# Glossary of Terms

This glossary defines key terms used throughout Atlas documentation.

## A

**AbstractModel**
: Base class that all models must inherit from. Defines the interface for model integration including `predict()` and `contributions()` methods.

**Acquisition Function**
: In Bayesian optimization, a function that determines which point to evaluate next based on the posterior distribution. Common types include Expected Improvement (EI) and Upper Confidence Bound (UCB).

**Adstock**
: See [Carryover Effect](#c).

**Allocation**
: The distribution of budget or resources across different channels, time periods, or categories.

**API (Application Programming Interface)**
: A set of protocols and tools for building software applications. The framework provides REST APIs for model serving and optimization.

## B

**Baseline**
: The reference point for comparison, typically the current or historical budget allocation used to measure improvement.

**Bayesian Optimization**
: An optimization technique that builds a probabilistic model of the objective function and uses it to select the most promising points to evaluate.

**Black-box Model**
: A model where the internal workings are unknown or inaccessible, only input-output relationships are observable.

**Budget**
: The total amount of resources (usually monetary) available for allocation across different channels or categories.

**Business Constraint**
: Limitations imposed by business rules, policies, or practical considerations (e.g., minimum spend requirements, market share limits).

## C

**Carryover Effect**
: The phenomenon where marketing impact extends beyond the initial period of spend, also known as adstock.

**Channel**
: A distinct marketing or distribution method (e.g., TV, digital, radio) that can receive budget allocation.

**Constraint**
: A limitation or restriction on the optimization problem, such as budget limits, bounds, or business rules.

**Contribution Analysis**
: The process of determining how much each input variable contributes to the model's output prediction.

**Convergence**
: The state when an optimization algorithm has found a solution that satisfies stopping criteria and further iterations don't significantly improve the result.

**Convex Optimization**
: A class of optimization problems where the objective function is convex and the feasible region is a convex set, guaranteeing a global optimum.

**CVXPY**
: A Python library for convex optimization that allows natural mathematical notation for problem specification.

## D

**Data Pipeline**
: The series of data processing steps from raw input to model-ready format.

**Diminishing Returns**
: The principle that each additional unit of input produces progressively smaller increases in output.

**Docker**
: A platform for developing, shipping, and running applications in containers, used for model isolation and deployment.

**Drift**
: The phenomenon where model performance degrades over time due to changes in the underlying data distribution.

## E

**Efficient Frontier**
: See [Pareto Frontier](#p).

**Elasticity**
: The percentage change in output (e.g., sales) resulting from a percentage change in input (e.g., marketing spend).

**Ensemble Model**
: A model that combines predictions from multiple individual models to improve overall performance.

**Epoch**
: One complete pass through the entire dataset during model training.

## F

**Feasible Region**
: The set of all possible solutions that satisfy all constraints.

**Feature**
: An individual measurable property or characteristic used as input to a model.

**Frequency Capping**
: Limiting the number of times an individual is exposed to an advertisement within a specific time period.

## G

**Global Optimum**
: The best possible solution across the entire search space, as opposed to a local optimum.

**Gradient**
: The vector of partial derivatives of a function, indicating the direction of steepest increase.

**Grid Search**
: An exhaustive search method that evaluates all combinations of a discrete set of parameter values.

## H

**Heuristic**
: A practical problem-solving approach that uses shortcuts to produce good-enough solutions quickly.

**Hill Transformation**
: A mathematical function used to model saturation effects in marketing response curves.

**Hyperparameter**
: A parameter whose value is set before the learning process begins, controlling the learning process itself.

## I

**Incrementality**
: The additional impact generated by a marketing activity beyond what would have occurred naturally.

**Integer Programming**
: Optimization where some or all variables are restricted to integer values.

**Iteration**
: A single step in an optimization algorithm where the solution is updated.

## J

**JSON (JavaScript Object Notation)**
: A lightweight data interchange format used for configuration and API communication.

## K

**KPI (Key Performance Indicator)**
: A measurable value that demonstrates how effectively objectives are being achieved (e.g., revenue, conversions, awareness).

## L

**Lever**
: An optimization variable that can be adjusted to influence outcomes (e.g., budget allocation to a channel).

**Linear Programming**
: A method for optimizing a linear objective function subject to linear constraints.

**Local Optimum**
: A solution that is optimal within a neighboring set of solutions but may not be the global optimum.

**Loss Function**
: A function that measures the difference between predicted and actual values, which optimization seeks to minimize.

## M

**Marginal ROI**
: The return on investment for the next incremental dollar spent.

**Marketing Mix Modeling (MMM)**
: Statistical analysis technique that measures the impact of marketing activities on sales.

**Metadata**
: Data that provides information about other data, such as model version, training date, or performance metrics.

**Multi-objective Optimization**
: Optimization involving multiple, often conflicting objectives that must be balanced.

## N

**Non-convex Optimization**
: Optimization problems where the objective function or constraints are non-convex, potentially having multiple local optima.

**Normalization**
: The process of scaling data to a standard range, typically [0, 1] or [-1, 1].

## O

**Objective Function**
: The function being optimized (maximized or minimized) in an optimization problem.

**Optuna**
: A hyperparameter optimization framework that uses advanced sampling algorithms for black-box optimization.

**Overfitting**
: When a model learns the training data too well, including noise, reducing its ability to generalize.

## P

**Pareto Frontier**
: The set of solutions where no objective can be improved without degrading another objective.

**Pareto Optimal**
: A solution is Pareto optimal if no other solution improves at least one objective without worsening another.

**Pipeline**
: A sequence of data processing steps, from raw input to final output.

**Prediction Interval**
: A range of values within which future observations are expected to fall with a certain probability.

## Q

**Quadratic Programming**
: Optimization of a quadratic objective function subject to linear constraints.

## R

**Reach**
: The number of unique individuals exposed to a marketing message.

**Regularization**
: Technique to prevent overfitting by adding a penalty term to the loss function.

**Response Curve**
: The relationship between marketing input (e.g., spend) and output (e.g., sales).

**ROI (Return on Investment)**
: The ratio of net profit to the cost of investment.

**ROAS (Return on Ad Spend)**
: Total revenue generated per dollar spent on advertising.

## S

**Saturation**
: The point at which additional marketing spend yields diminishing or no returns.

**Scenario Analysis**
: Evaluating different possible future situations and their potential impacts.

**SciPy**
: Scientific computing library for Python that includes optimization algorithms.

**Sensitivity Analysis**
: The study of how changes in input variables affect the output.

**Simplex Algorithm**
: An algorithm for solving linear programming problems.

**Stochastic Optimization**
: Optimization methods that incorporate randomness, useful for problems with uncertainty.

**Surrogate Model**
: A simplified approximation of a complex model used to speed up optimization.

## T

**Time Series**
: A sequence of data points indexed in time order.

**TPE (Tree-structured Parzen Estimator)**
: A Bayesian optimization algorithm used in Optuna for hyperparameter tuning.

**Trade-off**
: A situation where improving one objective requires degrading another.

## U

**Uncertainty Quantification**
: The process of quantifying and characterizing uncertainty in model predictions.

**Underfitting**
: When a model is too simple to capture the underlying patterns in the data.

## V

**Validation**
: The process of assessing whether a model's predictions are accurate on unseen data.

**Variable Bounds**
: Minimum and maximum allowed values for optimization variables.

**Vectorization**
: The process of converting operations to work on entire arrays rather than individual elements.

## W

**Warm Start**
: Initializing an optimization algorithm with a good starting point based on prior knowledge.

**Weight**
: The relative importance assigned to different objectives in multi-objective optimization.

**What-if Analysis**
: Exploring how changes in inputs affect outputs without actually implementing the changes.

## X

**Xarray**
: Python library for working with labeled multi-dimensional arrays, used for data management in the framework.

## Y

**Yield**
: The return or output generated from a given input or investment.

## Z

**Zero-sum**
: A situation where total gains equal total losses, common in competitive market share scenarios.

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## Technical Acronyms

**API**: Application Programming Interface  
**CI/CD**: Continuous Integration/Continuous Deployment  
**CPU**: Central Processing Unit  
**CSV**: Comma-Separated Values  
**GPU**: Graphics Processing Unit  
**HTTP**: Hypertext Transfer Protocol  
**JSON**: JavaScript Object Notation  
**KPI**: Key Performance Indicator  
**ML**: Machine Learning  
**MMM**: Marketing Mix Modeling  
**REST**: Representational State Transfer  
**ROI**: Return on Investment  
**ROAS**: Return on Ad Spend  
**SDK**: Software Development Kit  
**URL**: Uniform Resource Locator  
**UUID**: Universally Unique Identifier  
**YAML**: Yet Another Markup Language  

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## Mathematical Notation

**∇**: Gradient (nabla)  
**∂**: Partial derivative  
**Σ**: Summation  
**∏**: Product  
**∈**: Element of  
**⊆**: Subset of  
**∀**: For all  
**∃**: There exists  
**arg max**: Argument of the maximum  
**arg min**: Argument of the minimum  
**s.t.**: Subject to (in optimization)  
**w.r.t.**: With respect to  

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*This glossary is a living document. If you encounter terms that should be added or clarified, please contribute to the documentation.*