Resolving e commerce challenges with probabilistic programming
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The document discusses the application of Bayesian programming in resolving e-commerce challenges, outlining the Bayesian approach, its advantages, and key distributions. It includes case studies focusing on price-demand change analysis and hierarchical modeling to analyze price elasticity of demand for products. The presentation emphasizes using probabilistic programming as a statistical tool to incorporate expert knowledge, leverage data, and improve accuracy in predictions.
![1st place
Allstate
[2016]
1st place
Mercari
[2018]
2nd place
GE
[2014]
Problem solved:
Which potential
customers are at
risk of not repaying
their loans?
3rd place
Am Express
[2015]
3rd place
Deloitte
[2015]
Problem solved:
Which of our current
customers will stay
insured with us for
an entire policy
term?
Problem solved:
What is the best
price for the
product I want to
sell?
Problem solved:
How to predict
flight delays over
The US?
Problem solved:
What will future
rental prices for
properties across
Western Australia
be?
Our experience](https://image.slidesharecdn.com/copyofcopyofresolvinge-commercechallengeswithprobabilisticprogrammingblog-190704101004/85/Resolving-e-commerce-challenges-with-probabilistic-programming-50-320.jpg)
Resolving e commerce challenges with probabilistic programming
- 1. Resolving e-commerce challenges with probabilistic programming Liudmyla Kyrashchuk Magdalena Wójcik
- 2. Content of the presentation 1) What is the Bayesian approach? 2) Profits of going Bayesian 3) Recap of distributions 4) Toolbox for a Bayesian Hacker 5) Case Study #1 - Price-demand change analysis 6) Case Study #2 - Hierarchical modeling
- 3. Bayesian programming is a best all-in-one statistical tool for hackers. 🔨 My hypothesis:
- 4. What is the Bayesian approach? Thomas Bayes - XVIII century mathematician who interpreted probability as the degree of belief, and not the simple frequency of events.
- 5. Bayes’ Theorem Posterior probability of A given evidence B Prior probability of A Likelihood of collecting evidence B when A is true Probability of collecting B under all circumstances
- 6. Mandatory naive example 🤒 What is the probability of Bob having a relatively rare disease, given that he received positive result from the medical test? Disease occurs in 1 / 250 people. Test has True Positive Rate of 0.99.
- 7. Mandatory naive example 🤒 What is the probability of Bob having a relatively rare disease, given that he received positive result from the medical test? Disease occurs in 1 / 250 people. Test has True Positive Rate of 0.99. 0.99
- 8. Mandatory naive example 🤒 What is the probability of Bob having a relatively rare disease, given that he received positive result from the medical test? Disease occurs in 1 / 250 people. Test has True Positive Rate of 0.99. 0.004 0.99
- 9. Mandatory naive example 🤒 What is the probability of Bob having a relatively rare disease, given that he received positive result from the medical test? Disease occurs in 1 / 250 people. Test has True Positive Rate of 0.99. 0.004 0.99 0.99×1 + 0.01×249 250
- 10. Mandatory naive example 🤒 What is the probability of Bob having a relatively rare disease, given that he received positive result from the medical test? Disease occurs in 1 / 250 people. Test has True Positive Rate of 0.99. 0.004 0.99 0.28 0.99×1 + 0.01×249 250
- 11. Bayes’ Theorem in 🔍 of Data Scientist Posterior distribution Our updated belief Prior belief as a distribution Collected data Constant normalization term
- 12. Profits of going Bayesian ● Instead of one value, we get a distribution of likely values. ● We get information on certainty of model output. ● More ways to compare outcomes. ● Spot for expert knowledge already incorporated in the model. ● Easy way to include external knowledge when data set is small.
- 13. It’s where we put our beliefs. So we choose the distribution wisely: 1. Empirically - we have already done some experiments and have actual data, 2. With expertise - we have expert domain knowledge on the subject, 3. With intent - we have reasons to prefer some values over the others, 4. YOLO - we have no idea and wouldn’t like to affect the outcome. Choosing prior distribution
- 14. Uniform distribution all possible values fall between minimum and maximum bounds and have equal likelihood. Conditions: 1. The minimum value is fixed. 2. The maximum value is fixed. 3. All values between the minimum and maximum occur with equal likelihood. Recap of distributions
- 15. Normal distribution The most common distribution, which has 3 properties: 1. Some value (mean of the distribution) is the most likely. 2. The uncertain variable could as likely be above the mean as it could be below the mean (symmetrical about the mean). 3. The uncertain variable is more likely to be in the vicinity of the mean than further away. Recap of distributions
- 16. Poisson distribution describes the number of times an event occurs in a given interval. Conditions: 1. The number of possible occurrences in any interval is unlimited. 2. The occurrences are independent. The number of occurrences in one interval does not affect the number of occurrences in other intervals. 3. The average number of occurrences must remain the same from interval to interval Recap of distributions
- 17. Gamma distribution The gamma distribution is most often used as the distribution of the amount of time until the rth occurrence of an event in a Poisson process. Conditions: 1. The number of possible occurrences in any unit of measurement is not limited to a fixed number. 2. The occurrences are independent. 3. The average number of occurrences must remain the same from unit to unit. Recap of distributions
- 18. Bayesian Hacker’s Toolbox That’s a distribution, possibly over many dimensions. How do we even infer that?
- 19. Bayesian Hacker’s Toolbox - sampling! When there is no closed-form solution, we can approximate with sampling, using technique named MCMC (Markov Chain Monte Carlo). PyMC gives us also a set of pre-defined distributions.
- 20. Markov Chain Monte Carlo - easy explanation! 1. Generate random guesses (Monte Carlo part) 2. Generate next generation guesses based only on the guesses before that. (Markov Chain). Fun fact: this property defines that those chains are memoryless. 3. Accept new generation guesses if they “moving in the right direction”, otherwise reject them.
- 21. Case Studies
- 22. Case Study #1: Price-Demand change analysis We know when we changed the price for a particular product. What we don’t know are: ● Was this price change noticeable (enough to change the demand)? ● When the price change affected the demand change? ● Can models detect this from the data?
- 23. Price change effect on demand Price $99.98 Price $79.98 Real-world examples are often noisy and concern thousands of products at once. Below is an example of the noisy plot.
- 24. Price change effect on demand Price $99.98 Price $79.98 We’ll use a simplistic example for this demonstration.
- 25. First steps: sales distribution 1. Define the distribution of the data: We want to predict sales - what can be the distribution? Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal
- 26. First steps: sales distribution 1. Define the distribution of the data: We want to predict sales - what can be the distribution? Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Discrete
- 27. First steps: sales distribution 1. Define the distribution of the data: We want to predict sales - what can be the distribution? Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Discrete ● More than 3 unique values
- 28. First steps: sales distribution 1. Define the distribution of the data: We want to predict sales - what can be the distribution? Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Discrete ● More than 3 unique values Shows number of trials until the success is achieved Number of times event is occurred during the time interval
- 29. First steps: λ distribution 1. We choose the Poisson distribution: Poisson (λ) 2. Now we must define the distribution of the λ Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal
- 30. First steps: λ distribution 1. We choose the Poisson distribution: Poisson (λ) 2. Now we must define the distribution of the λ Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Continuous
- 31. First steps: λ distribution 1. We choose the Poisson distribution: Poisson (λ) 2. Now we must define the distribution of the λ Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Continuous ● Positive
- 32. First steps: λ distribution 1. We choose the Poisson distribution: Poisson (λ) 2. Now we must define the distribution of the λ Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Continuous ● Positive ● Time related
- 33. First steps: λ distribution 1. We choose the Poisson distribution: Poisson (λ) 2. Now we must define the distribution of the λ Normal Exponential Cauchy Zero Inflated Binomial Uniform Gamma Geometric Flat Binomial Beta Minimum extreme Half Flat Poisson Lognormal Negative binomial Logistic Weibull Student’s t Discrete uniform Negative Normal Way of thinking ● Continuous ● Positive ● Time related Event can occur at any time randomly Event is more/less likely occur over time Event can occur at any time not necessarily randomly
- 34. Now we build the model 1. Define & Run the model
- 35. Now we build the model 2. Check the results! On 16th day the demand changed
- 36. Conclusions 🤔 ? 1. For some products the change may not be noticeable. 2. For some products the change can be easily spotted. Why? How much the price changed? Dig deeper!
- 37. Case Study #2: Price elasticity of demand 💸 Calculate Price Elasticity of Demand for all products in store. Except some of them are very new and for some price almost never changed.
- 38. Case Study #2: Hierarchical model 🏔 Hierarchical models allows you to define the parameters taking to the account group means, using the informations about products similarity. Group level Product level
- 39. Shrinkage Products are “pulled” towards the group mean. Why is it important? If you have few data points or a new product, you can leverage this facts by using knowledge from the group mean. source
- 40. The simple model ⛰ 1. Distribution of the target - sales (Your target is λ = 𝑤*x +𝑤) 2. Distribution on the group’s level: a. 𝑤′1 b. 𝑤′0 3. Distributions on products level: a. 𝑤1 b. 𝑤0 1. Poisson (λ) 2. a. Normal ( 𝛍, 𝛔) b. Normal ( 𝛍, 𝛔) 3. a. Group’s 𝛍, 𝛔 b. Group’s 𝛍, 𝛔 Let’s build the model!
- 41. The simple model ⛰
- 43. Performance - explained Mean - average of distribution SD - standard deviation of distribution mc_error - standard error of posterior sample mean as estimate of theoretical expectation for given parameter. Rule of thumb: want MC error < 1 − 5% of posterior SD hpd_2.5 & hpd_97.5 - 2.5% and 97.5% percentiles of the posterior samples for each parameter give a 95% posterior credible interval N_eff - number of effective samples. Rule of thumb: want N_eff ~= number of samples Rhat - Gelman-Rubin convergence diagnostic, Rule of thumb: want Rhat ~= 1
- 44. More complex model 🏔 Add more levels (category, subcategory, etc) Add more parameters (𝑤2 , 𝑤3 ,... 𝑤n )
- 45. If smth wrong 🌋 1. Check if distribution matches the target formula 2. Plot prior distribution, maybe your prior believes are absurd 3. Plot posterior distribution, maybe your evaluations are too vague 4. Try to redefine the model with offset 5. Check possible suggestions here 6. If nothing works, reparametrize!
- 46. Useful links 👊 Library: PyMC3 Books: Bayesian Methods for Hackers (free) Statistical Rethinking Good guide to distribution description (free) Introduction to Bayesian Monte Carlo To follow: Thomas Wiecki (and his great blog) Richard McElreath (also, check out his awesome lectures on )
- 47. About us
- 48. 1 2 About us We are a Boutique Data Science consulting, specialising in leading digital transformations. We successfully realized custom projects and won Data Science competitions for startups to Fortune 500 companies, some of them listed below. We organize biggest Data Science community events called Kaggle Days in cooperation with Google-owned Kaggle. Demand for AI experts is extremely high nowadays - LogicAI is a company which has direct access to the top 3M data scientists in the world.
- 49. Our customers have access to 2.8mln world’s top talent We build world’s biggest offline Data Science community We build Data Science teams for our customers + = ”Great community with lots of diverse talent and skill sets.” “You rock. Being nice and generous is the most important thing in community events and you were!”
- 50. 1st place Allstate [2016] 1st place Mercari [2018] 2nd place GE [2014] Problem solved: Which potential customers are at risk of not repaying their loans? 3rd place Am Express [2015] 3rd place Deloitte [2015] Problem solved: Which of our current customers will stay insured with us for an entire policy term? Problem solved: What is the best price for the product I want to sell? Problem solved: How to predict flight delays over The US? Problem solved: What will future rental prices for properties across Western Australia be? Our experience
- 51. Some of our customers
- 52. Contact us