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Consumer Behavior Prediction using Parametric and Nonparametric Methods Elena Eneva CALD Masters Presentation 19 August 2002 Advisors: Alan Montgomery, Rich Caruana, Christos Faloutsos

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

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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%

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Price Elasticity consumer’s response to price change inelasticelastic Q is quantity purchased P is price of product

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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 Category Price of Product 1 Price of Product 2 Price of Product 3 Price of Product N... “I know your customers” Predictor Quantity bought of Product 1... Quantity bought of Product 2 Quantity bought of Product 3 Quantity bought of Product N Need to multiply this across many stores, many categories. convert to ln spaceconvert to original space

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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 robustness accuracy NN new LR Take Advantage: use the known functional form to bias the NN Build hybrid models from the baseline models

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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

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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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q is the quantity demanded p i is the price for the i th product K products overall The coefficients a and b i are determined by the condition that the sum of the square residuals is as small as possible. 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 can’t “forget” about the linearity

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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 model’s 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@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 Model Details which is an unbiased estimator for q. is a biased estimator for q, so we correct the bias by using by computing the integral over the distribution

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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

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