of membership rather than a hard label. It generalises K-means. On Nasdaq returns a two-component mixture — a calm Gaussian and a crisis Gaussian — reproduces the fat tails a single Gaussian misses.

8 min

K-Means Clustering

foundation models
clustering

K-means partitions unlabelled data into k groups by minimising within-cluster distance to a centroid. Lloyd’s algorithm, the elbow and silhouette for choosing k, and a Nasdaq test where it recovers calm, sell-off, and rally regimes it was never told about.

8 min

LightGBM

foundation models
ensembles

LightGBM is gradient boosting like XGBoost, but with leaf-wise tree growth and histogram-based splits that make it 25–50× faster at the same accuracy. What’s different, why it’s faster, and when leaf-wise growth overfits.

6 min

Linear Regression

foundation models
regression

Linear regression fits a line by minimising squared error; its slope is cov/var and its coefficients are interpretable effect sizes. Assumptions, how it learns, and an honest Nasdaq test — strong for beta, useless for prediction.

6 min

Logistic Regression

foundation models
classification

Logistic regression squashes a linear score through the sigmoid into a probability, trained by cross-entropy. Log-odds interpretability, the linear decision boundary, and an honest Nasdaq direction test (AUC ≈ 0.51).

6 min

Long Short-Term Memory (LSTM)

deep learning
neural networks

LSTMs fix the RNN’s vanishing gradient with a cell state whose additive, gated updates make the gradient through time a product of forget gates rather than repeated weight multiplication. The cell, the gates, the constant error carousel, and why longer memory still finds nothing in returns.

8 min

Model Explainability

quant-specific ML
explainability

Explainability turns ‘the model predicts X’ into ‘the model predicts X because…’. Global versus local explanations, why impurity-based feature importance is biased, permutation importance, partial dependence — demonstrated on a Nasdaq volatility model with a planted noise feature.

7 min

Neural Networks

deep learning
neural networks

A neural network stacks layers of weighted sums and nonlinear activations, trained by backpropagation and gradient descent. The forward pass, why the nonlinearity matters, universal approximation — and an honest Nasdaq test where its power mostly lets it overfit.

8 min

Overfitting in Trading Systems

quant-specific ML
validation

Even with clean data, no leakage, and honest validation, searching over many strategies inflates the best in-sample performance. The maximum-of-N mechanism, why in-sample rank says nothing about out-of-sample, the deflated Sharpe ratio, and the probability of backtest overfitting.

8 min

Principal Component Analysis

foundation models
dimensionality reduction

PCA rotates correlated features onto orthogonal axes ordered by variance, keeping the few that matter. The eigen-decomposition, the scree plot, and a Nasdaq test where PC1 turns out to be the market factor and PC2 a staples-vs-tech contrast.

7 min

Random Forests

foundation models
ensembles

A random forest bootstraps rows and randomises features to grow many decorrelated trees, then averages them so their variance cancels. The bagging maths, OOB validation, and a Nasdaq test where it finds volatility signal a single tree misses.

6 min

Recurrent Neural Networks

deep learning
neural networks

An RNN reads a sequence one step at a time, carrying a hidden state as memory, with the same weights shared across time. Backpropagation through time, the vanishing/exploding gradient that caps its memory, and an honest Nasdaq sequence test.

8 min

Regime-Aware Modelling

quant-specific ML
regimes

Markets are not one stationary process but alternate between persistent regimes. A hidden Markov model — a GMM with dynamics — detects calm and turbulent states on the Nasdaq, and a point-in-time regime-scaled strategy shows what regime awareness buys: real risk control, honestly framed. The final entry of the ML Library.

8 min

SHAP Values

quant-specific ML
explainability

SHAP assigns each feature its Shapley value: the fair share of a prediction under axioms from cooperative game theory, with contributions that sum exactly to the prediction minus the baseline. Exact Shapley computation, a per-day waterfall on the Nasdaq volatility model, and the beeswarm view.

7 min

Support Vector Machines

foundation models
classification

SVMs find the separating boundary with the widest margin, defined by a few support vectors, and use kernels to draw nonlinear boundaries without mapping to high dimensions. The margin, hinge loss, soft-margin C, and a Nasdaq test.

6 min

Time-Series Cross-Validation

quant-specific ML
validation

Walk-forward gives one out-of-sample path; you can’t tell a robust edge from a lucky split. The family of leakage-free temporal CV schemes — purged K-fold and combinatorial purged cross-validation — turns a single backtest into a distribution, on a Nasdaq volatility task.

8 min

Transformers

deep learning
neural networks

The transformer replaced recurrence with self-attention: each position attends to all others through learned query-key-value projections, giving unlimited-range dependencies and full parallelism. The mechanism, why it won, and the honest verdict when the most powerful architecture meets the Nasdaq.

8 min

Walk-Forward Validation

quant-specific ML
validation

Standard k-fold cross-validation shuffles time and leaks the future into training, inflating results. Walk-forward validation respects the arrow of time. Expanding vs rolling windows, purge and embargo, and a Nasdaq demo where shuffled CV reports a 0.87 ‘signal’ that is really 0.60.

7 min

XGBoost (Gradient Boosting)

foundation models
ensembles

Gradient boosting adds shallow trees sequentially, each fitting the negative gradient of the loss — gradient descent in function space. XGBoost’s regularisation and shrinkage, why it overfits without early stopping, and a Nasdaq volatility test.

6 min
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The roadmap

Foundation models

Linear regression · logistic regression · decision trees · random forests · XGBoost · LightGBM · support vector machines · K-means clustering · Principal Component Analysis · Gaussian Mixture Models.

Deep learning

Neural networks · activation functions · backpropagation · CNNs · RNNs · LSTMs · transformers · attention · embeddings.

Quant-specific machine learning

Feature engineering for returns · walk-forward validation · time-series cross-validation · avoiding data leakage · overfitting in trading systems · model explainability · SHAP values · regime-aware modelling.

Decision systems & reinforcement learning — the PhD tier

Markov decision processes & Bellman equations · Q-learning & deep Q-networks · policy gradients & actor-critic · proximal policy optimisation (PPO) · risk-sensitive & constrained RL · Bayesian change-point detection · Markov-switching regression · probability calibration & conformal prediction · multi-agent systems & credit assignment · market microstructure & execution modelling.

This tier builds the methodological foundations of my PhD research proposal — now complete, every entry to the same verified standard as everything above.

Market-state specialist methods — the proposal build tier

The updated Adaptive Market Intelligence proposal adds an econometrics-heavier specialist and combination layer, built out here one entry at a time to the same verified standard: ensemble methods & model combination, online expert weighting, state-space & Kalman filtering, EGARCH, GJR & HAR-RV, cross-asset dependence (DCC), CUSUM & concept-drift detection, Bayesian hypothesis reconciliation, liquidity-stress anomaly detection, supervised liquidity-stress modelling, contextual bandits and the strategy-suitability council — the specialist tier is now complete: every specialist, combination and consensus method the proposal names is built, verified and honestly evaluated on this site.