邏輯迴歸中的計算成本問題

Question

我正在從Courser的機器學習Andrew Ng課程開始。在本文中，我正在使用MatLab中的邏輯迴歸來計算成本函數，但我正在接收「使用sfminbx的錯誤（第27行）」 目標函數在初始點未定義，fminunc無法繼續。

我應該補充說下面的costFunction函數中的代價J是NaN，因爲log（sigmoid（X * theta））是一個-Inf向量。我相信這與例外有關。你能幫忙嗎？

我的成本函數如下所示：

function [J, grad] = costFunction(theta, X, y) 

    m = length(y); % number of training examples 
    J = 0; 
    grad = zeros(size(theta)); 

    h = sigmoid(theta * X); 
    J = - (1/m) * ((log(h)' * y) + (log(1 - h)' * (1 - y))); 
    grad = (1/m) * X' * (h - y); 

end 

我的代碼調用該函數如下所示：

data = load('ex2data1.txt'); 
X = data(:, [1, 2]); y = data(:, 3); 

[m, n] = size(X); 

% Add intercept term to x and X_test 
X = [ones(m, 1) X]; 

% Initialize fitting parameters 
initial_theta = zeros(n + 1, 1); 

% Compute and display initial cost and gradient 
[cost, grad] = costFunction(initial_theta, X, y); 

fprintf('Cost at initial theta (zeros): %f\n', cost); 
fprintf('Expected cost (approx): 0.693\n'); 
fprintf('Gradient at initial theta (zeros): \n'); 
fprintf(' %f \n', grad); 
fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n'); 

% Compute and display cost and gradient with non-zero theta 
test_theta = [-24; 0.2; 0.2]; 
[cost, grad] = costFunction(test_theta, X, y); 

fprintf('\nCost at test theta: %f\n', cost); 
fprintf('Expected cost (approx): 0.218\n'); 
fprintf('Gradient at test theta: \n'); 
fprintf(' %f \n', grad); 
fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n'); 
fprintf('\nProgram paused. Press enter to continue.\n'); 
pause; 


%% ============= Part 3: Optimizing using fminunc ============= 
% In this exercise, you will use a built-in function (fminunc) to find the 
% optimal parameters theta. 

% Set options for fminunc 
options = optimset('GradObj', 'on', 'MaxIter', 400, 'Algorithm', 'trust- 
region'); 

% Run fminunc to obtain the optimal theta 
% This function will return theta and the cost 

[theta, cost] = ... 
    fminunc(@(t)(costFunction(t, X, y)), initial_theta, options); 

end 

數據集如下所示：

34.62365962451697， 78.0246928153624,0 30.28671076822607,43.89499752400101,0 35.84740876993872,72.90219802708364,0 60.18259938620976,86.30855209546826,1 79.0327360507101,75.3443764369103,1 45.08327747668339,56.3163717815305,0 61.10666453684766,96.51142588489624,1 75.02474556738889,46.55401354116538,1 76.09878670226257,87.42056971926803,1 84.43281996120035,43.53339331072109,1 95.86155507093572,38.22527805795094,0 75.01365838958247 ，30.60326323428011,0 82.30705337399482,76.48196330235604,1 69.36458875970939,97.71869196188608,1 39.53833914367223,76.03681085115882,0 53.9710521485623,89.20735013750205,1 69.07014406283025,52.74046973016765,1 67。 94685547711617,46.67857410673128,0 70.66150955499435,92.92713789364831,1 76.97878372747498,47.57596364975532,1 67.37202754570876,42.83843832029179,0 89.67677575072079,65.79936592745237,1 50.534788289883,48.85581152764205,0 34.21206097786789,44.20952859866288,0 77.9240914545704,68.9​​723599933059,1 62.27101367004632， 69.95445795447587,1 80.1901807509566,44.82162893218353,1 93.114388797442,38.80067033713209,0 61.83020602312595,50.25610789244621,0 38.78580379679423,64.99568095539578,0 61.379289447425,72.80788731317097,1 85.40451939411645,57.05198397627 122,1 52.10797973193984,63.12762376881715,0 52.04540476831827,69.43286012045222,1 40.23689373545111,71.16774802184875,0 54.63510555424817,52.21388588061123,0 33.91550010906887,98.86943574220611,0 64.17698887494485,80.90806058670817,1 74.78925295941542,41.57341522824434,0 34.1836400264419,75.2377203360134， 0 83.90239366249155,56.30804621605327,1 51.54772026906181,46.85629026349976,0 94.44336776917852,65.56892160559052,1 82.36875375713919,40.61825515970618,0 51.04775177128865,45.82270145776001,0 62.22267576120188,52.06099194836679,0 77.19303492601364,70.45820000180959,1 97.77159928000232,86.7278223300282,1 62.07306379667647,96。76882412413983,1 91.56497449807442,88.69629254546599,1 79.94481794066932,74.16311935043758,1 99.2725269292572,60.99903099844988,1 90.54671411399852,43.39060180650027,1 34.52451385320009,60.39634245837173,0 50.2864961189907,49.80453881323059,0 49.58667721632031,59.80895099453265,0 97.64563396007767,68.86157272420604， 1 32.57720016809309,95.59854761387875,0 74.24869136721598,69.82457122657193,1 71.79646205863379,78.45356224515052,1 75.3956114656803,85.75993667331619,1 35.28611281526193,47.02051394723416,0 56.25381749711624,39.26147251058019,0 30.05882244669796,49.59297386723685,0 44.66826172480893,66.45008614558913,0 66.56089447242954,41.09209807936973,0 40.45755098375164,97.53518548909936,1 49.07256321908844,51.88321182073966,0 80.27957401466998,92.11606081344084,1 66.74671856944039,60.99139402740988,1 32.72283304060323,43.30717306430063,0 64.0393204150601 ，78.03168802018232,1 72.34649422579923,96.22759296761404,1 60.45788573918959,73.09499809758037,1 58.84095621726802,75.85844831279042,1 99.82785779692128,72.36925193383885,1 47.26426910848174,88.47586499559782,1 50.45815980285988,75.80985952982456,1 60.45555629271532,42.50840943572217,0 82.22666157785568,42.71987853716458,0 88.9138964166533,69.80378889835472,1 94.83450672430196,45.69430680250754,1 67.31925746917527,66.58935317747915,1 57.23870631569862,59.51428198012956,1 80.36675600171273,90.96014789746954,1 68.46852178591112 ，85.59430710452014,1 42.0754545384731,78.84478600148043,0 75.47770200533905,90.42453899753964,1 78.63542434898018,96.64742716885644,1 52.34800398794107,60.76950525602592,0 94.09433112516793,77.15910509073893,1 90.44855097096364 ，87.50879176484702,1 55.48216114069585,35.57070347228866,0 74.49269241843041,84.84513684930135,1 89.84580670720979,45.35828361091658,1 83.48916274498238,48.38028579728175,1 42.2617008099817,87.10385094025457,1 99.31500880510394,68.77540947206617,1 55.34001756003703,64.9319380069486,1 74.77589300092767,89.52981289513276 ，1

Answer 1

我看到的唯一問題是，你應該寫h = sigmoid(X * theta)，而不是h = sigmoid(theta * X)。我從代碼中獲取相同的賦值後，從代碼中得到了相同的答案。