ECS289: Scalable Machine Learning

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1 ECS289: Scalable Machine Learning Cho-Jui Hsieh UC Davis Sept 22, 2016

2 Course Information Website: ECS289G_Fall2016/main.html My office: Mathematical Sciences Building (MSB) 4232 Office hours: 1pm-2pm Wednesday My This is a 4-unit course

3 Course Information Goals: Understand the challenges in large-scale machine learning. Understand state-of-the-art approaches for addressing these challenges. Identify interesting open questions. Course Structure: Pick some important machine learning problems (classification, regression, recommender system,... ) Introduce the model Discuss the computational challenges Discuss algorithms to overcome these challenges. Prerequisites: Basic knowledge in linear algebra (matrix multiplication, inversion,... ) Basic knowledge in programming for the final project.

4 Grading Policy Class participation (15%) Paper presentation (35%) Final project (50%)

5 Paper presentation Form a group of 2 students. Read a NIPS, ICML, or KDD paper published in the past 3 years. The presentation should include: The problem to be solved in the paper Related work Previous approaches before this paper Weak points of those approaches The proposed approach Why the proposed algorithm is better. Algorithms (and theoretical guarantee) Any drawback of the proposed method? Send me the slides 3 days before the class; I will give some feedbacks to improve the slides Presentations on November 10, 15, 17, 22.

6 Final Project Topics include: Develop new algorithms or improve existing algorithms Implement parallel machine learning algorithms and test on large datasets Apply machine learning to some application Compare existing algorithms Survey of algorithms for a specific ML problem... Schedule: Final project proposal TBD Final project presentation 11/29, 12/1 Final project paper due 12/9

7 Syllabus Mathematical tools (optimization) Linear empirical risk minimization: classification and regression Matrix Completion Extreme classification Tree-based algorithms (random forest, gradient boosted decision tree) Kernel methods Deep learning Ranking

8 What is Machine Learning? Train and test data are usually assumed to be iid samples from the same distribution

9 Training Linear SVM/regression: Linear hyperplane Kernel SVM/regression: Nonlinear hyperplane Decision tree, random forest Nearest Neighbor...

10 Prediction Learn a model that best explains the observed data as well as generalizes to unseen data Scalability Issues: Time & space complexity of the (Training) Learning Algorithm Size of the Model Time complexity of Prediction (for real-time applications)

11 A simple example K-nearest neighbor classification Model size: storing all the training samples 1 billion samples, each reqruires 1 KBytes space 1000G memory Prediction time: Find the nearest training sample 1 billion samples, each distance evaluation requires 1 micro second 1000 secs per prediction

12 Topics in this course Classification Regression Matrix Completion (Recommender systems) Ranking Other Nonlinear Models

13 Machine Learning Problems: Classification Image classification Hand-written digit recognition Spam filters

14 Binary Classification Input: training samples {x 1, x 2,..., x n } and labels {y 1, y 2,..., y n } x i : d-dimensional vector y i : +1 or -1 Output: A decision function f such that f (x i ) > 0 if y i = 1, f (x i ) < 0 if y i = 1

15 Feature generation for documents Bag of words features for documents: number of features = number of potential words 10,000

16 Feature generation for documents Bag of n-gram features (n = 2): 10,000 words 10, potential features

17 Classification > 1 million dimensional space, > 1 billion training points

18 Scalability challenges Large number of features Large number of samples Data cannot fit into memory Splice-site: 10 million samples, 11 million features, > 1T memory Current solutions: Intellectually swap between memory and disk Online algorithms Parallel algorithms on distributed systems Other idea?

19 Challenges: large number of categories Multi-label (or multi-class) classification with large number of labels Image classification > labels Recommending tags for articles: millions of labels (tags)

20 Challenges: large number of categories Consider a problem with 1 million labels. Traditional approach: reduce to binary problems. Training: 1 million binary classification problems. Need 694 days if each binary problem can be solved in 1 minute Model size: 1 million models. Need 1 TB if each model requires 1MB. Prediction one testing data: 1 million binary prediction Need 1000 secs if each binary prediction needs 10 3 secs.

21 Machine Learning Problems: Regression Line fitting Stock price prediction Polynomial curve fitting (Figures from Dhillon et al)

22 (Figure from Dhillon et al) Machine Learning Problems: Recommender Systems Netflix Problem

23 Machine Learning Problems: Recommender Systems Collaborative Filtering (Figure from Dhillon et al)

24 Machine Learning Problems: Recommender Systems Latent Factor Model (Figure from Dhillon et al)

25 Machine Learning Problems: Recommender Systems Latent Factor Model (Figure from Dhillon et al)

26 Machine Learning Problems: Recommender Systems Latent Factor Model (Figure from Dhillon et al)

27 Recommender Systems: challenges Size of the matrix: billions of users, billions of items, >100 billions of observations Memory to store ratings: > 1200 GBytes How to incorporate Side information? User/Item profiles Temporal information, click sequence Prediction time: Recommend top-k items to a user: Need to compute a row of a matrix: O(mk) time m > 1, 000, 000, 000, k > 500: need > 100 seconds Recommend items to all users: 100 billion seconds 3170 years

28 Different architectures Machine learning on different scales: Embedded systems: mobile devices, robotic systems,... Single computer: multiple cores, but limited (32G) memory with large (1T) disk Single computer with GPU(s) Multiple computers: data centers, computing clusters need communication between computers The best algorithm and model can be totally different

29 Machine learning on embedded devices Examples: mobile devices, robotic systems, auto cars,... Small memory (model compression to reduce model size) Real time response (fast prediction time) Need new (distributed) learning algorithms: Local (non-iid) samples on each device Slow and un-reliable network connection Need to consider power consumption Privacy issues

30 Machine learning on a single computer Disk access is expensive. Data can fit in memory: Can apply many existing optimization algorithms How to make the algorithms faster by exploiting the problem structure Data cannot fit in memory (full data stored in disk): Online updates: Processing one or few data points at a time Out-of-core method: Load a block of data from disk to memory at a time Distributed systems

31 Machine learning on distributed systems Multiple computers, each with local memory and disk Inter-computer communication is slow Programming tools & computing models Message Passing Interface (MPI) Hadoop (map-reduce) Spark (map-reduce) Parameter servers

32 Popular topics in ML research

33 Topics in NIPS Figure from

34 Optimization (Almost) all the machine learning problems can be modeled as an optimization problem arg min f (θ) θ f : an estimator of prediction error θ: model parameter Find the best model to minimize prediction error Traditional optimization: Usually assume the objective function is convex Want to get a very accurate solution

35 Optimization for Big-Data Problems Parallel Optimization Synchronized vs asynchronous Different architecture: multi-core shared memory, distributed systems, GPU Convergence rate analysis Stochastic/Online optimization Each iteration only uses one or a subset of training data Convergence rate: global bound & dependency on data size

36 Optimization for Complex Functions Non-convex optimization: Examples: neural network, matrix decomposition,... Algorithms can converge to (1) global minimizer (2) local minimizer (3) saddle points Discrete optimization: Greedy algorithms for submodular optimization Submodular convexity for discrete function Relaxation to continuous optimization problems

37 Deep Neural Network Network design for different problems Scalability (parallel stochastic gradient descent) Geometry of the problem (local minimum, global minimum, saddle points... )

38 Matrix/Tensor Decomposition Learning low-dimensional embeddings (usually unsupervised) Netflix problem (recommender systems), word2vec New formulations, scalable optimization algorithms, and theoretical guarantee

39 Other Topics Bandit Reinforcement learning Topic modeling Extreme classification (Multiclass/multilabel with millions of labels) Graph mining Bayesian Clustering...

40 Coming up Next class: linear regression Questions?

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