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Thompson Sampling for Machine Learning - Ruben Mak

PyData Amsterdam 2018

In this talk I hope to give a clear overview of the opportunites for applying Thompson Sampling in machine learning. I will share some technical examples in recent developments (for example Bayesian Neural Networks using Edward) but more importantly I hope to trigger the audience to start thinking strategically about how we want our machine learning models to learn from new data.

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Thompson Sampling for Machine Learning - Ruben Mak

  1. 1. Thompson Sampling for Machine Learning R.J. Mak Greenhouse Group PyData Amsterdam 2018 May, 26, 2018
  2. 2. Introduction Group of online marketing agencies, part of GroupM Tech Hub Creative Hub Data Hub Data Science Team Data Technologist Team Data Insights Team Consumer Experience Marketing Team
  3. 3. Multi-Armed Bandit Problem How to optimally insert coins in slot machines when reward distributions of each machine are unknown? Exploitation vs. exploration tradeoff
  4. 4. Applications Any setting where data (observations) are costly. Pretty much any data science project, underemphasized. Deep learning: most focus on cases where data is (nearly) abundant. Classical examples: Finance Testing in online marketing (websites, ads) Budget allocation R&D Clinical trials
  5. 5. Applications
  6. 6. Thompson Sampling: some history Formulated by Thompson in 1933. Allied scientists in World War II, proposed to drop the Multi-armed bandit problem over Germany so that German scientists could also waste their time on it. 1997 proof of convergence. Asymptotic convergence results for contextual bandits were published in 2011. 2012 proven to be optimal for the case of Bernoulli rewards (Lai and Robbins lower bound for the cumulative regret).
  7. 7. Thompson Sampling Choosing the action that maximizes the expected reward with respect to a randomly drawn belief. Example of three slot machines, equal reward, probability of winning? Construct reward distribution. (Beta distribution). Sample from those distributions to choose the next slot machine.
  8. 8. Thompson sampling using numpy 1 import numpy as np 2 3 plays = np.array([100, 20, 20]) 4 wins = np.array([32, 8, 5]) 5 num_samples = 1000000 6 7 p_A_sample = np.random.beta(wins[0], plays[0] - wins[0], num_samples) 8 p_B_sample = np.random.beta(wins[1], plays[1] - wins[1], num_samples) 9 p_C_sample = np.random.beta(wins[2], plays[2] - wins[2], num_samples) 10 11 mab_wins = np.array([0.0, 0.0, 0.0]) 12 13 for i in range(num_samples): 14 winner = np.argmax([p_A_sample[i], p_B_sample[i], p_C_sample[i]]) 15 mab_wins[winner] += 1 16 17 mab_wins = mab_wins / num_samples 18 19 print(mab_wins)
  9. 9. Prediction probabilities vs. prediction distributions Prediction probabilities and prediction distributions both say something about uncertainty, what’s the difference? In the example of object detection, the probabilities are point estimates of how likely the thing in the picture is a certain object, for that specific picture. It captures the uncertainty from the input image. However, it does not capture the uncertainty from the data used to train the model. This is what we want to capture with a prediction distribution.
  10. 10. Prediction probabilities vs. prediction distributions
  11. 11. Traditional (frequentist) clinical trial Purely random split test subjects into two groups, group A gets the treatment, group B gets a placebo. Often assumption of homogeneous group is made (same effect for everybody), or, formally, a specific hypothesis needs to be made at the start of the research about specific heterogeneity. Medicine often has dangerous side effects for women (and possibly children, or other minorities). Time to market of new medicine also plays a role. Maurits Kaptein (JADS): ”It is unethical to use randomized controlled trials to personalize health-care”. {patient, time, treatment, dose} f → outcome
  12. 12. Edward Python package for probabilistic modeling and inference Build on top of Tensorflow Bayesian neural networks Non-Bayesian machine learning: point estimates of coefficients and predictions Bayesian: distributions of coefficients and predictions
  13. 13. Toy data set A medicine that causes side effects at a certain dose. This maximum dose is depending on gender and age, and some individual random noise. However, the (test subjects) population is mostly elderly male.
  14. 14. Edward in action Two-layer Bayesian neural network. Set priors uninformative but at least somewhere near results. Posteriors after 1000 iterations.
  15. 15. Edward results Biased for the lowest ages. Doesn’t capture interaction effect for lower ages. Thompson sampling: when searching max dose, treat test subjects with doses sampled from distribution.
  16. 16. Frequentist comparison Frequentists show the effect more clearly. Assuming you actually have the correct model assumptions. Posterior draws always normal distributions, no option to balance between including or not including interaction term.
  17. 17. Edward age as integer input Trying to smooth by taking age as single integer input variable. Bias variance trade-off. Better at capturing interaction effects, draws look nice. Doesn’t capture uncertainty for lowest ages.
  18. 18. Frequentist vs. Bayesian neural network Human hypothesis vs. discovering with machine learning. Simple and specific input variables (age and gender) vs. many more possible input variables (e.g. DNA or smart sensor data)? Problems with current scientific incentives of publication and going to market in pharmaceutics.
  19. 19. Data volume: data from practice The biggest problem is acquiring sufficient data to find specific relationships, interactions and effects. What if every treatment could be used as a data point? Remove the strict boundary between research and application. Thompson sampling in daily use: Continuously update distributions with data from practice. Sample optimal treatment from distributions.
  20. 20. Practical and ethical challenges Practical challenges. Would you want to be treated according to a randomly sampled belief or the most likely belief? Would you always want to be in an experiment? However, current system is unfair because: Unfair towards effects and side effects for minorities, because you need to wait until somebody comes with a hypothesis and start researching. Longer time for a medicine to go to market, unfair for patients that cannot get the treatment (yet).
  21. 21. Conclusion Consider the cost of data acquisition as an essential topic for any data scientist. Strategic design of data collection, consider Thompson sampling. Edward is definitely worth discovering. There is no such thing as a free lunch!

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