Big Data Infrastructure CS 489/698 Big Data Infrastructure (Winter 2016) Week 8: Data Mining (1/4) March 1, 2016 Jimmy Lin David R. Cheriton School of Computer Science University of Waterloo These slides are available at http://lintool.github.io/bigdata-2016w/ This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States See http://creativecommons.org/licenses/by-nc-sa/3.0/us/ for details Data Mining Analyzing Relational Data Analyzing Graphs Analyzing Text Structure of the Course “Core” framework features and algorithm design Supervised Machine Learning The generic problem of function induction given sample instances of input and output Classification: output draws from finite discrete labels Regression: output is a continuous value This is not meant to be an exhaustive treatment of machine Classification Source: Wikipedia (Sorting) Applications Spam detection Sentiment analysis Content (e.g., genre) classification Link prediction Document ranking Object recognition Fraud detection And much much more! Supervised Machine Learning training testing/deployment Model ? Machine Learning Feature Representations Objects are represented in terms of features: “Dense” features: sender IP, timestamp, # of recipients, length of message, etc. “Sparse” features: contains the term “viagra” in message, contains “URGENT” in subject, etc. Applications Spam detection Sentiment analysis Content (e.g., genre) classification Link prediction Document ranking Object recognition Fraud detection And much much more! Components of a ML Solution Data Features Model Optimization No data like more data! s/knowledge/data/g; (Banko and Brill, ACL 2001) (Brants et al., EMNLP 2007) Limits of Supervised Classification? Why is this a big data problem? Isn’t gathering labels a serious bottleneck? Solution: crowdsourcing Solution: bootstrapping, semi-supervised techniques Solution: user behavior logs Learning to rank Computational advertising Link recommendation The virtuous cycle of data-driven products Supervised Binary Classification Restrict output label to be binary Yes/No 1/0 Binary classifiers form a primitive building block for multiclass problems One vs. rest classifier ensembles Classifier cascades The Task label Given (sparse) feature vector Induce Such that loss is minimized loss function Typically, consider functions of a parametric form: model parameters Key insight: machine learning as an optimization problem! (closed form solutions generally not possible) Gradient Descent: Preliminaries Rewrite: Compute gradient: “Points” to fastest increasing “direction” So, at any point:* * Gradient Descent: Iterative Update Start at an arbitrary point, iteratively update: We have: Lots of details: Figuring out the step size Getting stuck in local minima Convergence rate … Gradient Descent Repeat until convergence: Intuition behind the math… New weights Old weights Update based on gradient Gradient Descent Source: Wikipedia (Hills) Lots More Details… Gradient descent is a “first order” optimization technique Often, slow convergence Conjugate techniques accelerate convergence Newton and quasi-Newton methods: Intuition: Taylor expansion Requires the Hessian (square matrix of second order partial derivatives): impractical to fully compute Logistic Regression Source: Wikipedia (Hammer) Logistic Regression: Preliminaries Given Let’s define: Interpretation: Relation to the Logistic Function After some algebra: The logistic function: 1 0.9 0.8 0.7 logistic(z) 0.6 0.5 0.4 0.3 0.2 0.1 0 -8 -7 -6 -5 -4 -3 -2 -1 0 z 1 2 3 4 5 6 7 8 Training an LR Classifier Maximize the conditional likelihood: Define the objective in terms of conditional log likelihood: We know Substituting: so: LR Classifier Update Rule Take the derivative: General form for update rule: Final update rule: Lots more details… Regularization Different loss functions … Want more details? Take a real machine-learning MapReduce Implementation mappers single reducer compute partial gradient mapper mapper mapper reducer iterate until convergence update model mapper Shortcomings Hadoop is bad at iterative algorithms High sensitivity to skew Iteration speed bounded by slowest task Potentially poor cluster utilization High job startup costs Awkward to retain state across iterations Must shuffle all data to a single reducer Some possible tradeoffs Number of iterations vs. complexity of computation per iteration E.g., L-BFGS: faster convergence, but more to compute Spark Implementation val points = spark.textFile(...).map(parsePoint).persist() var w = // random initial vector for (i <- 1 to ITERATIONS) { val gradient = points.map{ p => p.x * (1/(1+exp(-p.y*(w dot p.x)))-1)*p.y }.reduce((a,b) => a+b) w -= gradient } compute partial gradient mapper mapper mapper reducer update model mapper Questions? Source: Wikipedia (Japanese rock garden)