Methodology Index

This listing provides a single alphabetical listing of the various methodological tools that are a part of TMIP-EMAT.

Classification and Regression Trees (CART)
Classification and Regression Trees, or CART, is a simple machine learning technique for predicting a target variable. Within TMIP-EMAT, the CART algorithm is implemented as a Scenario Discovery method. It is a relatively greedy but long-standing approach to developing interesting boxes for model exploration. (Breiman, 1984).
Contrast Experiments
The contrast experiments method renders two different set of experiments on a common SPLOM. This visualization approach makes it easy to see if the overall shape of the distriubution of experiment inputs and outputs is similar or different. It is particularly useful in validating that TMIP-EMAT’s automatically generated meta-models are performing correctly.
Design of Experiments
A “design” of experiments is simply a set or list of particular experiments to be run, generated in some prescribed manner. Designs can be completely random (e.g., Monte Carlo simulation), partly random (e.g. Latin Hypercube), or completely deterministic (e.g., univariate sensitivity testing, reference experiments).
Display Experiments
The display_experiments method generates a SPLOM that diplays model inputs (uncertainties and policy levers) in one dimension and model outputs (performance measures) in the other.
Feature Scoring
This is a Scenario Discovery method for identifying what model inputs have the greatest relationship to the outputs, by computing a numerical value that summarizes the relative importance of each input in determining the level of the output.
Experimental Design
See Design of Experiments.
Exploratory Scoping
While not a methodological approach per se, TMIP-EMAT provides a notational structure to concretely define the manner in which the XLRM framework is to be operationalized for a given travel model (R) and its uncertainties (X), policy levers (L), and performance measures (M).
Interactive Visualizer
The Interactive Visualizer in TMIP-EMAT provides a set of tools that can display a dynamically generated selection of experiments in a number of visualizations, including histograms, scatter plots, and SPLOMs. The dimensional bounds of the select (the “box”) can be manipulated by a user programmatically or by clicking and dragging directly on the figures.
Latin Hypercube Design of Experiments
A Latin Hypercube is a space-filling mathematical process for making pseudo-random draws from a multi-dimensional space. This kind of design is not formally “random” but approximates a random distribution while ensuing a reasonable coverage across the spectrum of possible values in each dimension. Meta-models for deterministic simulation experiments, such as most transportation models, are best supported by a “space filling” design of experiments such as this.
Meta-model Creation
A main feature of TMIP-EMAT is the ability to automatically generate meta-models that provide a good approximation of the underlying core model in most situations. By default, metamodels derived through TMIP-EMAT include two stages, a linear regression model to capture overall trends and a gaussian process regression (GPR) model that can capture a wide variety of non-linear effects.
Monte Carlo Simulation
A Monte Carlo simulation is a simple random (or in more precise computer science terminology, pseudo-random) process for generating a design of experiments. It is not generally an efficient design, but with a large enough sample size efficiency is less relevant and simplicity can be valuable.
Multi-objective Optimization
With exploratory modeling, optimization is also often undertaken as a multi-objective optimization exercise, where multiple and possibly conflicting performance measures need to be addressed simultaneously. Instead of generating one unique “optimal” solution, this TMIP-EMAT method can be used to find a spectrum of different solutions. Each of them solves the problem at a different weighting of the various objectives. Decision makers can then review the various different solutions, and make judgements about the various trade-offs implicit in choosing one over another.
Patient Rule Induction Method (PRIM)
The Patient Rule Induction Method, or PRIM, is a Scenario Discovery method. This method is a “bump hunting” technique introduced by Friedman and Fisher (1999), which often provides insightful results for complex models.
Policy Contrast
The Policy Contrast method in TMIP-EMAT allows an analysst to compare the outcomes of two different sets of policies. The tool runs the model across a distribution of inputs, and displays the resulting distribution of performance measure outputs. Two sets of model runs are generated with the same design of experiments for all the non-contrasted distributions, so any variation in the performance measures can be unambiguously linked to the changes in the specific-value inputs, instead of being a result of input stocasticity.
Reference Experiment
A “design of expermiments” which contains only a single experiment, with all input values set to their default parameters.
Robust Optimization
Robust optimization is a variant of more traditional optimization problems. Rather than seeking a solution that provides the best outcome, a robust optimization problem is one where we try to find policies that yield good outcomes across a broad range of possible futures. It is common to employ various different criteria for what constitutes “good” or “broad”, by also borrowing methods from from the Multi-objective Optimization tools.
Scatter Plot Matrix (SPLOM)
The Scatter Plot Matrix, or SPLOM, is a visualization method. It is a collection of two-dimensional scatter plots arranged in a matrix, where each column of plots shares a common x-axis definition, and each row shares a common y-axis definition.
Scenario Discovery
This is a broad category of different methodologies used to discover important relationships between inputs and outputs across multiple dimensions.
Search over Levers
A Search over Levers is a particular style of multi-objective optimization for exploratory modeling in the XLRM framework, where the uncertainties are held constant at some particular value, and only the policy levers are manipulated by the search algorithm.
Threshold Scoring
A variant of Feature Scoring, where inputs are scored not with just a single numerical value, but with a range of values representing the relative importance of inputs for getting the output to be above or below various possible threshold values.
Univariate Sensitivity Testing
One of the simplest experimental designs is a set of univariate sensitivity tests. In this design, a set of baseline model inputs is used as a starting point, and then input parameters are changed one at a time to non-default values. Univariate sensitivity tests are excellent tools for debugging and quality checking the model code, as they allow modelers to confirm that each modeled input is (or is intentionally not) triggering some change in the model outputs.
Worst Case Discovery
Worst Case Discovery is a particular style of multi-objective optimization for exploratory modeling in the XLRM framework. In this analysis, the policy levers are held constant at some particular value, and only the exogenous uncertainties are manipulated by the search algorithm. In addition, the directionality of all objective dimensions is inverted, so that the search algorthim seeks to find values for the input that lead to worse outcomes instead of better ones.