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Decision theory

**Predictive analytics** encompasses a variety of techniques from statistics and data mining that process current and historical data in order to make “predictions” about future events. Such predictions rarely take the form of absolute statements, and are more likely to be expressed as values that correspond to the odds of a particular event or behavior taking place in the future.

In business, the models often process historical and transactional data to identify the risk or opportunity associated with a specific customer or transaction. These analyses weigh the relationship between many data elements to isolate each customer’s risk or potential, which guides the action on that customer.

Predictive analytics is widely used in making customer decisions. One of the most well-known applications is credit scoring, which is used throughout financial services. Scoring models process a customer’s credit history, loan application, customer data, etc., in order to rank-order individuals by their likelihood of making future credit payments on time. Predictive analytics are also used in insurance, telecommunications, retail, travel, healthcare, pharmaceuticals and other fields.

## Contents

- 1 Types of predictive analytics
- 2 Predictive analytics
- 3 Popular tools
- 4 Conclusion
- 5 References
- 6 See also
- 7 External links

## Types of predictive analytics

Generally, predictive analytics is used to mean predictive modeling. However, people are increasingly using the term to describe related analytic disciplines, such as descriptive modeling and decision modeling or optimization. These disciplines also involve rigorous data analysis, and are widely used in business for segmentation and decision making, but have different purposes and the statistical techniques underlying them vary.

### Predictive models

Predictive models analyze past performance to assess how likely a customer is to exhibit a specific behavior in the future in order to improve marketing effectiveness. This category also encompasses models that seek out subtle data patterns to answer questions about customer performance, such as fraud detection models. Predictive models often perform calculations during live transactions, for example, to evaluate the risk or opportunity of a given customer or transaction, in order to guide a decision.

### Descriptive models

Descriptive models “describe” relationships in data in a way that is often used to classify customers or prospects into groups. Unlike predictive models that focus on predicting a single customer behavior (such as credit risk), descriptive models identify many different relationships between customers or products. But the descriptive models do not rank-order customers by their likelihood of taking a particular action the way predictive models do. Descriptive models are often used “offline,” for example, to categorize customers by their product preferences and life stage.

### Decision models

Decision models describe the relationship between all the elements of a decision — the known data (including results of predictive models), the decision and the forecast results of the decision — in order to predict the results of decisions involving many variables. These models can be used in optimization, a data-driven approach to improving decision logic that involves maximizing certain outcomes while minimizing others. Decision models are generally used offline, to develop decision logic or a set of business rules that will produce the desired action for every customer or circumstance.

## Predictive analytics

### Definition

Predictive analytics is an area of statistical analysis that deals with extracting information from data and using it to predict future trends and behavior patterns. The core of predictive analytics relies on capturing relationships between explanatory variables and the predicted variables from past occurrences, and exploiting it to predict future outcomes.

### Current uses

Although predictive analytics can be put to use in many applications, we outline a few examples where predictive analytics has shown positive impact in recent years.

#### Analytical Customer Relationship Management (CRM)

Analytical Customer Relationship Management is a frequent commercial application of Predictive Analysis. Methods of predictive analysis are applied to customer data to pursue CRM objectives.

#### Direct marketing

Product marketing is constantly faced with the challenge of coping with the increasing number of competing products, different consumer preferences and the variety of methods (channels) available to interact with each consumer. Efficient marketing is a process of understanding the amount of variability and tailoring the marketing strategy for greater profitability. Predictive analytics can help identify consumers with a higher likelihood of responding to a particular marketing offer. Models can be built using data from consumers’ past purchasing history and past response rates for each channel. Additional information about the consumers demographic, geographic and other characteristics can be used to make more accurate predictions. Targeting only these consumers can lead to substantial increase in response rate which can lead to a significant reduction in cost per acquisition. Apart from identifying prospects, predictive analytics can also help to identify the most effective combination of products and marketing channels that should be used to target a given consumer.

#### Cross-sell

Often corporate organizations collect and maintain abundant data (e.g. customer records, sale transactions) and exploiting hidden relationships in the data can provide a competitive advantage to the organization. For an organization that offers multiple products, an analysis of existing customer behavior can lead to efficient cross sell of products. This directly leads to higher profitability per customer and strengthening of the customer relationship. Predictive analytics can help analyze customers’ spending, usage and other behavior, and help cross-sell the right product at the right time.

#### Customer retention

With the amount of competing services available, businesses need to focus efforts on maintaining continuous consumer satisfaction. In such a competitive scenario, consumer loyalty needs to be rewarded and customer attrition needs to be minimized. Businesses tend to respond to customer attrition on a reactive basis, acting only after the customer has initiated the process to terminate service. At this stage, the chance of changing the customer’s decision is almost impossible. Proper application of predictive analytics can lead to a more proactive retention strategy. By a frequent examination of a customer’s past service usage, service performance, spending and other behavior patterns, predictive models can determine the likelihood of a customer wanting to terminate service sometime in the near future. An intervention with lucrative offers can increase the chance of retaining the customer. Silent attrition is the behavior of a customer to slowly but steadily reduce usage and is another problem faced by many companies. Predictive analytics can also predict this behavior accurately and before it occurs, so that the company can take proper actions to increase customer activity.

#### Underwriting

Many businesses have to account for risk exposure due to their different services and determine the cost needed to cover the risk. For example, auto insurance providers need to accurately determine the amount of premium to charge to cover each automobile and driver. A financial company needs to assess a borrower’s potential and ability to pay before granting a loan. For a health insurance provider, predictive analytics can analyze a few years of past medical claims data, as well as lab, pharmacy and other records where available, to predict how expensive an enrollee is likely to be in the future. Predictive analytics can help underwriting of these quantities by predicting the chances of illness, default, bankruptcy, etc. Predictive analytics can streamline the process of customer acquisition, by predicting the future risk behavior of a customer using application level data. Proper predictive analytics can lead to proper pricing decisions, which can help mitigate future risk of default.

#### Collection analytics

Every portfolio has a set of delinquent customers who do not make their payments on time. The financial institution has to undertake collection activities on these customers to recover the amounts due. A lot of collection resources are wasted on customers who are difficult or impossible to recover. Predictive analytics can help optimize the allocation of collection resources by identifying the most effective collection agencies, contact strategies, legal actions and other strategies to each customer, thus significantly increasing recovery at the same time reducing collection costs.

#### Fraud detection

Fraud is a big problem for many businesses and can be of various types. Inaccurate credit applications, fraudulent transactions, identity thefts and false insurance claims are some examples of this problem. These problems plague firms all across the spectrum and some examples of likely victims are credit card issuers, Insurance companies, retail merchants, manufacturers, business to business suppliers and even services providers. This is an area where a predictive model is often used to help weed out the “bads” and reduce a businesses exposure to fraud.

#### Portfolio, product or economy level prediction

Often the focus of analysis is not the consumer but the product, portfolio, firm, industry or even the economy. For example a retailer might be interested in predicting store level demand for inventory management purposes. Or the Federal Reserve Board might be interested in predicting the unemployment rate for the next year. These type of problems can be addressed by predictive analytics using Time Series techniques (see below).

### Statistical techniques

The approaches and techniques used to conduct predictive analytics can broadly be grouped into regression techniques and machine learning techniques.

#### Regression Techniques

Regression models are the mainstay of predictive analytics. The focus lies on establishing a mathematical equation as a model to represent the interactions between the different variables in consideration. Depending on the situation, there is a wide variety of models that can be applied while performing predictive analytics. Some of them are briefly discussed below.

##### Linear Regression Model

The linear regression model analyzes the relationship between the response or dependent variable and a set of independent or predictor variables. This relationship is expressed as an equation that predicts the response variable as a linear function of the parameters. These parameters are adjusted so that a measure of fit is optimized. Much of the effort in model fitting is focused on minimizing the size of the residual, as well as ensuring that it is randomly distributed with respect to the model predictions.

The goal of regression is to select the parameters of the model so as to minimize the sum of the squared residuals. This is referred to as ordinary least squares (OLS) estimation and results in best linear unbiased estimates (BLUE) of the parameters.

Once the model has been estimated we would be interested to know if the predictor variables belong in the model – i.e. is the estimate of each variable’s contribution reliable? To do this we can check the statistical significance of the model’s coefficients which can be measured using the t-statistic. This amounts to testing whether the coefficient is significantly different from zero. How well the model predicts the dependent variable based on the value of the independent variables can be assessed by using the R2 statistic. It measures predictive power of the model i.e. the proportion of the total variation in the dependent variable that is “explained” (accounted for) by variation in the independent variables.

#### Discrete choice models

Multivariate regression (above) is generally used when the response variable is continuous with an unbounded range. Often the response variable may not be continuous but rather discrete. While mathematically it is feasible to apply multivariate regression to discrete ordered dependent variables, some of the assumptions behind the theory of multivariate linear regression no longer hold, and there are other techniques such as discrete choice models which are better suited for this type of analysis. If the dependent variable is discrete, some of those superior methods are logistic regression, multinomial logit and probit models. Logistic regression and probit models are used when the dependent variable is binary.

##### Logistic regression

In a classification setting, assigning outcome probabilities to observations can be achieved through the use of a logistic model, which is basically a method which transforms information about the binary dependent variable into an unbounded continuous variable and estimates a regular multivariate model (See Allison’s Logistic Regression for more information on the theory of Logistic Regression).

The Wald and likelihood-ratio test are used to test the statistical significance of each coefficient b in the model (analogous to the t tests used in OLS regression; see above). A test assessing the goodness-of-fit of a classification model is the Hosmer and Lemeshow test.

##### Multinomial logit regression

An extension of the binary logit model to cases where the dependent variable has more than 2 categories is the multinomial logit model. In such cases collapsing the data into two categories might not make good sense or may lead to loss in the richness of the data. The multinomial logit model is the appropriate technique in these cases, especially when the dependent variable categories are not ordered (for examples colors like red, blue, green).

##### Probit regression

Probit models offer an alternative to logistic regression for modeling categorical dependent variables. Even though the outcomes tend to be similar, the underlying distributions are different. Probit models are popular in social sciences like economics.

A good way to understand the key difference between probit and logit models, is to assume that there is a latent variable z.

We do not observe z but instead observe y which takes the value 0 or 1. In the logit model we assume that follows a logistic distribution. In the probit model we assume that follows a standard normal distribution. Note that in social sciences (example economics), probit is often used to model situations where the observed variable y is continuous but takes values between 0 and 1.

##### Logit vs. Probit

The Probit model has been around longer than the logit model. They look identical, except that the logistic distribution tends to be a little flat tailed. In fact one of the reasons the logit model was formulated was that the probit model was extremely hard to compute because it involved taking the integrals. Modern computing however has made this computation fairly simple. The coefficients obtained from the logit and probit model are also fairly close. However the odds ratio makes the logit model easier to interpret.

For practical purposes the only reasons for choosing the probit model over the logistic model would be:

- There is a strong belief that the underlying distribution is normal
- The actual event is not a binary outcome (e.g. Bankrupt/not bankrupt) but a proportion (e.g. Proportion of population at different debt level.

#### Time series models

Time series models are used for predicting or forecasting the future behavior of variables. These models account for the fact that data points taken over time may have an internal structure (such as autocorrelation, trend or seasonal variation) that should be accounted for. As a result standard regression techniques cannot be applied to time series data and methodology has been developed to decompose the trend, seasonal and cyclical component of the series. Modeling the dynamic path of a variable can improve forecasts since the predictable component of the series can be projected into the future.

Time series models estimate difference equations containing stochastic components. Two commonly used forms of these models are autoregressive models (AR) and moving average (MA) models. The Box-Jenkins methodology (1976) developed by George Box and G.M. Jenkins combines the AR and MA models to produce the ARMA (autoregressive moving average) model which is the cornerstone of stationary time series analysis. ARIMA (autoregressive integrated moving average models) on the other hand are used to describe non-stationary time series. Box and Jenkins suggest differencing a non stationary time series to obtain a stationary series to which an ARMA model can be applied. Non stationary time series have a pronounced trend and do not have a constant long-run mean or variance.

Box and Jenkins proposed a three stage methodology which includes: model identification, estimation and validation. The identification stage involves identifying if the series is stationary or not and the presence of seasonality by examining plots of the series, autocorrelation and partial autocorrelation functions. In the estimation stage, models are estimated using non-linear time series or maximum likelihood estimation procedures. Finally the validation stage involves diagnostic checking such as plotting the residuals to detect outliers and evidence of model fit.

In recent years time series models have become more sophisticated and attempt to model conditional heteroskedasticity with models such as ARCH (autoregressive conditional heteroskedasticity) and GARCH (generalized autoregressive conditional heteroskedasticity) models frequently used for financial time series. In addition time series models are also used to understand inter-relationships among economic variables represented by systems of equations using VAR (vector autoregression) and structural VAR models.

#### Survival or duration analysis

Survival analysis is another name for time to event analysis. These techniques were primarily developed in the medical and biological sciences, but they are also widely used in the social sciences like economics, as well as in engineering (reliability and failure time analysis).

Censoring and non-normality which are characteristic of survival data generate difficulty when trying to analyze the data using conventional statistical models such as multiple linear regression. The Normal distribution, being a symmetric distribution, takes positive as well as negative values, but duration by its very nature cannot be negative and therefore normality cannot be assumed when dealing with duration/survival data. Hence the normality assumption of regression models is violated.

A censored observation is defined as an observation with incomplete information. Censoring introduces distortions into traditional statistical methods and is essentially a defect of the sample data. The assumption is that if the data were not censored it would be representative of the population of interest. In survival analysis, censored observations arise whenever the dependent variable of interest represents the time to a terminal event, and the duration of the study is limited in time.

An important concept in survival analysis is the hazard rate. The hazard rate is defined as the probability that the event will occur at time t conditional on surviving until time t. Another concept related to the hazard rate is the survival function which can be defined as the probability of surviving to time t.

Most models try to model the hazard rate by choosing the underlying distribution depending on the shape of the hazard function. A distribution whose hazard function slopes upward is said to have positive duration dependence, a decreasing hazard shows negative duration dependence whereas constant hazard is a process with no memory usually characterized by the exponential distribution. Some of the distributional choices in survival models are: F, gamma, Weibull, log normal, inverse normal, exponential etc. All these distributions are for a non-negative random variable.

Duration models can be parametric, non-parametric or semi-parametric. Some of the models commonly used are Kaplan-Meier, Cox proportional hazard model (non parametric).

#### Classification and regression trees

Classification and regression trees (CART) is a non-parametric technique that produces either classification or regression trees, depending on whether the dependent variable is categorical or numeric, respectively.

Trees are formed by a collection of rules based on values of certain variables in the modeling data set

- Rules are selected based on how well splits based on variables’ values can differentiate observations based on the dependent variable
- Once a rule is selected and splits a node into two, the same logic is applied to each “child” node (i.e. it is a recursive procedure)
- Splitting stops when CART detects no further gain can be made, or some pre-set stopping rules are met

Each branch of the tree ends in a terminal node

- Each observation falls into one and exactly one terminal node
- Each terminal node is uniquely defined by a set of rules

#### Multivariate regression splines

Multivariate adaptive regression splines is a non-parametric technique that builds flexible models by fitting piecewise linear regressions.

An important concept associated with regression splines is that of a knot. Knot is where one local regression model gives way to another and thus is the point of intersection between two splines.

In multivariate and adaptive regression splines, basis functions are the tool used for generalizing the search for knots. Basis functions are a set of functions used to represent the information contained in one or more variables. Multivariate and Adaptive Regression Splines model almost always creates the basis functions in pairs.

Multivariate and adaptive regression spline approach deliberately overfits the model and then prunes to get to the optimal model. The algorithm is computationally very intensive and in practice we are required to specify an upper limit on the number of basis functions.

### Machine learning techniques

Machine learning, a branch of artificial intelligence, was originally employed to develop techniques to enable computers to learn. Today, since it includes a number of advanced statistical methods for regression and classification, it finds application in a wide variety of fields including medical diagnostics, credit card fraud detection, face and speech recognition and analysis of the stock market. In certain applications it is sufficient to directly predict the dependent variable without focusing on the underlying relationships between variables. In other cases, the underlying relationships can be very complex and the mathematical form of the dependencies unknown. For such cases, machine learning techniques emulate human cognition and learn from training examples to predict future events.

A brief discussion of some of these methods used commonly for predictive analytics is provided below. A detailed study of machine learning can be found in [TomMitchell]

#### Neural networks

Neural networks are nonlinear sophisticated modeling techniques that are able to model complex functions. They can be applied to problems of prediction, classification or control in a wide spectrum of fields such as finance, medicine, engineering, and physics.

Neural networks are used when the exact nature of the relationship between inputs and output is not known. A key feature of neural networks is that they learn the relationship between inputs and output through training. There are two types of training in neural networks used by different networks, supervised and unsupervised training, with supervised being the most common one.

Some examples of neural network training techniques are backpropagation, quick propagation, conjugate gradient descent, projection operator, Delta-Bar-Delta etc. Theses are applied to network architectures such as multilayer perceptrons, Kohonen networks, Hopfield networks, etc.

#### Radial basis functions

A radial basis function (RBF) is a function which has built into it a distance criterion with respect to a center. Such functions can be used very efficiently for interpolation and for smoothing of data. Radial basis functions have been applied in the area of neural networks where they are used as a replacement for the sigmoidal transfer function. Such networks have 3 layers, the input layer, the hidden layer with the RBF non-linearity and a linear output layer. The most popular choice for the non-linearity is the Gaussian. RBF networks have the advantage of not being locked into local minima as do the feed-forward networks such as the multilayer perceptron.

#### Support vector machines

Support Vector Machines (SVM) are used to detect and exploit complex patterns in data by clustering, classifying and ranking the data. They are learning machines that are used to perform binary classifications and regression estimations. They commonly use kernel based methods to apply linear classification techniques to non-linear classification problems. There are a number of types of SVM such as linear, polynomial, sigmoid etc.

#### Naïve Bayes

Naïve Bayes based on Bayes conditional probability rule is used for performing classification tasks. Naïve Bayes assumes the predictors are statistically independent which makes it an effective classification tool that is easy to interpret. It is best employed when faced with the problem of ‘curse of dimensionality’ i.e. when the number of predictors is very high.

#### k-nearest neighbours

The nearest neighbour algorithm (KNN) belongs to the class of pattern recognition statistical methods. The method does not impose a priori any assumptions about the distribution from which the modeling sample is drawn. It involves a training set with both positive and negative values. A new sample is classified by calculating the distance to the nearest neighbouring training case. The sign of that point will determine the classification of the sample. In the k-nearest neighbour classifier, the k nearest points are considered and the sign of the majority is used to classify the sample. The performance of the kNN algorithm is influenced by three main factors: (1) the distance measure used to locate the nearest neighbours; (2) the decision rule used to derive a classification from the k-nearest neighbours; and (3) the number of neighbours used to classify the new sample.

## Popular tools

There are numerous tools available in the marketplace which help with the execution of predictive analytics. These range from those which need very little user sophistication (eg. KXEN) to those that are designed for the expert practitioner (eg. SPSS, SAS modules such as STAT, ETS, OR etc.). The difference between these tools is often in the level of customization and heavy data lifting allowed. For traditional statistical modeling some of the popular tools are SAS, SPLUS, SPSS, STATA. For machine learning /data mining type of applications Enterprise Miner, Clementine, KXEN Analytic Framework, and Excel Miner are some of the popularly used options. Classification Tree analysis can be performed using CART software. R is a very powerful tool that can be used to perform almost any kind of statistical analysis, and is freely downloadable. WEKA is a freely available open-source collection of machine learning methods for pattern classification, regression, clustering, and some types of meta-learning, which can be used for predictive analytics. YALE is another freely available integrated open-source software environment for data mining and machine learning fully integrating WEKA and providing an even larger number of methods for predictive analytics. The widespread use of predictive analytics in industry has led to the proliferation of numerous service firms. Some of them are highly specialized (focusing for example on fraud detection or response modeling. Others provide predictive analytics services in support of a wide range of business problems. Predictive Analytics competitions are also fairly common and often pit academicians and Industry practitioners (see for example, KDD CUP).

## Conclusion

Predictive analytics adds great value to a businesses decision making capabilities by allowing it to formulate smart policies on the basis of predictions of future outcomes. A broad range of tools and techniques are available for this type of analysis and their selection is determined by the analytical maturity of the firm as well as the specific requirements of the problem being solved.

## References

Case studies:

- CRM at a Pay-TV Company: Using Analytical Models to Reduce Customer Attrition by Targeted Marketing for Subscription Services
- Predicting Customer Loyalty Using The Internal Transactional Database

Books:

- John R. Davies, Stephen V. Coggeshall, Roger D. Jones, and Daniel Schutzer, "Intelligent Security Systems," in Freedman, Roy S., Flein, Robert A., and Lederman, Jess, Editors (1995).
*Artificial Intelligence in the Capital Markets*, Chicago: Irwin. ISBN 1-55738-811-3. - Agresti, Alan (2002).
*Categorical Data Analysis*, Hoboken: John Wiley and Sons. ISBN 0-471-36093-7. - Enders, Walter (2004).
*Applied Time Series Econometrics*, Hoboken: John Wiley and Sons. ISBN 052183919X. - Greene, William (2000).
*Econometric Analysis*, London: Prentice Hall. ISBN 0-13-013297-7. - Mitchell, Tom (1997).
*Machine Learning*, New York: McGraw-Hill. ISBN 0-07-042807-7. - Tukey, John (1977).
*Exploratory Data Analysis*, New York: Addison-Wesley. ISBN 0.

## See also

## External links

- "Cloud 1305", Scalable Machine Learning, free software on the Amazon Ec2 cloud
- *Right-Time Response Systems* from ReadiMinds
- Predictive Analytics with Data Mining: How It Works
- Logistic regression
- Logistic regression
- Analytics and Scoring
- Free online chaos theory based analysis
- Business Inteligence

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