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solves week 3 programming exercise
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‎week3/ex2/costFunction.m

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function [J, grad] = costFunction(theta, X, y)
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%COSTFUNCTION Compute cost and gradient for logistic regression
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% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
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% parameter for logistic regression and the gradient of the cost
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% w.r.t. to the parameters.
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function J = logisticRegressionCost(theta, X, y)
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estimatedResults = sigmoid(X * theta);
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trainingSamples = length(y);
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J = -(1 / trainingSamples) * (
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y' * log(estimatedResults)
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+ (1 - y)' * log(1 - estimatedResults)
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);
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endfunction
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function gradient = gradientVector(theta, X, y)
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trainingExamples = length(y);
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gradient = (1 / trainingExamples) * (X' * (sigmoid(X * theta) - y));
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endfunction
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J = logisticRegressionCost(theta, X, y);
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grad = gradientVector(theta, X, y);
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end

‎week3/ex2/costFunctionReg.m

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function [J, grad] = costFunctionReg(theta, X, y, lambda)
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%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
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% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
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% theta as the parameter for regularized logistic regression and the
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% gradient of the cost w.r.t. to the parameters.
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function J = logisticRegressionRegularizedCost(theta, X, y)
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estimatedResults = sigmoid(X * theta);
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trainingExamples = length(y);
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J = (- 1 / trainingExamples) * (
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y' * log(estimatedResults)
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+ (1 - y)' * log(1 - estimatedResults)
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) + (lambda / (2 * trainingExamples)) * (
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sum(theta .^ 2) - theta(1) ^ 2
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);
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endfunction
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function gradient = gradientVector(theta, X, y)
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trainingExamples = length(y);
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gradient = (1 / trainingExamples) * (X' * (sigmoid(X * theta) - y));
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endfunction
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function gradient = regularizedGradientVector(theta, X, y)
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trainingExamples = length(y);
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gradient = gradientVector(theta, X, y);
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modifiedHypothesis = (lambda / trainingExamples) * theta;
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modifiedHypothesis(1) = 0;
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gradient += modifiedHypothesis;
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endfunction
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J = logisticRegressionRegularizedCost(theta, X, y);
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grad = regularizedGradientVector(theta, X, y);
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end

‎week3/ex2/ex2.mlx

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‎week3/ex2/ex2_companion.mlx

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‎week3/ex2/ex2data1.txt

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‎week3/ex2/ex2data2.txt

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‎week3/ex2/lib/jsonlab/AUTHORS.txt

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The author of "jsonlab" toolbox is Qianqian Fang. Qianqian
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is currently an Assistant Professor at Massachusetts General Hospital,
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Harvard Medical School.
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Address: Martinos Center for Biomedical Imaging,
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Massachusetts General Hospital,
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Harvard Medical School
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Bldg 149, 13th St, Charlestown, MA 02129, USA
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URL: http://nmr.mgh.harvard.edu/~fangq/
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Email: <fangq at nmr.mgh.harvard.edu> or <fangqq at gmail.com>
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The script loadjson.m was built upon previous works by
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- Nedialko Krouchev: http://www.mathworks.com/matlabcentral/fileexchange/25713
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date: 2009/11/02
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- François Glineur: http://www.mathworks.com/matlabcentral/fileexchange/23393
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date: 2009/03/22
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- Joel Feenstra: http://www.mathworks.com/matlabcentral/fileexchange/20565
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date: 2008/07/03
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This toolbox contains patches submitted by the following contributors:
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- Blake Johnson <bjohnso at bbn.com>
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part of revision 341
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- Niclas Borlin <Niclas.Borlin at cs.umu.se>
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various fixes in revision 394, including
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- loadjson crashes for all-zero sparse matrix.
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- loadjson crashes for empty sparse matrix.
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- Non-zero size of 0-by-N and N-by-0 empty matrices is lost after savejson/loadjson.
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- loadjson crashes for sparse real column vector.
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- loadjson crashes for sparse complex column vector.
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- Data is corrupted by savejson for sparse real row vector.
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- savejson crashes for sparse complex row vector.
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- Yul Kang <yul.kang.on at gmail.com>
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patches for svn revision 415.
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- savejson saves an empty cell array as [] instead of null
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- loadjson differentiates an empty struct from an empty array

‎week3/ex2/lib/jsonlab/ChangeLog.txt

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============================================================================
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JSONlab - a toolbox to encode/decode JSON/UBJSON files in MATLAB/Octave
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----------------------------------------------------------------------------
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JSONlab ChangeLog (key features marked by *):
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== JSONlab 1.0 (codename: Optimus - Final), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2015/01/02 polish help info for all major functions, update examples, finalize 1.0
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2014/12/19 fix a bug to strictly respect NoRowBracket in savejson
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== JSONlab 1.0.0-RC2 (codename: Optimus - RC2), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2014/11/22 show progress bar in loadjson ('ShowProgress')
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2014/11/17 add Compact option in savejson to output compact JSON format ('Compact')
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2014/11/17 add FastArrayParser in loadjson to specify fast parser applicable levels
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2014/09/18 start official github mirror: https://github.com/fangq/jsonlab
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== JSONlab 1.0.0-RC1 (codename: Optimus - RC1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2014/09/17 fix several compatibility issues when running on octave versions 3.2-3.8
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2014/09/17 support 2D cell and struct arrays in both savejson and saveubjson
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2014/08/04 escape special characters in a JSON string
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2014/02/16 fix a bug when saving ubjson files
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== JSONlab 0.9.9 (codename: Optimus - beta), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2014/01/22 use binary read and write in saveubjson and loadubjson
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== JSONlab 0.9.8-1 (codename: Optimus - alpha update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2013/10/07 better round-trip conservation for empty arrays and structs (patch submitted by Yul Kang)
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== JSONlab 0.9.8 (codename: Optimus - alpha), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2013/08/23 *universal Binary JSON (UBJSON) support, including both saveubjson and loadubjson
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== JSONlab 0.9.1 (codename: Rodimus, update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2012/12/18 *handling of various empty and sparse matrices (fixes submitted by Niclas Borlin)
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== JSONlab 0.9.0 (codename: Rodimus), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2012/06/17 *new format for an invalid leading char, unpacking hex code in savejson
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2012/06/01 support JSONP in savejson
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2012/05/25 fix the empty cell bug (reported by Cyril Davin)
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2012/04/05 savejson can save to a file (suggested by Patrick Rapin)
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== JSONlab 0.8.1 (codename: Sentiel, Update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2012/02/28 loadjson quotation mark escape bug, see http://bit.ly/yyk1nS
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2012/01/25 patch to handle root-less objects, contributed by Blake Johnson
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== JSONlab 0.8.0 (codename: Sentiel), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2012/01/13 *speed up loadjson by 20 fold when parsing large data arrays in matlab
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2012/01/11 remove row bracket if an array has 1 element, suggested by Mykel Kochenderfer
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2011/12/22 *accept sequence of 'param',value input in savejson and loadjson
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2011/11/18 fix struct array bug reported by Mykel Kochenderfer
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== JSONlab 0.5.1 (codename: Nexus Update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2011/10/21 fix a bug in loadjson, previous code does not use any of the acceleration
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2011/10/20 loadjson supports JSON collections - concatenated JSON objects
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== JSONlab 0.5.0 (codename: Nexus), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
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2011/10/16 package and release jsonlab 0.5.0
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2011/10/15 *add json demo and regression test, support cpx numbers, fix double quote bug
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2011/10/11 *speed up readjson dramatically, interpret _Array* tags, show data in root level
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2011/10/10 create jsonlab project, start jsonlab website, add online documentation
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2011/10/07 *speed up savejson by 25x using sprintf instead of mat2str, add options support
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2011/10/06 *savejson works for structs, cells and arrays
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2011/09/09 derive loadjson from JSON parser from MATLAB Central, draft savejson.m

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