A Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation

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A Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation Yue Ning 1 Yue Shi 2 Liangjie Hong 2 Huzefa Rangwala 3 Naren Ramakrishnan 1 1 Virginia Tech 2 Yahoo Research. Yue Shi is now with Facebook, Liangjie Hong is now with Etsy. 3 George Mason University August 27, 2017

Outline Introduction Problem Challenges The Proposed Framework Applications Adaptive Logistic Regression Adaptive Gradient Boosting Decision Tree Adaptive Matrix Factorization Experimental Evaluation Datasets & Metrics Comparison Methods Ranking Scores Summary

Challenges in Personalized Recommender Systems Alleviate average experiences for users.

Challenges in Personalized Recommender Systems Alleviate average experiences for users. Lack of generic empirical frameworks for different models.

Challenges in Personalized Recommender Systems Alleviate average experiences for users. Lack of generic empirical frameworks for different models. Distributed model learning and less access of data.

Example of Personal Models Global ndcg score 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.10.20.30.40.50.60.70.80.9 1 Personal ndcg score Global MAP score 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.10.20.30.40.50.60.70.80.9 1 Personal MAP score Figure: An example of global and personal models. Left figure showcases the ndcg score of users from global (y-axis) and personal (x-axis) models. (Right: MAP score).

System Framework Input Dataset C 1 C 2 Global Model: w (0) t u HashTable Mapping User Data g (1) g (2) g (3) g (t) Userid t u g (0:tu) Fetch t u Personal Model Personal Model Personal Model Personal Model Figure: System Framework. Component C 1 trains a global model. Component C 2 generates a hashtable based on users data distribution. Users request t u from C 2 and C 1 returns a subsequence of gradients g (0:tu) to users.

Adaptation Mechanism Global update Local update θ (T ) = θ (0) η t u 1 θ u = θ (0) η 1 t=1 θ: the global model parameter. T g (t) (θ) t=1 θ u : the personal model parameter. u: the index for one user. T g (t) (θ) η 2 g (t) (θ u ) t=t u t u : the index of global gradients for user u. g (t) (θ): global gradients g (t) (θ u ): personal gradients

How do we decide t u? Group users into C groups based on their data sizes in descending order. Decide the position p u = i C, C is # groups. i is the group assignment for user u. the first group (i=1) of users has the most data. Set t u = T p u T: total iterations in the global SGD algorithm Users with the most data have the earliest stop for global gradients.

Adaptive Logistic Regression Objective: min L(w) = f (w) + λr(w) (1) w f (w) is the negative log-likelihood. r(w) is a regularization function. Adaptation Procedure: Global update Local update w (0) u t u 1 = w (0) η 1 w u (T ) = w u (0) t=1 T t u η 2 t=1 g (t) (w) (2) g (t) (w u ) (3)

Adaptive Gradient Boosting Decision Tree Objective: L (t) = = N d N d l(y d, F (t 1) d + ρh (t) ) + Ω(h (t) ) l(y d, F (0) d + ρh (0:t) ) + Ω(h (t) ) (4) Adaptation Procedure: F (0) u = F (0) + ρh (0:tu) (5) F (T ) u = F (0) u + ρh (tu:t ) u (6)

Adaptive Matrix Factorization Objective: min (r ui µ b u b i q T u p i ) q,p,b u,i + λ( q u 2 + p i 2 + b 2 u + b 2 i ) (7) Adaptation Procedure: q (0) u = q (0) b (0) u = b (0) u η 1 t u t=0 u η 1 t u k=0 g (t) (q u ), q (T u ) = q (0) u g (t) (T ) (0) (b u ), b u = b u T t u η 2 t=0 T t u η 2 t=0 g (t) ( q u ) (8) g (t) ( b u ) (9)

Properties Generality: The framework is generic to a variety of machine learning models that can be optimized by gradient-based approaches. Extensibility: The framework is extensible to be used for more sophisticated use cases. Scalability: In this framework, the training process of a personal model for one user is independent of all the other users.

Datasets Table: Dataset Statistics News Portal # users 54845 # features 351 Movie Ratings # click events 2,378,918 Netflix Movielens # view events 26,916,620 # users 478920 1721 avg # click events per user 43 # items 17766 3331 avg # events per user 534 sparsity 0.00942 0.039 For LogReg and GBDT: News Portal dataset For Matrix Factorization: Movie rating datasets (Netflix, Movielens)

Metrics MAP: Mean Average Precision. MRR: Mean Reciprocal Rank. AUC: Area Under (ROC) Curve. ndcg: Normalized Discounted Cumulative Gain. RMSE: Root Mean Square Error MAE: Mean Absolute Error

Comparison Methods Table: Objective functions for different methods. Model LogReg N Global d=1 f (w) + λ w 2 2 Nu Local j=1 f (w u) + λ w u 2 2 Nu MTL j f (w u ) + λ1 2 w u w 2 + λ2 2 w u 2 Model GBDT N Global d l(y d, F (0) d + ρh (0:t) ) + Ω(h (t) ) Nu Local j l(y j, F (0) j + ρh (0:t) ) + Ω(h (t) ) MTL - Model MF Global u,i (r ui µ b u b i q T u p i ) + λ( q u 2 + p i 2 + bu 2 + bi 2 ) Local (r ui µ b i Nu u b i q T u p i) + λ( q u 2 + p i 2 + b u 2 + b i 2) MTL global+λ 2 [(q u q) 2 + (p i p) 2 + (b u A u ) 2 + (b i A i ) 2 ] Global: models are trained on all users data Local: models are learned locally on per user s data MTL: users models are averaged by a global parameter.

Ranking Performance - LogReg AUC score on Test MRR score on Test 0.74 0.72 0.7 0.68 0.66 0.64 0.62 0.6 0.58 0.56 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 Global Local MTL Adaptive 0 100 200 300 400 500 epochs (a) AUC Global Local MTL Adaptive MAP score on Test 0 20 40 60 80 100120140160180200 epochs (c) MRR ndcg score on Test 0.3 0.28 0.26 0.24 0.22 0.2 0.18 0.16 0.6 0.58 0.56 0.54 0.52 0.5 0.48 0.46 Global Local MTL Adaptive 0 20 40 60 80 100120140160180200 epochs (b) MAP Global Local MTL Adaptive 0 20 40 60 80 100120140160180200 epochs (d) ndcg AUC, MAP, MRR and ndcg scores on the test dataset with varying training epochs. The proposed adaptive LogReg models achieve higher scores with fewer epochs. Global models perform the worst.

Ranking Performance - GBDT Table: Performance comparison based on MAP, MRR, AUC and ndcg for GBDT. Each value is calculated from the average of 10 runs with standard deviation. Global-GBDT #Trees MAP MRR AUC ndcg 20 0.2094(1e-3) 0.3617(2e-3) 0.6290(1e-3) 0.5329(6e-4) 50 0.2137(1e-3) 0.3726(1e-3) 0.6341(1e-3) 0.5372(6e-4) 100 0.2150(8e-3) 0.3769(1e-3) 0.6356(8e-4) 0.5392(6e-4) 200 0.2161(5e-4) 0.3848(1e-3) 0.6412(6e-4) 0.5415(5e-4) Local-GBDT #Trees MAP MRR AUC ndcg 20 0.2262(2e-3) 0.4510(5e-3) 0.6344(3e-3) 0.5604(2e-3) 50 0.2319(2e-3) 0.4446(4e-3) 0.6505(2e-3) 0.5651(2e-3) 100 0.2328(1e-3) 0.4465(5e-3) 0.6558(2e-3) 0.5651(2e-3) 200 0.2322(2e-3) 0.4431(2e-3) 0.6566(1e-3) 0.5649(1e-3) Adaptive-GBDT #Trees MAP MRR AUC ndcg 20+50 0.2343(2e-3) 0.4474(4e-3) 0.6555(2e-3) 0.5661(2e-3) 50+50 0.2325(2e-3) 0.4472(1e-4) 0.6561(8e-4) 0.5666(6e-4) 10+100 0.2329(2e-3) 0.4423(3e-3) 0.6587(1e-3) 0.5650(3e-3)

Ranking Performance - GBDT Test MAP 0.6 0.59 0.58 0.57 0.56 0.55 0.54 0.53 0.52 0.51 0.5 Group1(GBDT) Global Local Adaptive (a) Group 1 Test MAP 0.15 0.14 0.13 0.12 0.11 0.1 0.09 0.08 0.07 0.06 0.05 Group7(GBDT) Global Local Adaptive (b) Group 7 Figure: MAP Comparison of Group 1 (least) and Group 7 (most) for GBDT methods. MAP score for the groups of users with least data (Group 1) and most data (Group 7) for GBDT models. Adaptive-GBDT outperform both global and local GBDT models in terms of MAP for all groups of users.

Ranking Performance - LogReg vs GBDT AUC score 0.7 0.68 0.66 0.64 0.62 0.6 0.58 0.56 0.54 0.52 Global-LogReg Local-LogReg MTL-LogReg Adaptive-LogReg 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 % of training samples (a) LogReg AUC score 0.68 0.67 0.66 0.65 0.64 0.63 0.62 0.61 0.6 Global-GBDT Local-GBDT Adaptive-GBDT 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 % of training samples (b) GBDT AUC score for Global-GBDT, Local-GBDT, and Adaptive-GBDT with # of training samples from 20% to 100%. On average of AUC, Adaptive-GBDT performs better than other methods. With the increase of training samples, GBDT based methods tend to perform better while LogReg methods achieve relatively stable scores.

Results - MF Test RMSE Test RMSE 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 Global Local MTL Adaptive 0.84 0.82 0.8 0.78 0.76 0.74 0.72 0.7 Global Local MTL Adaptive (a) ML-RMSE (b) ML-MAE 1.05 1 0.95 0.9 0.85 0.8 Global Local MTL Adaptive (c) Netflix-RMSE (d) Netflix-MAE Test MAE Test MAE 0.85 0.8 0.75 0.7 0.65 0.6 Global Local MTL Adaptive RMSE and MAE on MovieLens(ML) and Netflix datasets. The quartile analysis of the group level RMSE and MAE for different MF models. Gold: Adaptive-MF

Summary Effectively and efficiently build personal models that lead to improved recommendation performance over either the global model or the local model. Adaptively learn personal models by exploiting the global gradients according to individuals characteristic. Our experiments demonstrate the usefulness of our framework across a wide scope, in terms of both model classes and application domains.

Thank you! Q&A

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