Consumer Behavior Prediction using Parametric and Nonparametric Methods

1
Consumer Behavior Prediction using Parametric and
Nonparametric Methods

• Elena Eneva
• CALD Masters Presentation
• 19 August 2002
• Advisors Alan Montgomery, Rich Caruana,
• Christos Faloutsos

2
Outline

• Introduction
• Data
• Economics Overview
• Baseline Models
• New Hybrid Models
• Results
• Conclusions and Future Work

3
Background

• Retail chains are aiming to customize prices in
  individual stores
• Pricing strategies should adapt to the
  neighborhood demand
• Stores can increase operating profit margins by
  33 to 83

4
Price Elasticity
Q is quantity purchased P is price of product
consumers response to price change
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Data Example
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Data Example Log Space
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Assumptions

• Independence
• Substitutes fresh fruit, other juices
• Other Stores
• Stationarity
• Change over time
• Holidays

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The Model
Need to multiply this across many stores, many
categories.
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Converting to Original Space
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Existing Methods

• Traditionally using parametric models (linear
  regression)
• Recently using non-parametric models (neural
  networks)

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Our Goal

• Advantage of LR known functional form (linear in
  log space), extrapolation ability
• Advantage of NN flexibility, accuracy

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Datasets

• weekly store-level cash register data at the
  product level
• Chilled Orange Juice category
• 2 years
• 12 products
• 10 random stores selected

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Evaluation Measure

• Root Mean Squared Error (RMS)
• the average deviation between the predicted
  quantity and the true quantity

14
Models

• Hybrids
• Smart Prior
• MultiTask Learning
• Jumping Connections
• Frozen Jumping Connections

• Baselines
• Linear Regression
• Neural Networks

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Baselines

• Linear Regression
• Neural Networks

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Linear Regression

• q is the quantity demanded
• pi is the price for the ith product
• K products overall
• The coefficients a and bi are determined by the
  condition that the sum of the square residuals is
  as small as possible.

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Linear Regression
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Results RMS
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Neural Networks

• generic nonlinear function approximators
• a collection of basic units (neurons), computing
  a (non)linear function of their input
• backpropagation

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Neural Networks
1 hidden layer, 100 units, sigmoid activation
function
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Results RMS
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Hybrids

• Smart Prior
• MultiTask Learning
• Jumping Connections
• Frozen Jumping Connections

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Smart Prior

• Idea start the NN at a good set of weights,
  help it start from a smart prior.
• Take this prior from the known linearity
• NN first trained on synthetic data generated by
  the LR model
• NN then trained on the real data

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Smart Prior
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Results RMS
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Multitask Learning

• Idea learning an additional related task in
  parallel, using a shared representation
• Adding the output of the LR model (built over the
  same inputs) as an extra output to the NN
• Make the net share its hidden nodes between both
  tasks
• Custom halting function
• Custom RMS function

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MultiTask Learning
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Results RMS
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Jumping Connections

• Idea fusing LR and NN
• change architecture
• add connections which jump over the hidden
  layer
• Gives the effect of simulating a LR and NN all
  together

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Jumping Connections
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Results RMS
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Frozen Jumping Connections

• Idea you have the linearity, now use it!
• same architecture as Jumping Connections, plus
  really emphasizing the linearity
• freeze the weights of the jumping layer, so the
  network cant forget about the linearity

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Frozen Jumping Connections
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Frozen Jumping Connections
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Frozen Jumping Connections
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Results RMS
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Models

• Hybrids
• Smart Prior
• MultiTask Learning
• Jumping Connections
• Frozen Jumping Connections

• Baselines
• Linear Regression
• Neural Networks

• Combinations
• Voting
• Weighted Average

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Combining Models

• Idea Ensemble Learning
• Committee Voting equal weights for each models
  prediction
• Weighted Average optimal weights determined by
  a linear regression model
• 2 baseline and 3 hybrid models
• (Smart Prior, MultiTask Learning, Frozen Jumping
  Conections)

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Committee Voting

• Average the predictions of the models

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Results RMS
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Weighted Average Model Regression

• Linear regression on baselines and hybrid models
  to determine vote weights

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Results RMS
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Normalized RMS Error

• Compare model performance across stores
• Stores of different sizes, ages, locations, etc
• Need to normalize
• Compare to baselines
• Take the error of the LR benchmark as unit error

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Normalized RMS Error
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Conclusions

• Clearly improved models for customer choice
  prediction
• Will allow stores to price the products more
  strategically and optimize profits
• Maintain better inventories
• Understand product interaction

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Future Work Ideas

• analyze Weighted Average model
• compare extrapolation ability of new models
• use other domain knowledge
• shrinkage model a super store model with
  data pooled across all stores

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Acknowledgements

• I would like to thank my advisors
• and
• my CALDling friends and colleagues

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The Most Important Slide

• for this presentation and the paper
• www.cs.cmu.edu/eneva/research.htm
• eneva_at_cs.cmu.edu

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References

• Montgomery, A. (1997). Creating Micro-Marketing
  Pricing Strategies Using Supermarket Scanner Data
• West, P., Brockett, P. and Golden, L (1997) A
  Comparative Analysis of Neural Networks and
  Statistical Methods for Predicting Consumer
  Choice
• Guadagni, P. and Little, J. (1983) A Logit Model
  of Brand Choice Calibrated on Scanner data
• Rossi, P. and Allenby, G. (1993) A Bayesian
  Approach to Estimating Household Parameters

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Error Measure Unbiased ModelDetails
by computing the integral over the distribution
is a biased estimator for q, so we correct the
bias by using

• which is an unbiased estimator for q.

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On one hand
In log space, Price-Quantity relationship is
fairly linear
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On the other hand

• the derivation of consumers' demand responses to
  price changes without the need to write down and
  rely upon particular mathematical models for
  demand