A Comparative Study of Methods for Transductive Transfer Learning
Andrew Arnold, Ramesh Nallapati and William W. Cohen
Machine Learning Department, Carnegie Mellon University
5000 Forbes Avenue, Pittsburgh, PA 15213, USA
{aarnold, nmramesh, wcohen}@cs.cmu.edu
Abstract
The problem of transfer learning, where information
gained in one learning task is used to improve performance
in another related task, is an important new area of research.
While previous work has studied the supervised version
of this problem, we study the more challenging case of
unsupervised transductive transfer learning, where no labeled
data from the target domain are available at training.
We describe some current state-of-the-art inductive and
transductive approaches and then adapt these models to
the problem of transfer learning for protein name extraction.
In the process, we introduce a novel maximum entropy
based technique, Iterative Feature Transformation (IFT),
and show that it achieves comparable performance with
state-of-the-art transductive SVMs. We also show how simple
relaxations, such as providing additional information
like the proportion of positive examples in the test data, can
significantly improve the performance of some of the transductive
transfer learners.
1 Introduction
Consider the task of named entity recognition (NER).
Specifically, you are given a corpus of encyclopedia articles
in which all the personal name mentions have been labeled.
The standard supervised machine learning problem
is to learn a classifier over this training data that will successfully
label unseen test data drawn from the same distribution
as the training data, where “same distribution” could
mean anything from having the train and test articles written
by the same author to having them written in the same
language. Having successfully trained a named entity classifier
on this encyclopedia data, now consider the problem
of learning to classify tokens as names in instant messenger
data. Clearly the problems of identifying names in encyclopedia
articles and instant messages are closely related, and
learning to do well on one should help your performance
on the other. At the same time, however, there are serious
differences between the two problems that need to be ad-
dressed. For instance, capitalization, which will certainly
be a useful feature in the encyclopedia problem, may prove
less informative in the instant messenger data since the rules
of capitalization are followed less strictly in that domain.
Thus there seems to be some need for altering the classifier
learned on the first problem (called the source domain)
to fit the specifics of the second problem (called the target
domain). This is the problem of domain adaptation and is
considered a type of transfer learning.
The intuitive solution seems to be to simply train on the
target domain data. Since this training data would be drawn
from the same distribution as the data you will ultimately
test over, this approach avoids the transfer issue entirely.
The problem with this idea is that often large amounts of
labeled data are not available in the target domain. While
it has been shown that even small amounts of labeled target
data can greatly improve transfer results [4, 6], there has
been relatively little work, however, on the case when there
is no labeled target data available, that is, totally unsupervised
domain adaptation. In this scenario, one way to adapt
a model trained on the source domain is to make the unlabeled
target test data available to the model during training
time. Leveraging (unlabeled) test data during training time
is called transductive learning and is a well studied problem
in the scenario when the training data and test data come
from the same domain. However, transduction is not wellstudied
in a transfer setting, where the training and test data
come from different domains. Studying transfer learning in
a transductive setting will be the main focus of our work.
2 Learning paradigms and related work
Givenanexamplex and a class label y, the standard statistical
classification task is to assign a probability, p(y|x),
to x of belonging to class y. In the binary classification
case the labels are Y ∈{0, 1}. In the case we examine,
each example xi is represented as a vector of binary features
(f1(xi), ··· ,fF (xi)) where F is the number of features.
The data consists of two disjoint subsets: the training
set (Xtrain,Ytrain) ={(x1,y1) ··· , (xN ,yN)}, avail-
able to the model for its training and the test set Xtest =
(x1, ··· ,xM ), upon which we want to use our trained classifier
to make predictions. We discuss below a small subset
of the many possible different paradigms of learning associated
with the classification problem.
In the paradigm of inductive learning, (Xtrain,Ytrain)
are known, while both Xtest and Ytest are completely hidden
during training time. In the case of semi-supervised inductive
learning [20, 16, 9], the learner is also provided with
auxiliary unlabeled data Xauxiliary, that is not part of the
test set. It has been noted that such auxiliary data typically
helps boost the performance of the classifier significantly.
Another setting that is closely related to semi-supervised
learning is transductive learning [18, 11, 13], in which
Xtest (but, importantly, not Ytest), is known at training
time. That is, the learning algorithm knows exactly which
examples it will be evaluated on after training. This can be a
great asset to the algorithm, allowing it to shape its decision
function to match and exploit the properties seen in Xtest.
One can think of transductive learning as a special case of
semi-supervised learning in which Xauxiliary = Xtest.
In the three cases discussed above, Xtest and Xtrain are
both assumed to have been drawn from the same distribution,
D. In the setting of transfer learning, however,we
would like to apply our trained classifier to examples drawn
from a distribution different from the one upon which it was
trained. We therefore assume there are two different distributions,
D source and D target , from which data may be
drawn. Given this notation we can then precisely state the
transfer learning problem as trying to assign labels Y target
test
to test data X target
test
drawn from D target , given training data
(X source
train ,Ysource
train ) drawn from Dsource . In this paper we
focus on the subproblem of domain adaptation, wherewe
assume Y (the set of possible labels) is the same for both
D source and D target , while D source and D target themselves
are allowed to vary between domains. This is in contrast
to the related subproblem of multi-task learning [1, 17]
in which the marginal distribution of the data is assumed
not to change, while the task (and therefore the labels) is
allowed to vary from source to target.
In this paper we choose to focus on extensions to the
transfer learning setting that allow us to capture some information
about D target . One obvious such setting is inductive
transfer learning where we also provide a few auxiliary labeled
data (X target
auxiliary ,Ytarget
auxiliary ) from the target domain
in addition to the labeled data from the source domain. Due
to the presence of labeled target data, this method could also
be called supervised transfer learning and is the most common
setting used by researchers in transfer learning today.
In this work, however, we focus on a new and more challenging
paradigm, namely, transductive transfer learning,
where there is no auxiliary labeled data in the target domain
available for training, but where the unlabeled test set on the
target domain X target
test
can be seen during training. Again,
due to the lack of labeled target data, this setting could be
considered unsupervised transfer learning. It is important to
point out that transductive learning is orthogonal to transfer
learning. That is, one can have a transductive algorithm
that does or does not make the transfer learning assumption,
and vice versa. Much of the work in this paper is inspired
by the belief that, although distinct, these problems are nevertheless
intimately related. More specifically, when trying
to solve a transfer problem between two domains, it seems
intuitive that looking at the unlabeled test data of the target
domain during training will improve performance over
ignoring this source of information.
We note that the setting of inductive transfer learning,
in which labeled data from both source and target domains
are available for training, serves as a rough upper-bound to
the performance of a learner based on transductive transfer
learning, in which no labeled target data is available.
We also considered an additional artificial setting, which
we call relaxed transductive transfer learning, in our experiments.
This setting is almost equivalent to the transductive
transfer setting, but the model is allowed to know the proportion
of positive examples in the target domain. Although
this type of learning is not technically fully unsupervised, in
practice estimating this single parameter over the target domain
does not require nearly as much labeled target data
as learning all the parameters of a fully supervised transfer
model, and thus serves as a nice compromise between the
two extremes of transduction and supervision.
3 Methods considered
3.1 Maximum entropy models
3.1.1 Inductive learning
Entropy maximization (MaxEnt) [2, 14] is a way of modeling
the conditional distribution of labels given examples.
Given a set of training examples Xtrain ≡{x1,...,xN },
their labels Ytrain ≡ {y1,...,yN}, and the set of features
F ≡ {f1,...,fF }, MaxEnt learns a model consisting
of a set of weights corresponding to each class
Λ = {λ1,y...λF,y} y∈{0,1} over the features so as to
maximize the conditional likelihood of the training data,
p(Ytrain|Xtrain), given the model pΛ. In exponential parametric
form, this conditional likelihood can be expressed as:
pΛ(yi = y|xi) = 1
Z(xi) exp(
F�
fj(xi)λj,y) (1)
j=1
where Z is the normalization term. In order to avoid overfitting
the training data, these λ’s are often further constrained
to be near 0 by the use of a regularization term which tries to
minimize �Λ�2 �
2 ≡ j,y (λj,y) 2 . Thus the entire expression
being optimized is:
N�
argmax log pΛ(yi|xi) − β�Λ�
Λ
i=1
2 2
(2)
where β>0 is a parameter controlling the amount of regularization.
Maximizing this likelihood is equivalent to constraining
the joint expectations of each feature and label in
the learned model, EΛ[fj,y], to match empirical expectations
Etrain[fj,y] as shown below:
Etrain [fj,y] = 1
N�
fj(xi)δy(yi) (3)
N
EΛ [fj,y] = 1
N�
fj(xi)PΛ(y|xi)
N
i
(4)
where δy(yi) =1if y = yi and 0 otherwise.
3.1.2 Inductive transfer
Source trained prior models: One recently proposed
method [4] for transfer learning in MaxEnt models involves
modifying Λ’s regularization term. First a model
of the source domain, Λsource , is learned by training
on {X source
}. Then a model of the target do-
train ,Ysource
train
main is trained over � a limited set of labeled target data
target
, but instead of regularizing this Λ
� target
Xtrain ,Ytarget
train
to be near zero by minimizing �Λ target � 2 2, Λ target is instead
regularized towards the previously learned source values
Λ source by minimizing �Λ target − Λ source � 2 2. Thus the
modified optimization problem is:
argmax
Λ target
N target
train
�
i=1
i
log pΛ target (yi|xi)−β�Λ target −Λ source � 2 2
(5)
where N target
train is the number of labeled training examples
in the target domain. It should be noted that this model
requires Y target
train in order to learn Λtarget and is therefore a
supervised form of inductive transfer.
Feature space expansion: Another approach to the
problem of inductive transfer learning is explored by
Daumé [6, 7]. Here the idea is that there are certain features
that are common between different domains, and others that
are particular to one or the other. More specifically, we can
redefine our feature set F as being composed of two distinct
subsets F specific � F general , where the conditional distribution
of the features in F specific differ between X source
and X target , while the features in F general are identically
distributed in the source and target. Given this assumption,
there is an EM-like algorithm [7] for estimating the parameters
of these distributions. The idea is that by expanding the
feature space in this way MaxEnt will be able to assign different
weights to different versions of the same feature. If
a feature is common in both domains its general copy will
get most of the weight, while its specific copies (f source
and f target ) will get less weight, and vice versa.
3.1.3 Transductive transfer: IFT
In this subsection, we present a new approach for the unsupervised
setting of transductive transfer learning using
MaxEnt. For ease of notation we will use E source [fj,y]
to mean Ex∈D source [fj(x),y], and similarly for target.
One problem with transfer in MaxEnt is that the joint
distribution of the features with labels differs between the
source and target domains. In other words, E source [fj,y]
does not necessarily equal E target [fj,y]. If the expectations
in the train and test datasets are similar, then the
Λ learned on the training data will generalize well to the
test data. The more these distributions differ, however, the
less well the trained model will perform. Phrased in terms
of maximum entropy, we are trying to learn a transformation
G() of the feature space F such that the joint distributions
of the source and target features with their labels are
aligned:
E target [G(fj),y]=E source [G(fj),y] , ∀fj ∈F (6)
One could relax this condition even further by arguing
that it is enough to transform only one of the domains, say
the source data, so that data from both domains could be
separated by a single hyperplane. In maximum entropy
phraseology, the relaxed transformation is:
E target [fj,y]=E source [G(fj),y] , ∀fj ∈F (7)
The problem with this, of course, is that in the unsupervised
transductive transfer case, we do not have Y target and
therefore cannot estimate E target [fj,y]. Hence we approximate
E target [fj,y] using the joint estimates on the target
unlabeled data from a model learned from the source data
as shown below:
E target [fj,y] ≈ E target
Λsource [fj,y]
where N target
test
=
1
N target
test
N target
test
�
i=1
fj(xi)PΛsource(y, xi)
is the number of target domain (unlabeled)
test examples. These estimates may not reflect the true target
expectations, but it is the best we could do in the unsupervised
transductive setting. Now we use these expecta-
tions to define the source domain transformation G as:
∀
source
Ntrain i=1
G(fj(xi)) = fj
E target
Λsource [fj,yi]
E source [fj,yi]
where Esource [fj,yi] is given by the formula in (3) and
N source
train is the number of labeled training data in the source
domain. It is easy to show that the empirical featurelabel
joint expectations of the transformed source data
given by Esource [G(fj,y)] defined this way is equal to
E target
Λsource [fj,y], the model expectations of the original features
in the target domain, satisfying the condition in (7).
The effect is to rescale fj(x), putting more weight on features
that occur frequently in the target but rarely in the
(8)
source (in a conditional sense), and downweighting features
that are common in the source but seldom seen in the target.
This algorithm can be implemented in an iterative fashion
by first training the source model, computing the target expectations
using the source model, transforming the source
features and then retraining the source model.
In practice, since the target expectation E target
Λsource [fj,y] is
only approximate, we smooth the transformed features with
the original ones in each iteration as follows:
G ′ (fj(xi)) = θfj(xi)+(1−θ)G(fj(xi)) (9)
where θ controls the degree to which we use the target
conditional estimates to alter the source conditionals.
3.1.4 Relaxed transductive transfer: biased threshold
A natural way to exploit the known value of the proportion
of positive class labels in the target domain is to adjust the
decision threshold of the MaxEnt classifier so that the percentage
of unlabeled target examples predicted as positive
by the source-trained classifier is equal to the known value.
We call this intuitive algorithm biased thresholding, toreflect
the fact that the decision threshold is biased towards
the known information on class ratio.
3.2 Support vector machines
3.2.1 Inductive learning: inductive SVMs
Support vector machines (SVMs) [12] take a different approach
to the binary classification problem. Instead of explicitly
modeling the conditional distribution of the data and
using these estimates to predict labels, SVMs try to model
the data geometrically. Each example is represented as an
F -dimensional real-valued vector of features and is then
projected as a point in F -dimensional space. The inductive
SVM exploits the label information of the training data
and fits a discriminative hyperplane between the positively
and negatively labeled training examples in this space, so as
to best separate the two classes.
3.2.2 Inductive transfer: concatenated data
Recall that in the supervised inductive transfer case,
we are given the training sets (X source
train ,Ysource
train ) and
(X target
train ,Ytarget
train ). Since the SVM does not explicitly
model the data distribution, we simply concatenate the
source and target labeled data together and provide the entire
data for training. The hope is that it will improve on an
SVM trained purely on labeled source data, by re-adjusting
its hyperplane based on the labeled target data.
3.2.3 Transductive transfer: transductive SVMs
Transduction with SVMs, in contrast to probabilistic
models, is quite intuitive. Whereas, in the supervised case,
we tried to fit a hyperplane to best separate the labeled
training data, in the transductive case, we add in unlabeled
testing data which we must also separate. Since we do not
know the labels of the testing data, however, we cannot
perform a straight forward margin maximization, as in
the supervised case. Instead, one can use an iterative
algorithm [11] similar in flavor to the MaxEnt iterative
feature transformation (IFT) algorithm of section 3.1.3.
Specifically, a hyperplane is trained on the labeled source
data and then used to classify the unlabeled testing data. As
in IFT, one can adjust how confident the hyperplane must
be in its prediction in order to use a pseudo-label during the
next phase of training (since there are no probabilities, large
margin values are used as a measure of confidence). The
pseudo-labeled testing data is then, in turn, incorporated in
the next round of training. The idea is to iteratively adjust
the hyperplane (by switching presumed pseudo-labels)
until it is very confident on most of the testing points, while
still performing well on the labeled training points.
3.2.4 Relaxed transductive transfer: biased threshold
As with the maximum entropy approaches described in section
3.1.4, transductive SVMs used for transfer can also be
adjusted to match the prior proportion of positive examples
in the target domain. Specifically, whereas the SVM usually
just considers which side of the hyperplane a test example
is on in determining its label (i.e., a threshold of 0), this
threshold can be moved so that some points that lie nearest
on the negative side of the hyperplane and would normally
be given a negative label, would instead receive a positive
one, or vice verse.
4 Investigation
4.1 Domain
We now turn to protein name recognition, an interesting
problem domain [15, 19, 10] in which to test these methods.
In this setting you are given text related to biological
research (usually abstracts, captions, and full body text from
biological journal articles) which is known to contain mentions
of protein names. The goal is to identify which words
are part of a protein name mention, and which are not. One
major difficulty is that there is a large variance in how these
proteins are mentioned and annotated between different authors,
journals, and sub-disciplines of biology. Because of
this variance it is often difficult to collect a large corpus
of truly identically distributed training examples. Instead,
researchers are often faced with heterogeneous sources of
data, both for training and testing, thus violating one of
the key assumptions of most standard machine learning algorithms
and indicating a need for a transfer learning approach.
Table 1. Summary of data used in experiments
Corpus name (Abbr.) Abstracts Tokens % Positive
UTexas (UT) 748 216,795 6.6%
Yapex (Y) 200 60,530 15.0%
Yapex-train (YTR) 160 48,417 15.1%
Yapex-test (YTT) 40 12,113 14.5%
4.2 Data and evaluation
Our corpora are abstracts from biological journals coming
from two sources: University of Texas, Austin (UT) [3]
and Yapex [8]. Each abstract was tokenized and each token
was hand-labeled as either being part of a protein name or
not. We used a standard natural language toolkit [5] to compute
tens of thousands of binary features on each of these
tokens, encoding such information as capitalization patterns
and contextual information of surrounding words.
Some summary statistics for these data are shown in table
1. We purposely chose corpora that differed in two
important dimensions: the total amount of data collected
and the relative proportion of positively labeled examples
in each dataset. For all our experiments, we used the larger
UT dataset as our source domain and the smaller Yapex
dataset as our target. We also split the Yapex data into two
parts: Yapex-train (YTR) consisting of 80% of the data, and
Yapex-test (YTT), consisting of the remaining 20%.
Because of the relatively small proportion of positive examples
in both the UT and Yapex datasets, we are more interested
in achieving both high precision and recall of protein
name mentions instead of simply maximizing classification
accuracy and thus use the F 1 measure, which combines
precision and recall into one metric, as our main evaluation
measure.
4.3 Experiments and results
Table 2 summarizes the relative performance of the various
methods (cf. section 3) in four different learning settings
(cf. section 2). The inductive experiment is dominated
by MaxEnt’s 82% F1 compared to TSVM’s 73%. Moving
to the transductive transfer setting causes both methods’
performances to fall, but MaxEnt falls most sharply, causing
it to lose its entire lead over TSVM. TSVM is able to adjust
its hyperplane in light of the transfer test data and stabilize
its performance at 60%, even though it is unlabeled, because
it knows where these points lie relative to the labeled
training points in feature space. Similarly, we see the effect
of our iterative feature transformation algorithm (IFT, section
3.1.3) on MaxEnt’s transductive transfer performance.
Indeed, iteratively combining the approximate joint featurelabel
expectations in the target data with the true joints of
the source data improves the overall performance on the target
data. It seems this method is bounded, however, by the
quality of the initial target labels generated by the sourcetrained
classifier.
In the relaxed transductive transfer setting, where the target
dataset is still unlabeled but all algorithms are told the
expected proportion of positive examples, TSVM excels.
Again, while MaxEnt is able to make significant use of this
information (note the jump to 67% F1 from 54%), it seems
TSVM does a better job leveraging the prior knowledge into
better performance.
Finally, the last column of table 2 compares the performance
of the methods for inductive transfer learning: Regularize
and Expand, both described in section 3.1.2. We can
see that both methods handily outperform the transductive
transfer methods described in the second column of table 2,
and for the most part outperform even the relaxed transductive
transfer versions in column three. This should not be
surprising given the fact that the inductive transfer methods
can actually see some labeled examples from the target domain
and thus better estimate the conditional expectation of
the features in the target data. Likewise they can also assess
the proportion of positive examples and adjust their decision
functions accordingly. It is surprising, however, that
these methods do not significantly outperform the inductive
learning methods described in the first column of table 2.
This suggests that these inductive transfer methods are relying
almost entirely on their labeled target data to train their
classifiers, and are not making full use of the large amount
of labeled source data. The regularized maximum entropy
model does outperform the basic MaxEnt in the inductive
setting, but not by as much as might have been hoped for.
In order to measure how much these inductive transfer
methods’ explicit modeling of the transfer problem was responsible
for their performance, we compared them to the
baselines of ISVM, TSVM, and MaxEnt trained on a simple
concatenation of the labeled source and target training
data. These transfer-agnostic methods clearly benefited
from the addition of labeled target data (as compared
to column TransductiveTransfer), yet still yielded consistently
lower F1 than the transfer-aware Regularize and Expand
methods, suggesting that the mere presence of labeled
sets of both types (source and target) of data is not enough
to account for the transfer methods’ superior results. Instead,
it seems it is the modeling of the different domains in
the transfer problem, even in simple ways, that provides the
extra boost to performance.
5 Conclusions & future work
We have seen that even a small amount of prior knowledge
about the target domain can greatly improve performance
in a transductive transfer problem. We also notice
that even large amounts of source data cannot overcome the
Table 2. Summary of % accuracy (Acc), precision (Prec), recall (Rec), and F1 for regular maximum entropy (Basic), Iterative
Feature Transformation MaxEnt (IFT), prior-based regularized MaxEnt (Regularize), and feature expansion MaxEnt (Expand),
inductive SVM (ISVM), and transductive SVM (TSVM) models under the conditions of classic inductive learning, (Induction),
unsupervised transductive transfer learning, (TransductTransfer), relaxed transductive transfer, (RelaxTransductTransfer), and
supervised inductive transfer (InductTransfer).
Method
Acc
Induction
Prec Rec F1
TransductTransfer
Acc Prec Rec F1
RelaxTransductTransfer
Acc Prec Rec F1
InductTransfer
Acc Prec Rec F1
MAXIMUM ENTROPY
Basic 95 85 78 82 89 75 42 54 90 65 68 67 91 81 54 65
IFT, 1 iter - - - - 79 41 90 56 - - - - - - - -
IFT, 2 iters - - - - 82 45 86 59 - - - - - - - -
Regularize - - - - - - - - - - - - 96 87 84 85
Expand - - - - - - - - - - - - 93 84 62 72
SUPPORT VECTOR MACHINES
ISVM 92 78 58 67 90 86 40 54 90 86 40 55 92 86 52 65
TSVM 92 68 79 73 91 86 46 60 92 72 75 73 93 86 58 70
advantage of having access to labeled data drawn from the
target distribution. We have also seen the degree to which
pseudo-labeling based schemes (in both TSVM’s marginbased
model and our MaxEnt’s IFT-based model) can improve
performance by incorporating the unlabeled structure
of the target domain. Finally we have seen that, while both
the MaxEnt and SVM models perform well in the transductive
setting, the margin based SVM seems to adapt better to
the unlabeled data.
In the future, we would like to further investigate the theoretical
properties of the IFT-type algorithms while extending
these methods to use sequential, rather than simply binary,
classifiers like conditional random fields [17].
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