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Demystifying Neural Networks for Actuaries: Methods and Applications

This paper introduces actuaries to neural networks, showing their similarities to conventional statistics and discussing where their use can be helpful. It elucidates how to interpret neural network models and their advantages over other data mining methods. The paper covers supervised and unsupervised learning in neural networks, along with examples of fitting curves, approximating functions, and handling correlated variables. It also explores interpreting neural networks, interactions in modeling, and visualizing neural network results.

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Demystifying Neural Networks for Actuaries: Methods and Applications

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  1. Neural Networks Demystifiedby Louise FrancisFrancis Analytics and Actuarial Data Mining, Inc.louise_francis@msn.com

  2. Objectives of Paper • Introduce actuaries to neural networks • Show that neural networks are a lot like some conventional statistics • Indicate where use of neural networks might be helpful • Show how to interpret neural network models

  3. Data Mining • Neural networks are one of a number of data mining techniques • Methods primarily developed in artificial intelligence and statistical disciplines to find patterns in data • Typically applied to large databases with complex relationships

  4. Some Other Data Mining Methods • Decision trees • Clustering • Regression splines • Association rules

  5. Some Data Mining Advantages • Nonlinear relationships • Interactions • Multicollinearity

  6. Data Mining: Neural Networks • One of more established approaches • Somewhat glamorous • AI description: they function like neurons in the brain

  7. Neural Networks: Disadvantages • They are a black box • User gets a prediction from them, but the form of the fitted function is not revealed • Don’t know which variables are the most important in the prediction

  8. Kinds of Neural Networks • Supervised learning • Multilayer perceptron • Also known as backpropagation neural network • Paper explains this kind of NN • Unsupervised learning • Kohonen neural networks

  9. THREE LAYER NEURALNETWORK Hidden Layer (Processes Data) Input Layer (Input Data) Output Layer (Predicted Value) The MLP Neural Network

  10. The Activation Function • The sigmoid logistic function

  11. The Logistic Function

  12. The Logistic Function

  13. The Logistic Function

  14. Other • Data is usually normalized • Usually both independent and dependent variables transformed to lie in range between 0 and 1

  15. Logistic Function

  16. Fitting the curve • Typically use a procedure which is like gradient descent

  17. Fitting a nonlinear function

  18. Graph of nonlinear function

  19. Table 4 W0 W1 Node 1 -4.107 7.986 Node 2 6.549 -7.989 Fitted Weights

  20. Table 5 W0 W1 W2 6.154 -3.0501 -6.427 Hidden Layer

  21. Table 6 Computation of Predicted Values for Selected Values of X (1) (2) (3) (4) (5) (6) (7) ((1)-508)/4994 6.15-3.05*(3)-6.43*(4) 1/(1+exp(-(5)) 6.52+3.56*(6) X Normalized X Output of Node 1 Output of Node 2 Weighted Hidden Node Output Output Node Logistic Function Predicted Y 508.48 0.00 0.016 0.999 -0.323 0.420 7.889 1,503.00 0.22 0.088 0.992 -0.498 0.378 7.752 3,013.40 0.56 0.596 0.890 -1.392 0.199 7.169 4,994.80 1.00 0.980 0.190 1.937 0.874 9.369 Selected Fitted Values for function

  22. Hidden and Output Layer

  23. Fit of Curve with 2 Nodes

  24. Fit of Curve with 3 Nodes

  25. Universal Function Approximator • The multilayer perceptron neural network with one hidden layer is a universal function approximator • Theoretically, with a sufficient number of nodes in the hidden layer, any nonlinear function can be approximated

  26. Correlated Variables • Variables used in model building are often correlated. • It is difficult to isolate the effect of the individual variables because of the correlation between the variables.

  27. Example of correlated variables

  28. A Solution: Principal Components & Factor Analysis

  29. Factor Analysis: An Example

  30. Factor Analysis

  31. Factor Analysis

  32. Correlated Variables: An Example • Workers Compensation Line • Produce an economic inflation index • Wage Inflation • Medical Inflation • Benefit Level Index • In simplified example no other variable drives severity results

  33. Factor Analysis Example X1 = b1 Factor1 X2 = b2 Factor1 X3 = b3 Factor1 Index =.395 (Wage Inflation)+.498(Medical Inflation)+.113(Benefit Level Inflation)

  34. Factor Analysis Example

  35. Interpreting Neural Network • Look at weights to hidden layer • Compute sensitivities: • a measure of how much the predicted value’s error increases when the variables are excluded from the model one at a time

  36. Table 9: Factor Example Parameters Table 10 W0 Sensitivities of Variables in Factor Example W1 W2 W3 Benefit Level 2.549 -2.802 23.6% -3.010 0.662 Medical Inflation 33.1% Wage Inflation 6.0% Interpretation of Neural Network

  37. Interactions: Another Modeling Problem • Impact of two variables is more or less than the sum of their independent impacts.

  38. Interactions: Simulated Data

  39. Interactions: Neural Network

  40. Interactions: Regression

  41. Example With Messy Data

  42. Example With Messy Data

  43. Visualizing Neural Network Result

  44. Visualizing Neural Network Result

  45. Visualization of Law Change Effect

  46. Visualization of Inflation

  47. How Good Was the Fit?

  48. How Good Was the Fit?

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