The examples here will use the electronics category from the sentiment analysis dataset of Blitzer et al., which we include with precomputed word level ngram features and binary as well as regression labels (1-5 stars). The data is arranged in LIBSVM format, which is compatible with all the learning algorithms used in these examples. The results shown here should be easily reproducible and serve as a good first exercise.

Note that these exercises have been constructed the mechanics behind using the automatic kernel selection tools. The kernels and parameters and used here are NOT necessarily the best for the one dataset used here.

**Correlation Kernel Example:** The correlation based kernel weights each input feature by a quantity proportional to its correlation with the training labels. The following command will generate weighted features:

$ klweightfeatures --weight_type=corr --features --sparse --num_train=1000 elec.2-gram 1 \ > elec.2-gram.corr INFO: Loaded 2000 datapoints. INFO: Selecting 1000 training examples... INFO: Using 57466 features.

The `--features`

flag forces the output of explicit feature vectors, rather than the kernel matrix, and the `--sparse`

flag forces the use of sparse data-structure, which are both desirable in this case since the ngram-features are sparse. The `--num_train`

flag indicates that the kernel selection algorithm should use only the first 1000 data-points for training, and thus allows us to use the remaining points as a holdout set for evaluating performance. The `--alg_reg`

flag lets the kernel selection algorithm know the regularization value of the Finally, the `--weight_type`

flag selects which type of kernel selection algorithm is used. The first argument indicates the input dataset and the second argument regularizes the kernel which, in the case of the correlation kernel, restricts the kernel trace to equal 1.

The weighted features can then be used to train and test an svm model via libsvm or liblinear:

Separate train and test:

$ head -n1000 elec.2-gram.corr > elec.2-gram.corr.train $ tail -n+1001 elec.2-gram.corr > elec.2-gram.corr.test

Train:

$ svm-train -s 0 -t 0 -c 4096 elec.2-gram.corr.train model

Test:

$ svm-predict elec.2-gram.corr.test model pred Accuracy = 80% (800/1000) (classification)

**L2 Regularized Linear Combination:** Here we optimally weight the input features in order to maximize the kernel ridge regression (KRR) objective, subject to the L2 regularization constraint: `||mu - mu0|| < ker_reg||`

, where `mu`

is the vector of squared weights and `mu0`

and `ker_reg`

are user specified arguments.

$ klweightfeatures --weight_type=lin2 --features --sparse --num_train=1000 \ --alg_reg=4 --offset=1 --tol=1e-4 elec.1-gram.reg 1 > elec.1-gram.lin2 INFO: Loaded 2000 datapoints. INFO: Selecting 1000 training examples... ... INFO: iter: 18 obj: 333.919 gap: 0.000123185 INFO: iter: 19 obj: 333.922 gap: 6.15492e-05 INFO: Using 12876 features.

The algorithm will iterate until the tolerance, which is set by the `--tol`

flag, or maximum number of iterations is met. In this case `mu0`

is equal to zero (the default) and `ker_reg`

is specified by the second argument to the function. Since this selection is algorithm specific, we should also specify the regularization parameter we will use in the second step via the `--alg_reg`

flag. The `--offset`

flag adds the constant indicated offset to the dataset input if one is not already included. Finally, the `=--tol`

flag indicates at what precision the iterative method should stop.

(NOTE: the time taken for each iteration will be improved soon. There still remains some optimization to be made to the sparse-matrix data-structure).

We then train and test using kernel ridge regression (KRR), with input and output arguments that have been made to closely resemble libsvm. One main difference is that the user must specify to use sparse data-structures. If the data is dense, it is better to use highly efficient dense blas routines instead by omitting the `--sparse`

flag. To see a full list of command line arguments, run krr-train without any parameters.

Separate train and test:

$ head -n1000 elec.1-gram.lin2 > elec.1-gram.lin2.train $ tail -n+1001 elec.1-gram.lin2 > elec.1-gram.lin2.test

Train:

$ krr-train --sparse elec.1-gram.lin2.train 4 model

Test:

$ krr-predict --sparse elec.1-gram.lin2.test model pred INFO: Using primal solution to make predictions... INFO: RMSE: 1.34898

In this example we find the best linear combination of 5 character-level ngram kernels (1-gram, 2-gram, ..., 5-gram) with respect to the SVM objective.

$ klcombinefeatures --weight_type=lin1 --sparse --num_train=1000 \ --alg_reg=0.1 elec.list elec.comb ... INFO: iter: 9 constraint: -5.65079 theta: -5.65044 gap: 6.16132e-05 16: objval = -5.650437235e+00 infeas = 1.000000000e+00 (0) 17: objval = -5.650600323e+00 infeas = 0.000000000e+00 (0) OPTIMAL SOLUTION FOUND .* optimization finished, #iter = 12 Objective value = -5.650654 nSV = 792 INFO: iter: 10 constraint: -5.65065 theta: -5.6506 gap: 9.48414e-06

Here the argument `elec.list`

is a file with the paths to each basekernel written on a separate line, and the combined kernel is written to the file `elec.comb`

. The flag `--alg_reg`

indicates the regularization parameter that will be used with SVM.

This will produce a kernel with many features, but which are sparse, thus liblinear is a good choice for training a model:

Separate train and test:

$ head -n1000 elec.comb > elec.comb.train $ tail -n+1001 elec.comb > elec.comb.test

Train:

$ train -s 3 -c 0.1 -B -1 elec.comb.train model

Test:

$ predict elec.comb.test model pred Accuracy = 83.5% (835/1000)

klcombinekernels ... $ klcombinekernels --weight_type=lin2 --num_train=1000 \ --alg_reg=0.0001 --tol=1e-3 elec.kernel.list elec.kernel.comb ... INFO: iter: 13 obj: 2980.56 gap: 0.00217053 INFO: iter: 14 obj: 2980.47 gap: 0.00108526 INFO: iter: 15 obj: 2980.42 gap: 0.00054263

Here `elec.kernel.list`

with the path to each base kernel written on a line.

Separate train and test:

$ head -n1000 elec.kernel.comb > elec.kernel.comb.train $ tail -n+1001 elec.kernel.comb > elec.kernel.comb.test

Train:

$ krr-train --kernel elec.kernel.comb.train 0.0001 model

Test:

$ krr-predict --kernel elec.kernel.comb.test model pred INFO: Using dual solution to make predictions... INFO: Making predicitons... INFO: RMSE: 1.36997

-- AfshinRostamizadeh - 24 Aug 2009

Topic revision: r8 - 2009-08-27 - AfshinRostamizadeh

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