Read "Streaming Systems" 1&2, Streaming 101 Read "F1, a distributed SQL database that scales" Read "Zanzibar, Google’s Consistent, Global Authorization System" Read "Spanner, Google's Globally-Distributed Database" Read "Designing Data-intensive applications" 12, The Future of Data Systems IOS development with Swift Read "Designing Data-intensive applications" 10&11, Batch and Stream Processing Read "Designing Data-intensive applications" 9, Consistency and Consensus Read "Designing Data-intensive applications" 8, Distributed System Troubles Read "Designing Data-intensive applications" 7, Transactions Read "Designing Data-intensive applications" 6, Partitioning Read "Designing Data-intensive applications" 5, Replication Read "Designing Data-intensive applications" 3&4, Storage, Retrieval, Encoding Read "Designing Data-intensive applications" 1&2, Foundation of Data Systems Three cases of binary search TAMU Operating System 2 Memory Management TAMU Operating System 1 Introduction Overview in cloud computing 2 TAMU Operating System 7 Virtualization TAMU Operating System 6 File System TAMU Operating System 5 I/O and Disk Management TAMU Operating System 4 Synchronization TAMU Operating System 3 Concurrency and Threading TAMU Computer Networks 5 Data Link Layer TAMU Computer Networks 4 Network Layer TAMU Computer Networks 3 Transport Layer TAMU Computer Networks 2 Application Layer TAMU Computer Networks 1 Introduction Overview in distributed systems and cloud computing 1 A well-optimized Union-Find implementation, in Java A heap implementation supporting deletion TAMU Advanced Algorithms 3, Maximum Bandwidth Path (Dijkstra, MST, Linear) TAMU Advanced Algorithms 2, B+ tree and Segment Intersection TAMU Advanced Algorithms 1, BST, 2-3 Tree and Heap TAMU AI, Searching problems Factorization Machine and Field-aware Factorization Machine for CTR prediction TAMU Neural Network 10 Information-Theoretic Models TAMU Neural Network 9 Principal Component Analysis TAMU Neural Network 8 Neurodynamics TAMU Neural Network 7 Self-Organizing Maps TAMU Neural Network 6 Deep Learning Overview TAMU Neural Network 5 Radial-Basis Function Networks TAMU Neural Network 4 Multi-Layer Perceptrons TAMU Neural Network 3 Single-Layer Perceptrons Princeton Algorithms P1W6 Hash Tables & Symbol Table Applications Stanford ML 11 Application Example Photo OCR Stanford ML 10 Large Scale Machine Learning Stanford ML 9 Anomaly Detection and Recommender Systems Stanford ML 8 Clustering & Principal Component Analysis Princeton Algorithms P1W5 Balanced Search Trees TAMU Neural Network 2 Learning Processes TAMU Neural Network 1 Introduction Stanford ML 7 Support Vector Machine Stanford ML 6 Evaluate Algorithms Princeton Algorithms P1W4 Priority Queues and Symbol Tables Stanford ML 5 Neural Networks Learning Princeton Algorithms P1W3 Mergesort and Quicksort Stanford ML 4 Neural Networks Basics Princeton Algorithms P1W2 Stack and Queue, Basic Sorts Stanford ML 3 Classification Problems Stanford ML 2 Multivariate Regression and Normal Equation Princeton Algorithms P1W1 Union and Find Stanford ML 1 Introduction and Parameter Learning

Stanford ML 10 Large Scale Machine Learning

2017-02-07

Gradient Descent with Large Datasets

Learning with Large Datasets

Plot and vs training set size to estimate the type of problem (high bias or variance)

Stochastic Gradient Descent

Use 1 example in each iteration

  1. Randomly shuffle dataset
  2. Repeat {
    for {
    \[\theta_j := \theta_j - \alpha (h_{\theta}(x^{(i)})-y^{(i)})x_j^{(i)}\]
    (for )
    }
    }

Mini-Batch Gradient Descent

Use b examples in each iteration
b: mini-batch size (2-100)
Can be vectorized

Say

  1. Randomly shuffle dataset
  2. Repeat {
    for {
    \[\theta_j := \theta_j - \alpha \frac{1}{10}\sum_{k=i}^{i+9}(h_{\theta}(x^{(k)})-y^{(k)})x_j^{(k)}\]
    (for )
    }
    }

Stochastic Gradient Descent Convergence

During learning, compute before updating using .
Every 1000 iterations (say), plot averaged over the last 1000 examples processed by algorithm.
Can slowly decrease over time to improve convergence like:

Advanced Topics

Online Learning

Adapt to changing user perference

Algorithm:

Repeat forever {
Get corresponding to user
Update using :
\[\theta_j := \theta_j - \alpha (h_{\theta}(x)-y)x_j \mbox{ for } (j=0,1,…,n)\]
Discard this example
}

Map Reduce and Data Parallelism

For each iteration, divide the training set into several portions; use different machines to calculate summation of functions for all portions, then sum the results to update the parameters on the central server.


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