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Computational Advertising: The LinkedIn Way Deepak Agarwal, LinkedIn Corporation CIKM, San Francisco Oct 30 th, 2013

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Computational Advertising MatchMaker (Broder, CACM) –Placing the “best” ads in a given context for every user visit Match making at scale requires automation –serving with low marginal cost increases profit margins Automation through Machine Learning/Optimization New discipline called Computational Advertising ©2013 LinkedIn Corporation. All Rights Reserved.

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LinkedIn Advertising: Brand, Self-Serve, Sponsored updates

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Click Cost = Bid 3 x CTR 3 /CTR 2 Profile: region = US, age = 20 Context = profile page, 300 x 250 ad slot Ad request Sorted by Bid * CTR Response Prediction Engine Campaigns eligible for auction Automatic Format Selection Filter Campaigns (Targeting criteria, Frequency Cap, Budget Pacing) SERVING Serving constraint < 100 millisec

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Response Prediction: Important Input for optimization CTR of an ad format on some slot of a LinkedIn page –E.g. CTR of 160 x 600 ad slot formats CTR of an ad on some position for a selected ad format ©2013 LinkedIn Corporation. All Rights Reserved.

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Counting clicks and views using moving window Page type Estimate CTR of formats for each page type CTR pagetype,format = clicks pagetypel,format /views pagetype,format formats

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Onboarding new formats, avoiding starvation Explore/exploit dilemma FormatClicksViewsCTR% Traffic V1.21523624,9150.24%??? V2.034,87211,839,7410.29%??? V2.137,22412,594,4810.30%??? V3.0000.28%??? Exploit-only (greedy) Maximizes performance given current knowledge Cannot adapt to changing environment Explore-only (random) Serves old & new, good & bad evenly Ignores our knowledge about performance Explore/exploit (softmax) Exploit format that are known to be good but explore those that could be potentially good Profits from current knowledge while continuing to learn FormatClicksViewsCTR% Traffic V1.21523624,9152.4%0% V2.034,87211,839,7412.9%0% V2.137,22412,594,4813.0%100% V3.0002.8%0% FormatClicksViewsCTR% Traffic V1.21523624,9152.4%25% V2.034,87211,839,7412.9%25% V2.137,22412,594,4813.0%25% V3.0002.8%25% FormatClicksViewsCTR% Traffic V1.21523624,9152.4%7.8% V2.034,87211,839,7412.9%35.3% V2.137,22412,594,4813.0%36.3% V3.0002.8%20.7%

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Evaluating Explore/Exploit schemes We evaluated several explore/exploit techniques offline –Offline replay based on precision@1 on randomized data Provides unbiased estimates of online performance (Langford et al, 2009) Softmax + epsilon greedy on LinkedIn advertising, provided significant gains Thompson sampling, UCB, Softmax, epsilon-greedy with – moving window with Different training update frequencies (few minutes, few hours, daily) Epsilon-greedy + softmax, Thompson sampling, UCB among the promising schemes –Faster updates help with new formats initially, daily updates are fine if very few new formats introduced into the system (as in our application) –Segmenting by user attributes did not help much ©2013 LinkedIn Corporation. All Rights Reserved.

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CTR estimates for ads: Curse of dimensionality

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Mitigating the curse What segments ? What are good ones ? –Too few coarse segments: fails to personalize –Too many: curse of dimensionality, data sparseness Most segments have no clicks, 0/5 == 0/50 == 0/5M ? Pool data to mitigate sparseness Pooling with hundreds of millions of segments is challenging –Different ways to pool, we use logistic regression 10 0/5 profile page, ad 77, user from Palo Alto 20/20000 40/1000 Visits on profile page users from Palo Alto

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Taming curse of dimensionality: Logistic Regression 11 Dim 2 Dim 1 + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ -2.5

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CTR Prediction Model for Ads Feature vectors –Member feature vector: x i –Campaign feature vector: c j –Context feature vector: z k Model:

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CTR Prediction Model for Ads Feature vectors –Member feature vector: x i –Campaign feature vector: c j –Context feature vector: z k Model: Cold-start component Warm-start per-campaign component

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CTR Prediction Model for Ads Feature vectors –Member feature vector: x i –Campaign feature vector: c j –Context feature vector: z k Model: Cold-start component Warm-start per-campaign component Cold-start: Warm-start: Both can have L2 penalties.

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Model Fitting Single machine (well understood) –conjugate gradient –L-BFGS –Trusted region –… Model Training with Large scale data –Cold-start component Θ w is more stable Weekly/bi-weekly training good enough However: difficulty from need for large-scale logistic regression –Warm-start per-campaign model Θ c is more dynamic New items can get generated any time Big loss if opportunities missed Need to update the warm-start component as frequently as possible

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Model Fitting Single machine (well understood) –conjugate gradient –L-BFGS –Trusted region –… Model Training with Large scale data –Cold-start component Θ w is more stable Weekly/bi-weekly training good enough However: difficulty from need for large-scale logistic regression –Warm-start per-campaign model Θ c is more dynamic New items can get generated any time Big loss if opportunities missed Need to update the warm-start component as frequently as possible Large Scale Logistic Regression Per-item logistic regression given Θ c

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Large Scale Logistic Regression: Computational Challenge Hundreds of millions/billions of observations Hundreds of thousands/millions of covariates Fitting a logistic regression model on a single machine not feasible Model fitting iterative using methods like gradient descent, Newton’s method etc –Multiple passes over the data Problem: Find x to min(F(x)) Iteration n: x n = x n-1 – b n-1 F’(x n-1 ) b n-1 is the step size that can change every iteration Iterate until convergence Conjugate gradient, LBFGS, Newton trust region, …

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Compute using Map-Reduce Big Data Partition 1 Partition 2 … … Partition N Mapper 1 Mapper 2 … … Mapper N Reducer 1 Reducer 2 Reducer M … … Output 1

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Large Scale Logistic Regression Naïve: –Partition the data and run logistic regression for each partition –Take the mean of the learned coefficients –Problem: Not guaranteed to converge to global solution Alternating Direction Method of Multipliers (ADMM) –Boyd et al. 2011 –Set up constraints: each partition’s coefficient = global consensus –Solve the optimization problem using Lagrange Multipliers –Advantage: converges to global solution

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Large Scale Logistic Regression via ADMM BIG DATA Partition 1 Partition 2 Partition 3 Partition K Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Consensus Computation Consensus Computation Iteration 1

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Large Scale Logistic Regression via ADMM BIG DATA Partition 1 Partition 2 Partition 3 Partition K Logistic Regression Logistic Regression Consensus Computation Consensus Computation Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Iteration 1

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Large Scale Logistic Regression via ADMM BIG DATA Partition 1 Partition 2 Partition 3 Partition K Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Logistic Regression Consensus Computation Consensus Computation Iteration 2

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Large Scale Logistic Regression via ADMM Notation –(X i, y i ): data in the i th partition –β i : coefficient vector for partition i –β: Consensus coefficient vector –r(β): penalty component such as ||β|| 2 2 Optimization problem

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ADMM updates LOCAL REGRESSIONS Shrinkage towards current best global estimate UPDATED CONSENSUS

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ADMM at LinkedIn Lessons and Improvements –Initialization is important (ADMM-M) Use the mean of the partitions’ coefficients Reduces number of iterations by 50% –Adaptive step size (learning rate) (ADMM-MA) Exponential decay of learning rate –Together, these optimizations reduce training time from 10h to 2h

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Explore/Exploit with Logistic Regression 26 + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ COLD START COLD + WARM START for an Ad-id POSTERIOR of WARM-START COEFFICIENTS E/E: Sample a line from the posterior (Thompson Sampling)

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Thompson sampling We only sample from posterior of warm-start coefficients –Cold-start coefficients estimated with lots of data ©2013 LinkedIn Corporation. All Rights Reserved. Covariance assumed diagonal to reduce run-time computation LASER: Logistic without Exploration LASER-EE: Logistic with Exploration

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Models Considered CONTROL: per-campaign CTR counting model COLD-ONLY: only cold-start component LASER: our model (cold-start + warm-start) LASER-EE: our model with Explore-Exploit using Thompson sampling

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Metrics Model metrics –Test Log-likelihood –AUC/ROC –Observed/Expected ratio Business metrics (Online A/B Test) –CTR –CPM (Revenue per impression)

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Observed / Expected Ratio Observed: #Clicks in the data Expected: Sum of predicted CTR for all impressions Not a “standard” classifier metric, but in many ways more useful for this application What we usually see: Observed / Expected < 1 –Quantifies the “winner’s curse” aka selection bias in auctions When choosing from among thousands of candidates, an item with mistakenly over-estimated CTR may end up winning the auction Particularly helpful in spotting inefficiencies by segment –E.g. by bid, number of impressions in training (warmness), geo, etc. –Allows us to see where the model might be giving too much weight to the wrong campaigns High correlation between O/E ratio and model performance online

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Offline: ROC Curves

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Online A/B Test Three models –CONTROL (10%) –LASER (85%) –LASER-EE (5%) Segmented Analysis –8 segments by campaign warmness Degree of warmness: the number of training samples available in the training data for the campaign Segment #1: Campaigns with almost no data in training Segment #8: Campaigns that are served most heavily in the previous batches so that their CTR estimate can be quite accurate

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Daily CTR Lift Over Control

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Daily CPM Lift Over Control

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CPM Lift By Campaign Warmness Segments

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O/E Ratio By Campaign Warmness Segments

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Number of Campaigns Served Improvement from E/E

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Insights Overall performance: –LASER and LASER-EE are both much better than control –LASER and LASER-EE performance are very similar Segmented analysis by campaign warmness –Segment #1 (very cold) LASER-EE much worse than LASER due to its exploration property LASER much better than CONTROL due to cold-start features –Segments #3 - #5 LASER-EE significantly better than LASER Winner’s curse hit LASER –Segment #6 - #8 (very warm) LASER-EE and LASER are equivalent Number of campaigns served –LASER-EE serves significantly more campaigns than LASER –Provides healthier market place

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Theory vs. Practice Textbook Data is stationary Training data is clean Training is hard, testing and inference are easy Models don’t change Complex algorithms work best Reality Features, items changing constantly Fraud, bugs,tracking delays, online/offline inconsistencies, etc. All aspects have challenges at web scale Never-ending processes of improvement Simple models with good features and lots of data win

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Solutions to Practical Problems Rapid model development cycle –Quick reaction to changes in data, product –Write once for training, testing, inference Can adapt to changing data –Integrated Thompson sampling explore/exploit –Automatic training –Multiple training frequencies for different parts of model Good tools yield good models –Reusable components for feature extraction and transformation –Very high-performance inference engine for deployment –Modelers can concentrate on building models, not re-writing common functions or worrying about production issues

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Summary Reducing dimension through logistic regression coupled with explore/exploit schemes like Thompson sampling effective mechanism to solve response prediction problems in advertising Partitioning model components by cold-start (stable) and warm-start (non-stationary) with different training frequencies effective mechanism to scale computations ADMM with few modifications effective model training strategy for large data with high dimensionality Methods work well for LinkedIn advertising, significant improvements ©2013 LinkedIn Corporation. All Rights Reserved.

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Collaborators I won’t be here without them, extremely lucky to work with such talented individuals Liang Zhang Bo Long Jonathan Traupman Romer Rosales Doris Xin

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Current Work Investigating Spark and various other fitting algorithms –Promising results, ADMM still looks good on our datasets Stream Ads –Multi-response prediction (clicks, shares, likes, comments) –Filtering low quality ads extremely important Revenue/Engagement tradeoffs (Pareto optimal solutions) Stream Recommendation –Holistic solution to both content and ads on the stream Large scale ML infrastructure at LinkedIn –Powers several recommendation systems ©2013 LinkedIn Corporation. All Rights Reserved.

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We are hiring ! Interns for summer 2014 (contact me dagarwal@linkedin.com) dagarwal@linkedin.com Full-time –Graduating PhDs, experienced researchers ©2013 LinkedIn Corporation. All Rights Reserved.

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Backup slides ©2013 LinkedIn Corporation. All Rights Reserved.

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LASER Configuration Feature processing pipeline –Sources: transform external data into feature vectors –Transformers: modify/combine feature vectors –Assembler: Packages features vectors for training/inference Configuration language –Model structure can be changed extensively –Library of reusable components –Train, test, and deploy models without any code changes –Speeds up model development cycle

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LASER Transformer Pipeline User Source Context Source Item Source Subset Interaction Assembler Request User profile Item Training or Inference

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LASER Performance Real time inference –About 10µs per inference (1500 ads = 15ms) –Reacts to changing features immediately “Better wrong than late” –If a feature isn’t immediately available, back off to prior value Asynchronous computation –Actions that block or take time run in background threads Lazy evaluation –Sources & transformers do not create feature vectors for all items –Feature vectors are constructed/transformed only when needed Partial results cache –Logistic regression inference is a series of dot products –Scalars are small; cache can be huge –Hardware-like implementation to minimize locking and heap pressure

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