
Salford System È¨  Á¦Ç°  CART  MARS  ±â¼úÁö¿ø  White Papers  °¡°Ý/ÁÖ¹®  ¹®ÀÇ  
Product OverviewFrequently Asked Questions About MARS Review of MARS in the Jan 2000 issue of PCAI Magazine (PDF file) 
Technical OverviewCitations of MARS in the literature (PDF file) Friedman's Article on MARS Methodology (NOTE:14 MB PDF file) 
Interface & Unique Functionality 
MARS is an innovative and flexible modeling tool that automates the building of accurate predictive models for continuous and binary dependent variables. Multivariate Adaptive Regression Splines was developed in the early 1990s by Jerry Friedman, a world renowed statistician and one of the codevelopers of CART. Salford Systems' MARS, based on the original code, has been substantially enhanced with new features and capabilities in exclusive collaboration with Friedman. MARS excels at finding optimal variable transformations and interactions, the complex data structure that often hides in high dimensional data. In doing so, this new generation approach to data mining uncovers business critical data patterns and relationships that are difficult, if not impossible, for other approaches to uncover. Given a target variable and a set of candidate predictor variables, MARS automates all aspects of model development, including:
Large numbers of variables are examined using efficient algorithms, and all promising variables are identified. Every variable selected for entry into the model is repeatedly checked for nonlinear response. Highly nonlinear functions can be traced with precision via essentially piecewise regression. MARS repeatedly searches through the interactions allowed by the analyst. Unlike recursive partitioning schemes, MARS models may be constrained to forbid interactions of certain types, thus allowing some variables to enter only as main effects, while allowing other variables to enter as interactions, but only with a specified subset of other variables. Certain variables are deemed to be meaningful (possibly non missing) in the model only if particular conditions are met (e.g., X has a meaningful non missing value only if categorical variable Y has a value in some range). The user can choose to reserve a random subset of data for test, or use vfold cross validation to tune the final model selection parameters. MARS enables analysts to rapidly search through all possible models and to quickly identify the optimal solution, providing insights that can lead to a definitive competitive advantage. And, because the software can be exploited via an easy to use GUI, intelligent default settings, and aesthetically appealing output, for the first time analysts at all levels can easily access MARS' innovations. MARS for Windows also incorporates two alternative control modes that extend the program's features and capabilities. In addition to controlling MARS with the GUI, you can also issue commands at the command prompt or submit a command file. User Friendly Graphical User Interface MARS' easy to use GUI allows the user to control the variables and functional forms to be entered into the model and the interactions to be considered or forbidden, while allowing the MARS algorithm to optimize those parts of the model the analyst chooses to leave free. Once the model is selected, the user can easily remove or add terms, instantly see the impact of changes on model fit, review diagnostics that assist in model selection, save the model and apply the model to new data for prediction. MARS Output MARS output is an easy to deploy regression model that can be automatically applied to new data from within MARS itself or exported as ready to run SAS^{®} and C source code. To facilitate interpretation of the model, the output also includes interpretive summary reports as well as exportable two and three dimensional curve and surface plots: For a very technical detailed discussion of the MARS methodology, a PDF version of Friedman's original 1991 article, Multivariate Adaptive Regression Splines published in Annuals of Statistics, 19, 1141 (March), can be downloaded by clicking here (note file is 14 MB). For a much shorter and less technical overview, see our white paper on MARS, Overview of the MARS Methodology. 
ApplicationsMARS is an ideal data modeling tool when the analyst needs to both accurately predict a future outcome and to understand the "why" underlying the predictive model. For example, if the goal is to predict new credit card customers monthly charges on the basis of detailed credit bureau data, or how dollars spent on a high ticket consumer good vary with dollars spent on other products, MARS is capable of generating a highly accurate predictive equation. And, in addition to delivering predictive accuracy, MARS allows the analyst to more fully understand the underlying data patterns and relationships, thereby allowing him/her to tell a story and use these insights to make more strategic decisions. MARS' models may be as simple as straight lines or as complex as multidimensional surfaces with cliffs, ridges, and sharp twists and turns. Whether the outcome the analyst is trying to predict has only a few drivers each with their own separate relationship or whether many factors interact in complex ways to determine the outcome, MARS is capable of discovering and representing this relationship in an accurate and understandable way. Response modeling problems MARS can solve, for example, given binary (yes/no) response outcomes are: 1) will a homeowner refinance their mortgage in the next quarter? 2) will a household respond to a direct mail offer? or 3) will a bank customer sign up for a new credit card? MARS can also estimate the probability that a treatment for a medical condition will succeed or the probability that a policyholder will file a claim. MARS is also ideal for solving predictive modeling problems involving continuous outcomes such as:
In addition to using MARS as a model building tool, data analysts use MARS as an exploratory tool to refine more conventional models (e.g., linear and logistic regression). By automatically detecting variable transformations and interactions, for example, MARS slashes the time required to build a logistic regression model by more than half and significantly improves the model's predictive accuracy. MARS can also be used in conjunction with decision trees to build high performance hybrid models. Successful MARS hybrids have been used to accurately predict whether a household will respond to a direct mail offer, refinance a mortgage, apply for a new credit card and a myriad of other marketing research challenges. 
Files SupportedThe MARS data translation engine, DBMS/COPY^{®}, supports data conversion  both direct reading and writing  of over 80 file formats, including:
System Requirements
Available PlatformsMARS is now available for Win/NT, Linux and UNIX platforms, including Dec ALPHA, HP, Sun Solaris 2.5 and 2.6, SGI IRIX 6.2+ and IBM RS6000. 
ScalabilityMARS requires that all training data
reside in RAM, so the larger the data set to be analyzed, the larger the
RAM needed to analyze it. The exact amount of RAM required will vary
from problem to problem. The table below is intended as a guide for
the maximum number of candidate predictor variables that can be
specified in a MARS analysis for the given sample size and amount of RAM
workspace:
* MARS run with default settings and with following assumptions: no missing values or categorical variables in training data; maximum interactions set to 1; maximum basis functions set to number of specified predictors. NOTE that each variable containing a missing value counts as two predictors. ** Maximum number of numbers (in millions) based on above assumptions. *** Custom compiles up to 32 GB available on UNIX platforms. Maximum number of candidate predictor variables that can be specified regardless of available RAM is 8,192. Rule
of Thumb for Calculating Required RAM
Increasing the Number of Variables
MARS Can Handle

Salford System È¨  Á¦Ç°  CART  MARS  °¡°Ý/ÁÖ¹®  White Papers  ±â¼úÁö¿ø  ¹®ÀÇ 