I have 300 data samples with around 4000 dimension feature each. Each input has a 5 dim. output which is in the range of -2 to 2. I am trying to fit a lasso model to it. I went through a few posts which talk about cross validation strategies like this one: Leave one out cross validation algorithm in matlab
But I saw that lasso does not support leaveout in Matlab! http://www.mathworks.com/help/stats/lasso.html
How can I train a model using leave one out cross validation and fit a model using lasso on my dataset? I am trying to do this in matlab. I would like to get a set of weights which I will be able to use for future predictions on other data.
I tried using glmnet: http://www.stanford.edu/~hastie/glmnet_matlab/intro.html but I couldn't compile it on my machine due to lack of proper mex compiler.
Any solutions to my problem? Thanks :)
EDIT
I am also trying to use lasso function in-built with MATLAB. It has an option to perform cross validation. It outputs B and Fit Statistics, where B is Fitted coefficients, a p-by-L matrix, where p is the number of predictors (columns) in X, and L is the number of Lambda values.
Now given a new test sample, how can I calculate the output using this model?
You can use a leave-one-out approach regardless of your training method. As explained here, you can use crossvalind to split the data into training and test sets.
[Train, Test] = crossvalind('LeaveMOut', N, M)
Related
I am trying to build a multiple linear regression in MATLAB with 20 predictors, which are categorical with 4 levels each. I am using the function "regress", like this (these are not the actual variables):
X = [ones(size(x1)) x1 x2 x3...x20];
[b,bint,r,rint] = regress(Y, X);
Before this, I transformed the vectors x1,x2...x20 in categorical variables with dummyvar.
I get this error and a lot of 0's in the b coefficients and this error:
Warning: X is rank deficient to within machine precision.
In the dummyvar documentation it is mentioned:
To use the dummy variables in a regression model, you must either delete a column (to create a reference group) or fit a regression model with no intercept term.
I tried not using the intercept ones(size(x1)) and I get the same error.
I would appreciate any input on how to solve this.
Try to simplify the problem down to the minimum working example, and then post that here, so we can reproduce it and help you through. See https://en.wikipedia.org/wiki/Rank_(linear_algebra)
for examples of rank deficiency.
I would like to draw learning curves for a given SVM classifier. Thus, in order to do this, I would like to compute the training, cross-validation and test error, and then plot them while varying some parameter (e.g., number of instances m).
How to compute training, cross-validation and test error on libsvm when used with MATLAB?
I have seen other answers (see example) that suggest solutions for other languages.
Isn't there a compact way of doing it?
Given a set of instances described by:
a set of features featureVector;
their corresponding labels (e.g., either 0 or 1),
if a model was previously inferred via libsvm, the MSE error can be computed as follows:
[predictedLabels, accuracy, ~] = svmpredict(labels, featureVectors, model,'-q');
MSE = accuracy(2);
Notice that predictedLabels contains the labels that were predicted by the classifier for the given instances.
We recently studied the Naïve Bayesian Classifier in our Machine Learning class and now I'm trying to implement it on the Fisher Iris dataset as a self-exercise. The concept is easy and straightforward, with some trickiness involved for continuous attributes. I read up several literature resources which recommended using a Gaussian approximation to compute probability of test data values, so I'm going with it in my code.
Now I'm trying to run it initially for 50% training and 50% test data samples, but something is missing. The current code is always predicting class 1 (I used integers to represent the classes) for all test samples, which is obviously wrong.
My guess is that the problem may be due to normalization being omitted by the code? Though I think adding normalization would still yield proportionate results, and so far my attempts to normalize have produced the same classification results.
Can someone please suggest if there is anything obvious missing here? Or if I'm not approaching this right? Since most of the code is 'mechanics', I have made prominent (****************) the 2 lines that are responsible for the calculations. Any help is appreciated, thanks!
nsamples=75; % 50% samples
% acquire training set and test set
[trainingSample,idx] = datasample(data,nsamples,'Replace',false);
testData = data(setdiff(1:150,idx),:);
% define Gaussian function
%***********************************************************%
Phi=#(mu,sig2,x) (1/sqrt(2*pi*sig2))*exp(-((x-mu)^2)/2*sig2);
%***********************************************************%
for c=1:3 % for 3 classes in training set
clear y x mu sig2;
index=1;
for i=1 : length(trainingSample)
if trainingSample(i,5)==c
y(index,:)=trainingSample(i,:); % filter current class samples
index=index+1; % for conditional probabilities
end
end
for j=1:size(testData,1) % iterate over test samples
clear pf p;
for i=1:4 % iterate over columns
x=testData(j,i); % representing attributes
mu=mean(y(:,i));
sig2=var(y(:,i));
pf(i) = Phi(mu,sig2,x); % calc conditional probability
end
% calc class likelihood; prior * posterior
%*****************************************************%
pc(j,c) = size(y,1)/nsamples * pf(1)*pf(2)*pf(3)*pf(4);
%*****************************************************%
end
end
% find the predicted class for each test sample
% by taking the max probability calculated
for i=1:size(pc,1)
[~,q]=max(pc(i,:));
predicted(i)=q;
actual(i)=testData(i,5);
end
Normalization shouldn't be necessary since the features are only compared to each other.
p(class|thing) = p(class)p(thing|class) =
= p(class)p(feature_1|class)p(feature_2|class)...p(feature_N|class)
So when fitting the parameters for the distribution feature_i|class it will just rescale the parameters (for the new "scale") in this case (mu, sigma2), but the probabilities will remain the same.
It's hard to read the matlab code due to alot of indexing and splitting of training/testing etc. Which is a possible problem source.
You should try something with a lot less non-necessary stuff around it (I would recommend python with scikit-learn for example, alot of helpers for splitting data and such http://scikit-learn.org/).
It's really important that you separate the training and test data, and only train the model with training data and test the trained model with the test data. (Is this done?)
Next step is to check the parameters which is easiest done with either printing them out (sanity check) or..
for each feature render the gaussian bells fitted next to a histogram of the data to see that they match (remember that each histogram bar must be of height number_of_samples_within_range/total_number_of_samples.
Visualising the data and the model is really important to know what is happening.
I am new to Matlab. Is there any sample code for classifying some data (with 41 features) with a SVM and then visualize the result? I want to classify a data set (which has five classes) using the SVM method.
I read the "A Practical Guide to Support Vector Classication" article and I saw some examples. My dataset is kdd99. I wrote the following code:
%% Load Data
[data,colNames] = xlsread('TarainingDataset.xls');
groups = ismember(colNames(:,42),'normal.');
TrainInputs = data;
TrainTargets = groups;
%% Design SVM
C = 100;
svmstruct = svmtrain(TrainInputs,TrainTargets,...
'boxconstraint',C,...
'kernel_function','rbf',...
'rbf_sigma',0.5,...
'showplot','false');
%% Test SVM
[dataTset,colNamesTest] = xlsread('TestDataset.xls');
TestInputs = dataTset;
groups = ismember(colNamesTest(:,42),'normal.');
TestOutputs = svmclassify(svmstruct,TestInputs,'showplot','false');
but I don't know that how to get accuracy or mse of my classification, and I use showplot in my svmclassify but when is true, I get this warning:
The display option can only plot 2D training data
Could anyone please help me?
I recommend you to use another SVM toolbox,libsvm. The link is as follow:
http://www.csie.ntu.edu.tw/~cjlin/libsvm/
After adding it to the path of matlab, you can train and use you model like this:
model=svmtrain(train_label,train_feature,'-c 1 -g 0.07 -h 0');
% the parameters can be modified
[label, accuracy, probablity]=svmpredict(test_label,test_feaure,model);
train_label must be a vector,if there are more than two kinds of input(0/1),it will be an nSVM automatically.
train_feature is n*L matrix for n samples. You'd better preprocess the feature before using it. In the test part, they should be preprocess in the same way.
The accuracy you want will be showed when test is finished, but it's only for the whole dataset.
If you need the accuracy for positive and negative samples separately, you still should calculate by yourself using the label predicted.
Hope this will help you!
Your feature space has 41 dimensions, plotting more that 3 dimensions is impossible.
In order to better understand your data and the way SVM works is to begin with a linear SVM. This tybe of SVM is interpretable, which means that each of your 41 features has a weight (or 'importance') associated with it after training. You can then use plot3() with your data on 3 of the 'best' features from the linear svm. Note how well your data is separated with those features and choose a basis function and other parameters accordingly.
I run
Y_testing_obtained = classify(X_testing, X_training, Y_training);
and the error I get is
Error using ==> classify at 246
The pooled covariance matrix of TRAINING must be positive definite.
X_training is 1550 x 5 matrix. Can you please tell me what this error means, i.e. why is it appearing, and how to work around it?
Thanks
Explanation: When you run the function classify without specifying the type of discriminant function (as you did), Matlab uses Linear Discriminant Analysis (LDA). Without going into too much details on LDA, the algorithms needs to calculate the covariance matrix of X_testing in order to solve an optimisation problem, and this matrix has to be positive definite (see Wikipedia: Positive-definite matrix). The underlying assumption is that your data is represented by a multivariate probability distribution, which always has a positive definite covariance matrix unless one or more variables are exact linear combinations of the others.
To solve your problem: It is possible that one of your variables is a linear combination of the others. You can try selecting a sensible subset of your variables, or perform Principal Component Analysis (PCA) on the training data and then classify using the first few principal components. Or, you could specify the type of discriminant function and choose one of the two naive Bayes classifiers, for example:
Y_testing_obtained = classify(X_testing, X_training, Y_training, 'diaglinear');
As a side note, you also need to have more observations (rows) than variables (columns), but in your case this is not the problem as you seem to have 1550 observations and 5 variables.
Finally, you can also have a look at the answers posted to a similar question on the Matlab forum.
Try regularizing the data using cvshrink function in Matlab