README.md
In matloff/rectools: Advanced Recommender System
rectools
Advanced Package for Recommender Systems
A featured-filled package of tools from the recommender systems
(RS) world, plus some new methods.
Recommender Systems
In RS, we have data in which some "users" rate some "items,"
and we wish to predict how users would rate other items. Example
applications are:
-
Moviegoers rate films (the "Hello World" of RS).
-
Link prediction in graphs (where will the next new edge be created?).
-
Will a certain user have a bad reaction to a certain prescription
drug?
-
How well will sports team A do against team B?
Here we will focus on collaborative systems, in which the user and
item data are combined to produce predicted ratings.
Package Features
-
Incorporate user and item covariate information, including item
category preferences.
-
New methods, and novel variations on common models.
-
Parallel computation.
-
Plotting.
-
Focus group finder.
Example: InstEval data
Let's start with a concrete example, the InstEval data that is
bundled with the lmer4 package, which is included with rectools.
The data consist of student valuations of instructors at the famous
Swiss university ZTH. There are 73421 ratings submitted by 2972
students of 1128 instructors. Ratings are on a scale of 1 to 5.
Not surprisingly, the ratings matrix is mostly unknown; most students
did not rate most instructors. The goal is to "complete" the matrix,
i.e. predict how well all the students would like all the instructors.
For convenience, rectools includes a function that loads this data,
processes it (e.g. creating dummy variables for the school's
departments), and assigning the result to ivl:
> getInstEval()
> ivl[28888,] # look at some example record
s d y studage lectage service dpt15 dpt5 dpt10
28888 1178 220 5 3 5 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
28888 1 0 0 0 0 0 0 0 0 0
The data frame ivl follows the standard input format in the RS
world: user ID, item ID, rating, covariates.
In that record 28888, for instance, Student 1178 gave a rating of 5 to
Instructor 220. The class was not a service class (i.e. not for
nonmajors) in Department 12 (dpt15 etc. are dummy variables.) The
student was in his/her third semester (studage = 3), and had taken the
course 5 semesters earlier.
(For more information on the data, type '?InstEval')
Nearest-neighbors/similarity model:
The basic idea here is as follows. To predict the rating user i would
give to item j, find some users who are similar to user i and who have
rated item j, and average their ratings of that item. The CRAN package
recommderlab is one implementation of this idea, but our
rectools package uses its own implementation, including novel
enhancements.
The functions used are formUserData(), to initialize the database, and
predict.usrData(), that does the actual prediction. The latter
function calls cosDist() to compute distances/similarities.
To keep our example below simple, we won't use the covariates, just the
student and instructor IDs, and the ratings. Let's use student 28 in
our example, and predict how well the user might like instructor 122.
> ud <- formUserData(ivl[,1:3])
> u28 <- ud[[28]]
> u28$itms
[1] 17 65 269 750 1002 1589 2097
> predict(ud,u28,122,10) # would User 28 like Item 122?
[1] 4.3
Here's what happened above. First, the R list ud will have
one element per user, with components itms and
ratings showing what items this user has rated and
what ratings he/she gave.
The call to predict() is a little more complicated. It is what is
called a generic function in R. When R sees this call, it will ask,
"What is the class of ud?" Upon learning that ud is an object
of class usrData. R then dispatched the call to the method
predict.usrData() function then found the 10 closest users in our
dataset who had rated item 122, and averaged their ratings for that
item, yielding 4.3.
Matrix factorization model:
Let A denote the matrix of ratings, with Yij, the rating user
i has for item j, in row i, column j. Most of A is unknown, and we wish to
predict the unknown values. Nonnegative Matrix Factorization (NMF)
does this as follows:
We find fully known nonnegative matrices W and H, each of rank k, such
that A is approximately equal to the product WH. Here k is a
user-defined tuning parameter, typically much smaller than the number of
rows and columns of A. It is kept small to avoid overfitting but large
enough to capture most of the structure of the data. Default value is k
= 10.
Here we piggyback on the R package recosystem, adding convenient
wrappers and adding a parallel computation capability. The
functions involved are trainReco(), predictReco() and so on.
Once again, let's try this on the InstEval data:
> tr <- trainReco(ivl[,1:3])
> names(tr)
[1] "P" "Q"
> dim(tr$P) # W
[1] 2972 10
> dim(tr$Q) # H'
[1] 2160 10
> class(tr)
[1] "RecoS3"
> testSet <- data.frame(s=28,d=122)
> predict(tr,testSet)
[1] 5.310598
Here trainReco() did the factorization, returning an object of class
"RecoS3" whose components are W and the transpose of H. As our example
for prediction, we again took student number 28 and instructor number 122.
Since ud is of class "RecoS3", the R interpreter dispatched our
predict() call to predict.RecoS3.
Note that before we could do any prediction, we needed to train our
model, a machine learning term meaning to fit the model to our dataset.
Here the fitting consisted of finding the matrices W and H, and from now
on, we can use them to make as many predictions as we want.
Random effects ANOVA model:
A simple statistical random effects latent factor model, often called a
baseline model in the RS literature, is
E(Y) = μ + αi + βj
where Yij is the rating, with αi and
βj being specific latent (i.e. hidden) effects
for user i and item j,
e.g. moviegoer i and movie j.
Though typically Maximum Likelihood Estimation is used for random
effects models in statistics, this is computationally infeasible on
large data sets. Instead, we use the Method of Moments, which provides
a closed-form solution, estimating αi by Yi. - Y..,
where the first term is the mean of all observed ratings by user i and
the second is the overall mean of all ratings. We estimate
βj similarly, and estimate μ by the overall mean Y..
The predicted value of Yij is then
Y.. + (Yi. - Y..) + (Y.j - Y..) = Yi. Y.j - Y..
Let's see how student 1178 would like instructor 99. For now, let's not
include the covariates.
> mmout <- trainMM(ivl[,1:3]) # exclude covariates
> predict(mmout,data.frame(s=1178,d=99))
[1] 3.676795
We fit our model by calling trainMM(), then did our prediction.
We do make MLE available. Here αi and
βj are assumed to have independent normal distributions
with different variances. (The error term εij =
Yij - EYij is assumed independent of
αi and βj, with variance constant
across i and j.) We piggyback R's lme4 package, forming a wrapper
for our application, and adding our function predict.ydotsMLE() for
prediction, also an lme4 wrapper suited for our context. Since MLE
computation can be voluminous, our package offers a parallel version.
One important advantage of the MLE version is that it lends itself to
the case of binary Y, with the logistic model.
Covariates are allowed for both the MM and MLE versions, as well as for
other methods in rectools. Let's try predicting student 1178 and
instructor 99 again, this time using covariates.
> mmout1 <- trainMM(ivl)
We now will start building the a test set for the prediction. We'll use
student 1178 and instructor 99 again, adding the conditions that the
course in question is not a service course, and was taken in the
student's 6th semester, which was 2 semesters earlier than now.
Now that we are using covariates, we'll need to determine what they are
for this student and this instructor. We already saw above that
studage is 3 for student 1178. We also need to find the department
of instructor 99, so let's find a record involving that instructor.
> which(ivl$d == 99)
[1] 3015 3604 6214 9347 13507 18235 22131 23514 25397
[10] 31402 46502 55132 57645 59201 66132 68640 69885 73205
> ivl[3015,]
s d y studage lectage service dpt15 dpt5 dpt10
3015 124 99 4 3 4 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
3015 0 0 0 0 0 0 0 1 0 0
Ah, it's department 1. We'll now create the test set, a one-row data
frame, as in the MM example above, but instead of typing in all those
department variables by hand, we'll take one of the rows and modify it.
> testset <- ivl[28888,-3] # no 'y' in our test set
> testset
s d studage lectage service dpt15 dpt5 dpt10
28888 1178 220 3 5 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
28888 1 0 0 0 0 0 0 0 0 0
> testset$d <- 99
> testset$dpt12 <- 0
> testset$dpt1 <- 1
> testset$studage <- 6
> testset$lectage <- 2
> testset # check it
s d studage lectage service dpt15 dpt5 dpt10
28888 1178 99 6 2 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
28888 0 0 0 0 0 0 0 1 0 0
Now go ahead with the prediction:
> mmout1 <- trainMM(ivl)
> predict(mmout1,testset)
[1] 3.727755
Cross validation:
The MM, MLE, NMF and cosine methods all have wrappers to do
cross-validation, reporting the accuracy measures exact prediction; mean
absolute deviation; and l2. In our experiments so far, MM seems to give
the best accuracy (and the greatest speed).
Plotting:
Some plotting capability is provided, currently in the functions
plot.ydotsMM() and plot.xvalb(). The former, for instance, can be
used to assess the normality and independence assumptions of the MLE
model, and to identify a possible need to consider separate analyses for
subpopulations.
FURTHER INFORMATION ON RECOMMENDER SYSTEMS
C. Aggarwal, Recommender Systems: the Textbook, Springer, 2016.
K. Gao and A. Owen, Efficient Moment Calculations for Variance
Components in Large Unbalanced Crossed Random Effects Models, 2016.
M. Hahsler, recommderlab, CRAN vignette.
D. Jannach et al, Recommender Systems: an Introduction, Cambridge
University Press, 2010.
Y. Koren et al, Matrix Factorization Techniques for Recommender
Systems, IEEE Computer, 2009.
N. Matloff, Collaborative Filtering in Recommender Systems:
a Short Introduction, 2016.
N. Matloff, A Tour of Recommender Systems, 2018 (in progress).
P. Perry, Fast Moment-Based Estimation for Hierarchical Models, 2015.
matloff/rectools documentation built on March 31, 2022, 12:09 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
rectools
Advanced Package for Recommender Systems
A featured-filled package of tools from the recommender systems (RS) world, plus some new methods.
Recommender Systems
In RS, we have data in which some "users" rate some "items," and we wish to predict how users would rate other items. Example applications are:
-
Moviegoers rate films (the "Hello World" of RS).
-
Link prediction in graphs (where will the next new edge be created?).
-
Will a certain user have a bad reaction to a certain prescription drug?
-
How well will sports team A do against team B?
Here we will focus on collaborative systems, in which the user and item data are combined to produce predicted ratings.
Package Features
-
Incorporate user and item covariate information, including item category preferences.
-
New methods, and novel variations on common models.
-
Parallel computation.
-
Plotting.
-
Focus group finder.
Example: InstEval data
Let's start with a concrete example, the InstEval data that is bundled with the lmer4 package, which is included with rectools. The data consist of student valuations of instructors at the famous Swiss university ZTH. There are 73421 ratings submitted by 2972 students of 1128 instructors. Ratings are on a scale of 1 to 5.
Not surprisingly, the ratings matrix is mostly unknown; most students did not rate most instructors. The goal is to "complete" the matrix, i.e. predict how well all the students would like all the instructors.
For convenience, rectools includes a function that loads this data, processes it (e.g. creating dummy variables for the school's departments), and assigning the result to ivl:
> getInstEval()
> ivl[28888,] # look at some example record
s d y studage lectage service dpt15 dpt5 dpt10
28888 1178 220 5 3 5 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
28888 1 0 0 0 0 0 0 0 0 0
The data frame ivl follows the standard input format in the RS world: user ID, item ID, rating, covariates.
In that record 28888, for instance, Student 1178 gave a rating of 5 to Instructor 220. The class was not a service class (i.e. not for nonmajors) in Department 12 (dpt15 etc. are dummy variables.) The student was in his/her third semester (studage = 3), and had taken the course 5 semesters earlier.
(For more information on the data, type '?InstEval')
Nearest-neighbors/similarity model:
The basic idea here is as follows. To predict the rating user i would give to item j, find some users who are similar to user i and who have rated item j, and average their ratings of that item. The CRAN package recommderlab is one implementation of this idea, but our rectools package uses its own implementation, including novel enhancements.
The functions used are formUserData(), to initialize the database, and predict.usrData(), that does the actual prediction. The latter function calls cosDist() to compute distances/similarities.
To keep our example below simple, we won't use the covariates, just the student and instructor IDs, and the ratings. Let's use student 28 in our example, and predict how well the user might like instructor 122.
> ud <- formUserData(ivl[,1:3])
> u28 <- ud[[28]]
> u28$itms
[1] 17 65 269 750 1002 1589 2097
> predict(ud,u28,122,10) # would User 28 like Item 122?
[1] 4.3
Here's what happened above. First, the R list ud will have one element per user, with components itms and ratings showing what items this user has rated and what ratings he/she gave.
The call to predict() is a little more complicated. It is what is called a generic function in R. When R sees this call, it will ask, "What is the class of ud?" Upon learning that ud is an object of class usrData. R then dispatched the call to the method predict.usrData() function then found the 10 closest users in our dataset who had rated item 122, and averaged their ratings for that item, yielding 4.3.
Matrix factorization model:
Let A denote the matrix of ratings, with Yij, the rating user i has for item j, in row i, column j. Most of A is unknown, and we wish to predict the unknown values. Nonnegative Matrix Factorization (NMF) does this as follows:
We find fully known nonnegative matrices W and H, each of rank k, such that A is approximately equal to the product WH. Here k is a user-defined tuning parameter, typically much smaller than the number of rows and columns of A. It is kept small to avoid overfitting but large enough to capture most of the structure of the data. Default value is k = 10.
Here we piggyback on the R package recosystem, adding convenient wrappers and adding a parallel computation capability. The functions involved are trainReco(), predictReco() and so on.
Once again, let's try this on the InstEval data:
> tr <- trainReco(ivl[,1:3])
> names(tr)
[1] "P" "Q"
> dim(tr$P) # W
[1] 2972 10
> dim(tr$Q) # H'
[1] 2160 10
> class(tr)
[1] "RecoS3"
> testSet <- data.frame(s=28,d=122)
> predict(tr,testSet)
[1] 5.310598
Here trainReco() did the factorization, returning an object of class "RecoS3" whose components are W and the transpose of H. As our example for prediction, we again took student number 28 and instructor number 122. Since ud is of class "RecoS3", the R interpreter dispatched our predict() call to predict.RecoS3.
Note that before we could do any prediction, we needed to train our model, a machine learning term meaning to fit the model to our dataset. Here the fitting consisted of finding the matrices W and H, and from now on, we can use them to make as many predictions as we want.
Random effects ANOVA model:
A simple statistical random effects latent factor model, often called a baseline model in the RS literature, is
E(Y) = μ + αi + βj
where Yij is the rating, with αi and βj being specific latent (i.e. hidden) effects for user i and item j, e.g. moviegoer i and movie j.
Though typically Maximum Likelihood Estimation is used for random effects models in statistics, this is computationally infeasible on large data sets. Instead, we use the Method of Moments, which provides a closed-form solution, estimating αi by Yi. - Y.., where the first term is the mean of all observed ratings by user i and the second is the overall mean of all ratings. We estimate βj similarly, and estimate μ by the overall mean Y.. The predicted value of Yij is then
Y.. + (Yi. - Y..) + (Y.j - Y..) = Yi. Y.j - Y..
Let's see how student 1178 would like instructor 99. For now, let's not include the covariates.
> mmout <- trainMM(ivl[,1:3]) # exclude covariates
> predict(mmout,data.frame(s=1178,d=99))
[1] 3.676795
We fit our model by calling trainMM(), then did our prediction.
We do make MLE available. Here αi and βj are assumed to have independent normal distributions with different variances. (The error term εij = Yij - EYij is assumed independent of αi and βj, with variance constant across i and j.) We piggyback R's lme4 package, forming a wrapper for our application, and adding our function predict.ydotsMLE() for prediction, also an lme4 wrapper suited for our context. Since MLE computation can be voluminous, our package offers a parallel version.
One important advantage of the MLE version is that it lends itself to the case of binary Y, with the logistic model.
Covariates are allowed for both the MM and MLE versions, as well as for other methods in rectools. Let's try predicting student 1178 and instructor 99 again, this time using covariates.
> mmout1 <- trainMM(ivl)
We now will start building the a test set for the prediction. We'll use student 1178 and instructor 99 again, adding the conditions that the course in question is not a service course, and was taken in the student's 6th semester, which was 2 semesters earlier than now.
Now that we are using covariates, we'll need to determine what they are for this student and this instructor. We already saw above that studage is 3 for student 1178. We also need to find the department of instructor 99, so let's find a record involving that instructor.
> which(ivl$d == 99)
[1] 3015 3604 6214 9347 13507 18235 22131 23514 25397
[10] 31402 46502 55132 57645 59201 66132 68640 69885 73205
> ivl[3015,]
s d y studage lectage service dpt15 dpt5 dpt10
3015 124 99 4 3 4 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
3015 0 0 0 0 0 0 0 1 0 0
Ah, it's department 1. We'll now create the test set, a one-row data frame, as in the MM example above, but instead of typing in all those department variables by hand, we'll take one of the rows and modify it.
> testset <- ivl[28888,-3] # no 'y' in our test set
> testset
s d studage lectage service dpt15 dpt5 dpt10
28888 1178 220 3 5 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
28888 1 0 0 0 0 0 0 0 0 0
> testset$d <- 99
> testset$dpt12 <- 0
> testset$dpt1 <- 1
> testset$studage <- 6
> testset$lectage <- 2
> testset # check it
s d studage lectage service dpt15 dpt5 dpt10
28888 1178 99 6 2 0 0 0 0
dpt12 dpt6 dpt7 dpt4 dpt8 dpt9 dpt14 dpt1 dpt3 dpt11
28888 0 0 0 0 0 0 0 1 0 0
Now go ahead with the prediction:
> mmout1 <- trainMM(ivl)
> predict(mmout1,testset)
[1] 3.727755
Cross validation:
The MM, MLE, NMF and cosine methods all have wrappers to do cross-validation, reporting the accuracy measures exact prediction; mean absolute deviation; and l2. In our experiments so far, MM seems to give the best accuracy (and the greatest speed).
Plotting:
Some plotting capability is provided, currently in the functions plot.ydotsMM() and plot.xvalb(). The former, for instance, can be used to assess the normality and independence assumptions of the MLE model, and to identify a possible need to consider separate analyses for subpopulations.
FURTHER INFORMATION ON RECOMMENDER SYSTEMS
C. Aggarwal, Recommender Systems: the Textbook, Springer, 2016.
K. Gao and A. Owen, Efficient Moment Calculations for Variance Components in Large Unbalanced Crossed Random Effects Models, 2016.
M. Hahsler, recommderlab, CRAN vignette.
D. Jannach et al, Recommender Systems: an Introduction, Cambridge University Press, 2010.
Y. Koren et al, Matrix Factorization Techniques for Recommender Systems, IEEE Computer, 2009.
N. Matloff, Collaborative Filtering in Recommender Systems: a Short Introduction, 2016.
N. Matloff, A Tour of Recommender Systems, 2018 (in progress).
P. Perry, Fast Moment-Based Estimation for Hierarchical Models, 2015.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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