PPT-Dual Decomposition Inference for Graphical Models over Strings

Nanyun Violet Peng Ryan Cotterell Jason Eisner J ohns Hopkins University 1 Attention Dont care about phonology Listen anyway This is a general method for inferring strings. Alan Ritter. Problem: Non-IID Data. Most real-world data is not IID. (like coin flips). Multiple correlated variables. Examples:. Pixels in an image. Words in a document. Genes in a microarray. We saw one example of how to deal with this. Algorithms for Efficient. Large Margin . Structured Prediction. Ming-Wei Chang . and Scott Wen-tau Yih. Microsoft Research. 1. Motivation. . Many NLP tasks are structured. Parsing, Coreference, Chunking, SRL, Summarization, Machine translation, Entity Linking,…. Graphical Model Inference. View observed data and unobserved properties as . random variables. Graphical Models: compact graph-based encoding of probability distributions (high dimensional, with complex dependencies). Rahul Sharma and Alex Aiken (Stanford University). 1. Randomized Search. x. = . i. ;. y = j;. while . y!=0 . do. . x = x-1;. . y = y-1;. if( . i. ==j ). assert x==0. No!. Yes!.  . 2. Invariants. Dualmethodsprimal:minimizef(x)+g(Ax)dual:maximizeg(z)f(ATz)reasonswhydualproblemmaybeeasiertosolvebyrst-ordermethods:dualproblemisunconstrainedorhassimpleconstraints(forexample,z0)dualobjecti Chapter 14 . The pinhole camera. Structure. Pinhole camera model. Three geometric problems. Homogeneous coordinates. Solving the problems. Exterior orientation problem. Camera calibration. 3D reconstruction. (Markov Nets). (Slides from Sam . Roweis. ). Connection to MCMC:. . . MCMC requires sampling a node given its . markov. blanket. . Need to use P(. x|MB. (x)). . . For . Bayes. nets MB(x) contains more. Source: “Topic models”, David . Blei. , MLSS ‘09. Topic modeling - Motivation. Discover topics from a corpus . Model connections between topics . Model the evolution of topics over time . Image annotation. Thesis defense . 4/5/2012. Jaesik Choi. Thesis Committee: . Assoc. Prof. Eyal Amir (Chair, Director of research). Prof. Dan Roth. . Prof. Steven M. Lavalle. Prof. David Poole (University of British Columbia). Konstantinos Theodorakos. January 2015. Modern Processor Design. “Free lunch is over”. Lower Power consumption is favored on multi-core/processor architectures. CBD Parallelization . intention. Why Parallelize CBD models?. Local Primal-Dual Gaps. Dhruv Batra (TTIC). Joint work with: . Daniel . Tarlow. (U Toronto), Sebastian . Nowozin. (MSRC), . Pushmeet. . Kohli. (MSRC), Vladimir . Kolmogorov. (UCL). Overview. Discrete . Chapter . 2 . Introduction to probability. Please send errata to s.prince@cs.ucl.ac.uk. Random variables. A random variable . x. denotes a quantity that is uncertain. May be result of experiment (flipping a coin) or a real world measurements (measuring temperature). Chapter 19 . Temporal models. 2. Goal. To track object state from frame to frame in a video. Difficulties:. Clutter (data association). One image may not be enough to fully define state. Relationship between frames may be complicated. Part 1: Overview and Applications . Outline. Motivation for Probabilistic Graphical Models. Applications of Probabilistic Graphical Models. Graphical Model Representation. Probabilistic Modeling. 1. when trying to solve a real-world problem using mathematics, it is common to define a mathematical model of the world, e.g..