Encyclopedia
A concise, cross-linked reference. Each entry connects to related concepts and the articles that go deeper.
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A
A* Search
A best-first graph search that expands the node minimizing the sum of the cost already incurred and an estimate of the cost remaining.
Activation Function
The non-linear function applied to a layer’s output, without which a network of any depth would collapse to a single linear transformation.
Anomaly Detection
Finding the few observations that were not produced by the process that produced the rest. The defining difficulty is not the algorithm but the base rate: at 0.5% anomalies, a detector that never fires is 99.5% accurate, and most standard metrics inherit that number rather than measuring skill.
Arc Consistency
A property of a constraint problem in which every value in every variable’s domain has at least one supporting value in each neighbouring domain, and the algorithm that enforces it by deleting the values that do not.
Autocorrelation
The correlation of a series with a lagged copy of itself, measuring how long the influence of an observation persists. It is the structure that makes time-series data informative and the reason ordinary standard errors do not apply to it.
Automated Planning
Finding a sequence of actions that achieves a goal, where states are sets of ground fluents and actions are schemas describing only what they change.
B
Backpropagation
The algorithm that computes the gradient of a neural network’s loss with respect to every weight, by applying the chain rule backwards through the network.
Bagging and Random Forests
Ensemble methods that reduce variance by averaging many models fitted to bootstrap resamples, with random forests additionally decorrelating the trees by restricting the features available at each split.
Bayes’ Theorem
A rule for updating the probability of a hypothesis in light of new evidence, by inverting a conditional probability.
Bayesian Network
A directed acyclic graph whose nodes are random variables and whose edges express direct influence, with a conditional probability table at each node, that together define a full joint distribution as a product of local factors.
Belief State
The probability distribution an agent holds over the states it might be in, given everything it has done and perceived - the thing it can act on when the state itself is hidden.
Bellman Equation
The self-consistency condition that the utility of a state equals its immediate reward plus the discounted value of the best action available from it, averaged over the outcomes that action cannot control.
Bias-Variance Trade-off
The decomposition of a model’s expected prediction error into bias, variance, and irreducible noise, and the tension that reducing one of the first two typically increases the other.
C
Causal Graph
A drawing of assumed cause-and-effect relationships as arrows between variables, used to decide which variables must be adjusted for and which must not - a question the data alone cannot answer.
Condition Number
The ratio of the largest to the smallest curvature of a loss surface, which alone determines how fast gradient descent can converge on it.
Confidence Interval
A range computed from data by a procedure that, repeated over many samples, contains the true value a stated proportion of the time. The stated proportion is a property of the procedure, not of any particular interval it produces.
Confounding
A variable that influences both the treatment and the outcome, so that a comparison between the treated and the untreated measures the difference between the groups as well as the effect of the treatment.
Conjugate Prior
A prior chosen so that the posterior belongs to the same family, which turns Bayesian updating into arithmetic on the parameters and makes the prior readable as a number of imagined observations.
Constraint Satisfaction Problem
A problem stated as a set of variables, a domain of permitted values for each, and constraints restricting which combinations of values may be taken simultaneously, so that a general solver can reason about its structure without any domain knowledge.
Convolutional Neural Network
A neural network that applies learned filters across an input’s spatial extent, sharing weights so the same pattern is detected wherever it occurs.
Cross-Entropy
A measure of the difference between two probability distributions, used as the standard loss function for classification.
Cross-Validation
A resampling method that estimates a model’s test error by repeatedly fitting it on part of the data and evaluating it on the part held out.
D
Decision Tree
A model that predicts by applying a sequence of threshold tests on individual features, splitting the data into increasingly homogeneous groups.
Dominant Strategy
A strategy that yields a better outcome than an alternative regardless of what the other players do, and a dominant one if it beats every alternative.
E
Entropy
A measure of the uncertainty in a random variable, equal to the average number of bits needed to encode its outcome.
Expectation–Maximization
An iterative method for maximum-likelihood estimation when some variables are unobserved: it computes the posterior distribution over the hidden variables under the current parameters, then refits the parameters as though those expected counts had been observed.
Expected Utility
The probability-weighted average utility of an action’s possible outcomes, and the quantity a rational agent maximises when choosing what to do under uncertainty.
F
G
H
Hidden Markov Model
A temporal model in which a single discrete state variable evolves as a Markov chain and emits one observation per time step, so the state must be inferred from a noisy proxy rather than seen directly.
Hierarchical Clustering
An unsupervised method that builds a tree of nested clusters by repeatedly fusing the two least dissimilar groups, so that cutting the tree at any height yields a clustering.
K
k-Means Clustering
An unsupervised algorithm that partitions observations into k groups by alternately assigning points to the nearest centroid and recomputing the centroids.
k-Nearest Neighbours
A nonparametric classifier that predicts the class of a point by taking a majority vote among the k training observations closest to it.
Kalman Filter
The exact filtering algorithm for a continuous state that moves linearly with Gaussian noise and is measured linearly with Gaussian noise, carrying the whole belief as a mean and a variance.
Kullback-Leibler Divergence
The number of extra bits per symbol paid for describing one distribution with a code built for another. It is zero only when the two agree, it is never negative, and it is not symmetric, so it is a cost rather than a distance.
L
Learning Rate Schedule
A rule that changes the step size over the course of training, large early so the run can travel and small late so it can settle.
Linear Discriminant Analysis
A generative classifier that models each class as a Gaussian and inverts those models with Bayes’ theorem; assuming one covariance matrix shared by all classes gives a linear decision boundary, and one per class gives a quadratic one.
Linear Regression
A model that predicts a numeric response as a weighted sum of the predictors, fitted by minimizing squared error.
Logistic Regression
A classification model that predicts the probability of a class by passing a linear combination of predictors through the logistic function.
M
Markov Decision Process
A formal model of sequential decision-making in which outcomes are partly random, defined by states, actions, transition probabilities, and rewards.
Matrix Factorisation
A model that explains a sparse table of interactions as the product of two small matrices, giving every user and every item a short vector of learned traits whose dot product predicts the missing entries.
Maximum Likelihood Estimation
A method of fitting a model by choosing the parameter values that make the observed data most probable.
Minimax
A decision rule for two-player zero-sum games in which each player chooses the move maximizing their own worst-case outcome against optimal opposition.
Mixed Strategy
A strategy that selects among the available actions according to a probability distribution rather than choosing one deterministically.
Multiple Comparisons
The inflation of false positives that occurs whenever more than one test, metric, segment or stopping point is allowed to produce the headline. Each additional chance raises the probability that something crosses the threshold by luck alone.
Mutual Information
How many bits observing one variable tells you about another. It is zero exactly when the two are independent, it catches dependence of any shape rather than linear dependence only, and nothing computed downstream can increase it.
N
Naive Bayes
A classifier that applies Bayes’ theorem while assuming all features are conditionally independent given the class.
Nash Equilibrium
A combination of strategies, one per player, such that no player can improve their outcome by changing strategy alone.
Neural Network
A model composed of layers of simple units, each computing a weighted sum followed by a non-linear function, fitted by gradient descent using backpropagation.
O
P
p-value
The probability of observing data at least as extreme as the data in hand, computed under the assumption that the null hypothesis is true. It measures how unusual the sample would be in a world where the effect is absent, and nothing else.
PAC Learning
A definition of learnability in which an algorithm must return, with high probability, a hypothesis whose true error is within a chosen tolerance - using a number of samples that is bounded in advance rather than discovered afterwards.
Partially Observable MDP
A Markov decision process in which the agent cannot observe its state directly, only noisy percepts of it - solved in principle by treating the distribution over states as the state of an ordinary, fully observable MDP.
Perplexity
The exponential of a model’s average cross entropy, read as the number of equally likely options it is effectively choosing between at each step.
Planning Graph
A layered structure alternating literal levels and action levels, annotated with mutual-exclusion links, that bounds in polynomial time what a planning problem can achieve by a given step.
Precision and Recall
Two rates that split what accuracy hides: precision is the share of predicted positives that are real, and recall is the share of real positives that were found.
Pretraining and Fine-Tuning
The two-stage recipe of first training a model on a large generic corpus, then adapting it to a specific task with a much smaller labelled dataset.
Principal Component Analysis
A technique that re-expresses data in new uncorrelated coordinates ordered by how much variance each explains, allowing dimension reduction by keeping only the first few.
Prisoner’s Dilemma
A game in which each player has a dominant strategy, yet both playing it produces an outcome worse for both than mutual cooperation would have been.
Q
R
Regularization
Any technique that constrains a model’s effective complexity in order to reduce variance and improve generalization, typically by penalizing large parameter values.
ROC Curve
A plot of a classifier’s true positive rate against its false positive rate as the decision threshold is swept across its whole range, summarising every available trade between the two kinds of error.
S
Self-Attention
A mechanism that lets every position in a sequence attend to every other, computing each output as a weighted sum of values whose weights come from query-key similarity.
Softmax
A function that turns a vector of real scores into a probability distribution by exponentiating each score and dividing by the total, preserving their order while making them positive and summing to one.
Spline
A piecewise polynomial joined at chosen points called knots, constrained so that the function and its lower derivatives stay continuous there, giving local flexibility without the wild behaviour of a high-degree polynomial.
Stationarity
A property of a series whose statistical behaviour does not depend on when you look at it: the mean, the variance and the correlation structure are the same in every window. Almost every classical method assumes it, and most real series lack it.
Statistical Power
The probability that a test rejects the null hypothesis when a specified alternative is true. It is the chance of finding an effect that is genuinely there, and it is fixed by the design before any data are collected.
Stochastic Gradient Descent
Gradient descent in which each step uses the gradient of a small random sample of the data rather than all of it, trading an exact direction for far more steps per unit of compute.
Support Vector Machine
A classifier that separates classes with the boundary leaving the widest possible margin, determined only by the closest training points.
T
Tokenization
The process of splitting text into the discrete units a language model actually operates on, typically subword fragments rather than whole words.
Transformer
A neural architecture built on stacked self-attention and feed-forward layers, which replaced recurrence as the standard for sequence modelling.
V
VC Dimension
The size of the largest set of points a family of classifiers can label in every possible way. It measures capacity by what a class can do rather than by how many members it has, which is what makes it usable for infinite families.
Viterbi Algorithm
A dynamic programming algorithm that finds the single most likely sequence of hidden states given a sequence of observations, by carrying forward the best path to each state rather than the total probability of reaching it.