## Propensity SVM
^{rank} ## Ranking SVM for Learning from Partial-Information FeedbackAuthor: Thorsten Joachims <thorsten@joachims.org> Version: 1.00 |

*Propensity SVM ^{rank}* is an instance of

- T. Joachims, A. Swaminathan, T. Schnabel
*Unbiased Learning-to-Rank with Biased Feedback,*Proceedings of the International Conference on Web Search and Data Mining (WSDM), 2017. [PDF]

The implementation was developed on Linux with gcc, but compiles also on Cygwin, Windows (using MinGW) and Mac (after small modifications, see FAQ). The source code is available at the following location:

https://osmot.cs.cornell.edu/svm_proprank/current/svm_proprank.tar.gz

- Linux (64-bit): https://osmot.cs.cornell.edu/svm_proprank/current/svm_proprank_linux64.tar.gz
- Cygwin (64-bit): https://osmot.cs.cornell.edu/svm_proprank/current/svm_proprank_cygwin64.tar.gz
- Cygwin (32-bit): https://osmot.cs.cornell.edu/svm_proprank/current/svm_proprank_cygwin.tar.gz
- Windows (32-bit): https://osmot.cs.cornell.edu/svm_proprank/current/svm_proprank_windows.zip

Please send me email and let me know that you got it. The archive contains the source code of the most recent version of *SVM ^{rank}*, which includes the source code of

gunzip –c svm_proprank.tar.gz | tar xvf –This expands the archive into the current directory, which now contains all relevant files. You can compile

makeThis will produce the executables

Propensity SVM* ^{rank}* consists of a learning module (

svm_proprank_learn -c 20.0 train.dat model.datwhich trains a propensity-weighted Ranking SVM on the training set

General Options: -? -> this help -v [0..3] -> verbosity level (default 1) -y [0..3] -> verbosity level for svm_light (default 0) Learning Options: -c float -> C: trade-off between training error and margin (default 0.01) -p [1,2] -> L-norm to use for slack variables. Use 1 for L1-norm, use 2 for squared slacks. (default 1) -o [1,2] -> Rescaling method to use for loss. 1: slack rescaling 2: margin rescaling (default 2) -l [0..] -> Loss function to use. 0: zero/one loss ?: see below in application specific options (default 1) Optimization Options (see [2][5]): -w [0,..,9] -> choice of structural learning algorithm (default 3): 0: n-slack algorithm described in [2] 1: n-slack algorithm with shrinking heuristic 2: 1-slack algorithm (primal) described in [5] 3: 1-slack algorithm (dual) described in [5] 4: 1-slack algorithm (dual) with constraint cache [5] 9: custom algorithm in svm_struct_learn_custom.c -e float -> epsilon: allow that tolerance for termination criterion (default 0.001000) -k [1..] -> number of new constraints to accumulate before recomputing the QP solution (default 100) (-w 0 and 1 only) -f [5..] -> number of constraints to cache for each example (default 5) (used with -w 4) -b [1..100] -> percentage of training set for which to refresh cache when no epsilon violated constraint can be constructed from current cache (default 100%) (used with -w 4) SVM-light Options for Solving QP Subproblems (see [3]): -n [2..q] -> number of new variables entering the working set in each svm-light iteration (default n = q). Set n < q to prevent zig-zagging. -m [5..] -> size of svm-light cache for kernel evaluations in MB (default 40) (used only for -w 1 with kernels) -h [5..] -> number of svm-light iterations a variable needs to be optimal before considered for shrinking (default 100) -# int -> terminate svm-light QP subproblem optimization, if no progress after this number of iterations. (default 100000) Kernel Options: -t int -> type of kernel function: 0: linear (default) 1: polynomial (s a*b+c)^d 2: radial basis function exp(-gamma ||a-b||^2) 3: sigmoid tanh(s a*b + c) 4: user defined kernel from kernel.h -d int -> parameter d in polynomial kernel -g float -> parameter gamma in rbf kernel -s float -> parameter s in sigmoid/poly kernel -r float -> parameter c in sigmoid/poly kernel -u string -> parameter of user defined kernel Output Options: -a string -> write all alphas to this file after learning (in the same order as in the training set) Application-Specific Options: The following loss functions can be selected with the -l option: 1 IPS-weighted rank of relevant documents. NOTE: When the propensities of all relevant train docs are equal to 1, then SVM-light in '-z p' mode (with c_light = c_rank/n, where n is the number of training clicks) and unweighted SVM-rank with Swapped Pairs loss are equivalent.

SVM^{rank} learns a linear ranking policy (i.e.
a rule `w*x` without explicit threshold). The loss function to be
optimized is selected using the '-l' option, and the only option implemented so far is the (propensity-weighted) rank of the relevant documents.

You can in principle use kernels in SVM^{rank} using the '-t' option just like in SVM^{light}, but it is painfully slow. I recommend against it.

The file format of the training and test files is the same as for the conventional *SVM ^{rank}*
(see here for further details), but there are some exceptions as elaborated on below. In particular, one needs to specify the inverse-propensity-score (IPS) weight via the

<qid> .=. <positive integer>

For each document that is revealed to be relevant, one has to specify a separate qid. The lines in the input files have to be sorted by increasing qid. For each qid, the relevant document has target value 1, the other documents in the candidate set for the query (possibly some of which are relevant as well) have target value 0. Note that if there are multiple relevant documents for the same query, one would generate multiple qid (with the same feature vectors) where only a single document has target 1. For each relevant document, you need to specify the IPS-Weight via the cost parameter.

To clarify the file format, consider the following example with two queries. In query 1, documents A and C are relevant, but only A is revealed as relevant (with propensity 0.5). In query 2, documents B and C and D are relevant, but only B and C are revealed as relevant (with propensities 0.3 and 0.1 respectively). This leads to the following file forFiles in this format can be given to

1 qid:1 cost:2.0 1:1 2:1 3:0 4:0.2 5:0 # 1A

0 qid:1 1:0 2:0 3:1 4:0.1 5:1 # 1B

0 qid:1 1:0 2:1 3:0 4:0.4 5:0 # 1C

0 qid:1 1:0 2:0 3:1 4:0.3 5:0 # 1D

1 qid:2 cost:3.3 1:1 2:0 3:1 4:0.4 5:0 # 2B

0 qid:2 1:0 2:0 3:1 4:0.2 5:0 # 2A

0 qid:2 1:0 2:0 3:1 4:0.1 5:0 # 2C

0 qid:2 1:0 2:0 3:1 4:0.2 5:0 # 2D

0 qid:2 1:0 2:0 3:1 4:0.1 5:1 # 2E

1 qid:3 cost:10.0 1:0 2:0 3:1 4:0.1 5:0 # 2C

0 qid:3 1:0 2:0 3:1 4:0.2 5:0 # 2A

0 qid:3 1:1 2:0 3:1 4:0.4 5:0 # 2B

0 qid:3 1:0 2:0 3:1 4:0.2 5:0 # 2D

0 qid:3 1:0 2:0 3:1 4:0.1 5:1 # 2E

`svm_proprank_classify` is called as follows:

svm_proprank_classify test.dat model.dat predictions

For each line in `test.dat,` the predicted ranking score is written to
the file `predictions`. There is one line per test example in `predictions` in the same order as in
`test.dat`.
From these scores, the predicted ranking can be recovered via sorting.

You will find an example problem at

https://osmot.cs.cornell.edu/svm_light/examples/example4.tar.gz

It contains a propensity-scored training sample and a propensity-scored test sample with 100 clicks each. Unpack the archive with

gunzip -c example4.tar.gz | tar xvf -

This will create a subdirectory `example4`.
To run the example, execute the commands:

`svm_proprank_learn -c 0.01 example4/train.dat example4/model`

`svm_proprank_classify example4/test.dat example4/model example4/predictions`

The estimated ranking accuracy is written to STDOUT by the classification module.

Avg Rank of Positive Examples: 17.15 (via SNIPS Estimator [Swaminathan & Joachims, 2015d])

The numbers written in the predictions file can be used to rank the test examples. The values in the predictions file do not have a meaning in an absolute sense - they are only used for ordering.

It can also be interesting to look at the "training error" of the propensity ranking SVM.

`svm_proprank_classify example4/train.dat example4/model example4/predictions.train`

Avg Rank of Positive Examples: 4.61 (via SNIPS Estimator [Swaminathan & Joachims, 2015d])

Note that scores are comparable only between examples with the same qid.

This software is free only for non-commercial use. It must not be distributed without prior permission of the author. The author is not responsible for implications from the use of this software.

- none

- none

**[1] **T. Joachims, *Training Linear SVMs in Linear Time,* Proceedings of
the ACM Conference on Knowledge Discovery and Data Mining (KDD), 2006.
[Postscript] [PDF]

**[2] **T. Joachims, *A Support
Vector Method for Multivariate Performance Measures*, Proceedings of the
International Conference on Machine Learning (ICML), 2005.
[Postscript] [PDF]

**[3] **Tsochantaridis, T. Joachims, T. Hofmann, and Y. Altun, Large Margin
Methods for Structured and Interdependent Output Variables, Journal of Machine
Learning Research (JMLR), 6(Sep):1453-1484, 2005.
[PDF]

**[4] **I. Tsochantaridis, T. Hofmann, T. Joachims, Y. Altun. *Support Vector
Machine Learning for Interdependent and Structured Output Spaces*.
International Conference on Machine Learning (ICML), 2004.
[Postscript] [PDF]

**[5] **T. Joachims, Making Large-Scale SVM Learning Practical. Advances in Kernel Methods - Support Vector Learning, B. Schölkopf and C. Burges and A. Smola (ed.), MIT Press, 1999.
[Postscript (gz)]
[PDF]

**[6] **T. Joachims, T. Finley, Chun-Nam Yu, *Cutting-Plane Training of
Structural SVMs*, Machine Learning Journal, 2009.
[PDF]

[7]
T. Joachims, *Optimizing Search
Engines Using Clickthrough Data*, Proceedings of the ACM Conference on
Knowledge Discovery and Data Mining (KDD), ACM, 2002.
[Postscript] [PDF]

**[8] **T. Joachims, A. Swaminathan, T. Schnabel, *Unbiased Learning-to-Rank with Biased Feedback*, International Conference on Web Search and Data Mining (WSDM), 2017.
[PDF]

**[9] **A. Swaminathan, T. Joachims, *The Self-Normalized Estimator for Counterfactual Learning*, Neural Information Processing Systems (NIPS), 2015.
[PDF]