My name is John Blankinship, and I am offering a neural network predictive modeling service. I have developed a set of C-language programs for the training, validation and delivery of Multilayer Perceptron neural network models. Given a training set of observations, I am reasonably confident that I can build a neural network predictive model that will outperform an existing model with respect to independent validation data. If I cannot develop a superior predictive model, then there is no charge for my service. Multilayer Perceptron (MLP) neural networks can be applied to regression problems with continuous responses or to classification problems with binary or categorical responses — with continuous or discrete predictor variables. Using this software and given a training set of observations, I will:

- build a Multilayer Perceptron neural network predictive model that will probably outperform a classical regression, decision tree or even another neural network model — especially for complex data mapping problems with significant nonlinearities or interactions.
- assess model performance and adequacy with respect to both training and independent validation data.
- provide a "Weights File" and C-language functions for model delivery and implementation.

The primary target audience for this service are complex data mapping problems with significant nonlinearities or interactions for which:

- a training set of observations already exists
- the number of training examples is large (typically > 1000 although smaller training sets are possible), but not too large (< approximately 30,000)
- the number of input variables is not very large (≤ approximately 20)
- the client is seeking superior predictive performance

This service is relatively unique and goes to great lengths to develop a superior predictive model:

- To facilitate learning, the learning rate is dynamically tuned during training.
- Training data are randomly partitioned into a "Train Segment" and a "Test Segment." During training on the Train Segment, the network's predictive performance is continually monitored with respect to the Test Segment to help avoid overtraining.
- To help find the best model and to avoid unsatisfactory local minima, a large number (almost 200) number of candidate models are built and tested for a variety of network configurations and initial weight vectors.
- Model selection among the candidate models is based solely on predictive performance with respect to independent test data in the Test Segment.
- The Cross-Entropy error function is provided for classification problems.
- To help determine the most effective set of predictor variables, an optional neural network-based forward variable selection capability is available.

Output deliverables are as follows:

__Model Development and Analysis Package__— This includes: (1) output report from the "MLP Test" program which tests a large number of candidate neural networks to find the best one, (2) output report from the "MLP Net" program which provides detailed training results for the selected network, (3) scored training and validation data sets, and (4) output report from the "MLP Stats" program which provides performance and diagnostic results for both the training and validation data sets. The validation data is different from the Test Segment used during training, and is not used in any way during model development. This model validation includes an analysis of variance, product moment and rank correlation analyses of actual vs. predicted responses, classification performance, an analysis of residuals, and a sensitivity analysis of the importance of each input variable. In most cases, the Model Development and Analysis Package will be available approximately 2-7 days after the training data set is received and checked.

__Model Delivery Package__— To implement the neural network model on virtually any computer platform, this includes: (1) a text "Weights File" containing all connection weights, network size parameters and scaling factors, and (2) a C-language function which uses the Weights File to compute predicted output responses for a vector of input variables. If the client decides to purchase the actual predictive model after examining the results of the Model Development and Analysis Package, the Model Delivery Package will be available 1-2 days after the go-ahead is received.

Additional information and sample output deliverables from the Model Development and Analysis Package and the Model Delivery Package are available upon request.

Sincerely, John Blankinship ([email protected])

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