PPT-Dual Coordinate Descent

Algorithms for Efficient Large Margin Structured Prediction MingWei Chang and Scott Wentau Yih Microsoft Research 1 Motivation Many NLP tasks are structured Parsing Coreference Chunking SRL Summarization Machine translation Entity Linking. ntuedutw KaiWei Chang b92084csientuedutw ChihJen Lin cjlincsientuedutw Department of Computer Science National Taiwan University Taipei 106 Taiwan S Sathiya Keerthi selvarakyahooinccom Yahoo Research Santa Clara USA S Sundararajan ssrajanyahooinccom com Abstract We present and study a distributed optimization algorithm by employing a stochas tic dual coordinate ascent method Stochastic dual coordinate ascent methods en joy strong theoretical guarantees and often have better performances than sto Nesterov January 2010 Abstract In this paper we propose new methods for solving hugescale optimization problems For problems of this size even the simplest fulldimensional vector operations are very expensive Hence we propose to apply an optimizatio Bradley jkbradlecscmuedu Aapo Kyrola akyrolacscmuedu Danny Bickson bicksoncscmuedu Carlos Guestrin guestrincscmuedu Carnegie Mellon University 5000 Forbes Ave Pittsburgh PA 15213 USA Abstract We propose Shotgun a parallel coordi nate descent algorit How Yep Take derivative set equal to zero and try to solve for 1 2 2 3 df dx 1 22 2 2 4 2 df dx 0 2 4 2 2 12 32 Closed8722form solution 3 26 brPage 4br CS545 Gradient Descent Chuck Anderson Gradient Descent Parabola Examples in R Finding Mi This can be generalized to any dimension brPage 9br Example of 2D gradient pic of the MATLAB demo Illustration of the gradient in 2D Example of 2D gradient pic of the MATLAB demo Gradient descent works in 2D brPage 10br 10 Generalization to multiple Gradient descent is an iterative method that is given an initial point and follows the negative of the gradient in order to move the point toward a critical point which is hopefully the desired local minimum Again we are concerned with only local op Our method is based on alternating direction method of multi pliers ADMM to deal with complex regulariza tion functions such as structured regularizations Although the original ADMM is a batch method the proposed method offers a stochastic update ru Daniel Tarlow. 1. , Dhruv . Batra. 2. . Pushmeet Kohli. 3. , Vladimir Kolmogorov. 4. 1: University of Toronto 3: Microsoft Research Cambridge. 2: TTI Chicago 4: University College London. . International Conference on Machine Learning (ICML), . Pritam. . Sukumar. & Daphne Tsatsoulis. CS 546: Machine Learning for Natural Language Processing. 1. What is Optimization?. Find the minimum or maximum of an objective function given a set of constraints:. Weshowthatlinearconvergencecanbeattainedifan“es-sentialstrongconvexity”property(3)holds,whilesublin-earconvergenceata“1=K”ratecanbeprovedforgeneralconvexfunctions.Ouranalysisalsode University of Edinburgh. . Optimization & Big Data Workshop . Edinburgh, 6. th. . to 8. th. . May, 2015. Randomized dual coordinate ascent with arbitrary sampling. Joint work with Peter Richtárik (Edinburgh) & Tong Zhang (Rutgers & Baidu). 3 weeks. Unit Planning Team:. Stacy Dustman (ET), Pam Keith (ET), Kendra . Bookout. (ES),. Paige Brown (NS), Traci Rhoades (RG). 5. th. Grade Unit 5. Essential Questions. How can I use the coordinate plane to solve real-world and mathematical problems?. . RECTANGULAR or Cartesian. . CYLINDRICAL. SPHERICAL. Choice is based on symmetry of problem. Examples:. Sheets - RECTANGULAR. Wires/Cables - CYLINDRICAL. Spheres - SPHERICAL. To understand the Electromagnetics, we must know basic vector algebra and coordinate systems. So let us start the coordinate systems..