Multi-task learning (MTL) is a subfield of
machine learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence.
Machine ...
in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models separately.
Early versions of MTL were called "hints".
In a widely cited 1997 paper, Rich Caruana gave the following characterization:
Multitask Learning is an approach to inductive transfer
Transfer learning (TL) is a research problem in machine learning (ML) that focuses on storing knowledge gained while solving one problem and applying it to a different but related problem. For example, knowledge gained while learning to recognize ...
that improves generalization
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteri ...
by using the domain information contained in the training signals of related tasks as an inductive bias
The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered.
In machine learning, one aims to construct algorithms that a ...
. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better.
In the classification context, MTL aims to improve the performance of multiple classification tasks by learning them jointly. One example is a spam-filter, which can be treated as distinct but related classification tasks across different users. To make this more concrete, consider that different people have different distributions of features which distinguish spam emails from legitimate ones, for example an English speaker may find that all emails in Russian are spam, not so for Russian speakers. Yet there is a definite commonality in this classification task across users, for example one common feature might be text related to money transfer. Solving each user's spam classification problem jointly via MTL can let the solutions inform each other and improve performance.
Further examples of settings for MTL include
multiclass classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary c ...
and
multi-label classification
In machine learning, multi-label classification or multi-output classification is a variant of the classification problem where multiple nonexclusive labels may be assigned to each instance. Multi-label classification is a generalization of mult ...
.
Multi-task learning works because
regularization
Regularization may refer to:
* Regularization (linguistics)
* Regularization (mathematics)
* Regularization (physics)
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in ...
induced by requiring an algorithm to perform well on a related task can be superior to regularization that prevents
overfitting
mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitt ...
by penalizing all complexity uniformly. One situation where MTL may be particularly helpful is if the tasks share significant commonalities and are generally slightly under sampled.
However, as discussed below, MTL has also been shown to be beneficial for learning unrelated tasks.
[Romera-Paredes, B., Argyriou, A., Bianchi-Berthouze, N., & Pontil, M., (2012) Exploiting Unrelated Tasks in Multi-Task Learning. http://jmlr.csail.mit.edu/proceedings/papers/v22/romera12/romera12.pdf]
Methods
Task grouping and overlap
Within the MTL paradigm, information can be shared across some or all of the tasks. Depending on the structure of task relatedness, one may want to share information selectively across the tasks. For example, tasks may be grouped or exist in a hierarchy, or be related according to some general metric. Suppose, as developed more formally below, that the parameter vector modeling each task is a
linear combination of some underlying basis. Similarity in terms of this basis can indicate the relatedness of the tasks. For example, with
sparsity
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...
, overlap of nonzero coefficients across tasks indicates commonality. A task grouping then corresponds to those tasks lying in a subspace generated by some subset of basis elements, where tasks in different groups may be disjoint or overlap arbitrarily in terms of their bases. Task relatedness can be imposed a priori or learned from the data.
Hierarchical task relatedness can also be exploited implicitly without assuming a priori knowledge or learning relations explicitly.
[Hajiramezanali, E. & Dadaneh, S. Z. & Karbalayghareh, A. & Zhou, Z. & Qian, X. Bayesian multi-domain learning for cancer subtype discovery from next-generation sequencing count data. 32nd Conference on Neural Information Processing Systems (NIPS 2018), Montréal, Canada. ] For example, the explicit learning of sample relevance across tasks can be done to guarantee the effectiveness of joint learning across multiple domains.
Exploiting unrelated tasks
One can attempt learning a group of principal tasks using a group of auxiliary tasks, unrelated to the principal ones. In many applications, joint learning of unrelated tasks which use the same input data can be beneficial. The reason is that prior knowledge about task relatedness can lead to sparser and more informative representations for each task grouping, essentially by screening out idiosyncrasies of the data distribution. Novel methods which builds on a prior multitask methodology by favoring a shared low-dimensional representation within each task grouping have been proposed. The programmer can impose a penalty on tasks from different groups which encourages the two representations to be
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
. Experiments on synthetic and real data have indicated that incorporating unrelated tasks can result in significant improvements over standard multi-task learning methods.
[Romera-Paredes, B., Argyriou, A., Bianchi-Berthouze, N., & Pontil, M., (2012) Exploiting Unrelated Tasks in Multi-Task Learning. http://jmlr.csail.mit.edu/proceedings/papers/v22/romera12/romera12.pdf]
Transfer of knowledge
Related to multi-task learning is the concept of knowledge transfer. Whereas traditional multi-task learning implies that a shared representation is developed concurrently across tasks, transfer of knowledge implies a sequentially shared representation. Large scale machine learning projects such as the deep
convolutional neural network
In deep learning, a convolutional neural network (CNN, or ConvNet) is a class of artificial neural network (ANN), most commonly applied to analyze visual imagery. CNNs are also known as Shift Invariant or Space Invariant Artificial Neural Netwo ...
GoogLeNet, an image-based object classifier, can develop robust representations which may be useful to further algorithms learning related tasks. For example, the pre-trained model can be used as a feature extractor to perform pre-processing for another learning algorithm. Or the pre-trained model can be used to initialize a model with similar architecture which is then fine-tuned to learn a different classification task.
Group online adaptive learning
Traditionally Multi-task learning and transfer of knowledge are applied to stationary learning settings. Their extension to non-stationary environments is termed Group online adaptive learning (GOAL). Sharing information could be particularly useful if learners operate in continuously changing environments, because a learner could benefit from previous experience of another learner to quickly adapt to their new environment. Such group-adaptive learning has numerous applications, from predicting
financial time-series, through content recommendation systems, to visual understanding for adaptive autonomous agents.
Mathematics
Reproducing Hilbert space of vector valued functions (RKHSvv)
The MTL problem can be cast within the context of RKHSvv (a
complete
Complete may refer to:
Logic
* Completeness (logic)
* Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable
Mathematics
* The completeness of the real numbers, which implies t ...
inner product space
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often den ...
of
vector-valued function
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could ...
s equipped with a
reproducing kernel
In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions f and g in ...
). In particular, recent focus has been on cases where task structure can be identified via a separable kernel, described below. The presentation here derives from Ciliberto et al., 2015.
RKHSvv concepts
Suppose the training data set is
, with
,
, where indexes task, and
. Let
. In this setting there is a consistent input and output space and the same
loss function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost ...
for each task: . This results in the regularized machine learning problem:
where
is a vector valued reproducing kernel Hilbert space with functions
having components
.
The reproducing kernel for the space
of functions
is a symmetric matrix-valued function
, such that
and the following reproducing property holds:
The reproducing kernel gives rise to a representer theorem showing that any solution to equation has the form:
Separable kernels
The form of the kernel induces both the representation of the
feature space
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern r ...
and structures the output across tasks. A natural simplification is to choose a ''separable kernel,'' which factors into separate kernels on the input space and on the tasks
. In this case the kernel relating scalar components
and
is given by
. For vector valued functions
we can write
, where is a scalar reproducing kernel, and is a symmetric positive semi-definite
matrix. Henceforth denote
.
This factorization property, separability, implies the input feature space representation does not vary by task. That is, there is no interaction between the input kernel and the task kernel. The structure on tasks is represented solely by . Methods for non-separable kernels is an current field of research.
For the separable case, the representation theorem is reduced to
. The model output on the training data is then , where is the
empirical kernel matrix with entries
, and is the
matrix of rows
.
With the separable kernel, equation can be rewritten as
where is a (weighted) average of applied entry-wise to and . (The weight is zero if
is a missing observation).
Note the second term in can be derived as follows:
:
Known task structure
= Task structure representations
=
There are three largely equivalent ways to represent task structure: through a regularizer; through an output metric, and through an output mapping.
= Task structure examples
=
Via the regularizer formulation, one can represent a variety of task structures easily.
* Letting
(where
is the ''T''x''T'' identity matrix, and
is the ''T''x''T'' matrix of ones) is equivalent to letting control the variance
of tasks from their mean
. For example, blood levels of some biomarker may be taken on patients at
time points during the course of a day and interest may lie in regularizing the variance of the predictions across patients.
* Letting
, where
is equivalent to letting
control the variance measured with respect to a group mean:
. (Here
the cardinality of group r, and
is the indicator function). For example, people in different political parties (groups) might be regularized together with respect to predicting the favorability rating of a politician. Note that this penalty reduces to the first when all tasks are in the same group.
* Letting
, where
is the
Laplacian
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the ...
for the graph with
adjacency matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.
In the special case of a finite simp ...
''M'' giving pairwise similarities of tasks. This is equivalent to giving a larger penalty to the distance separating tasks ''t'' and ''s'' when they are more similar (according to the weight
,) i.e.
regularizes
.
* All of the above choices of A also induce the additional regularization term
which penalizes complexity in f more broadly.
Learning tasks together with their structure
Learning problem can be generalized to admit learning task matrix A as follows:
Choice of
must be designed to learn matrices ''A'' of a given type. See "Special cases" below.
= Optimization of
=
Restricting to the case of
convex
Convex or convexity may refer to:
Science and technology
* Convex lens, in optics
Mathematics
* Convex set, containing the whole line segment that joins points
** Convex polygon, a polygon which encloses a convex set of points
** Convex polytope ...
losses and
coercive
Coercion () is compelling a party to act in an involuntary manner by the use of threats, including threats to use force against a party. It involves a set of forceful actions which violate the free will of an individual in order to induce a desi ...
penalties Ciliberto ''et al.'' have shown that although is not convex jointly in ''C'' and ''A,'' a related problem is jointly convex.
Specifically on the convex set
, the equivalent problem
is convex with the same minimum value. And if
is a minimizer for then
is a minimizer for .
may be solved by a barrier method on a closed set by introducing the following perturbation:
The perturbation via the barrier
forces the objective functions to be equal to
on the boundary of
.
can be solved with a block coordinate descent method, alternating in ''C'' and ''A.'' This results in a sequence of minimizers
in that converges to the solution in as
, and hence gives the solution to .
= Special cases
=
Spectral penalties - Dinnuzo ''et al'' suggested setting ''F'' as the Frobenius norm
. They optimized directly using block coordinate descent, not accounting for difficulties at the boundary of
.
Clustered tasks learning - Jacob ''et al'' suggested to learn ''A'' in the setting where ''T'' tasks are organized in ''R'' disjoint clusters. In this case let
be the matrix with
. Setting
, and
, the task matrix
can be parameterized as a function of
:
, with terms that penalize the average, between clusters variance and within clusters variance respectively of the task predictions. M is not convex, but there is a convex relaxation
. In this formulation,
.
= Generalizations
=
Non-convex penalties - Penalties can be constructed such that A is constrained to be a graph Laplacian, or that A has low rank factorization. However these penalties are not convex, and the analysis of the barrier method proposed by Ciliberto et al. does not go through in these cases.
Non-separable kernels - Separable kernels are limited, in particular they do not account for structures in the interaction space between the input and output domains jointly. Future work is needed to develop models for these kernels.
Applications
Spam filtering
Using the principles of MTL, techniques for collaborative
spam filtering
Various anti-spam techniques are used to prevent email spam (unsolicited bulk email).
No technique is a complete solution to the spam problem, and each has trade-offs between incorrectly rejecting legitimate email (false positives) as opposed to ...
that facilitates personalization have been proposed. In large scale open membership email systems, most users do not label enough messages for an individual local
classifier to be effective, while the data is too noisy to be used for a global filter across all users. A hybrid global/individual classifier can be effective at absorbing the influence of users who label emails very diligently from the general public. This can be accomplished while still providing sufficient quality to users with few labeled instances.
Web search
Using boosted
decision trees
A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains condit ...
, one can enable implicit data sharing and regularization. This learning method can be used on web-search ranking data sets. One example is to use ranking data sets from several countries. Here, multitask learning is particularly helpful as data sets from different countries vary largely in size because of the cost of editorial judgments. It has been demonstrated that learning various tasks jointly can lead to significant improvements in performance with surprising reliability.
Software package
The Multi-Task Learning via StructurAl Regularization (MALSAR) Matlab package implements the following multi-task learning algorithms:
* Mean-Regularized Multi-Task Learning
* Multi-Task Learning with Joint Feature Selection
* Robust Multi-Task Feature Learning
* Trace-Norm Regularized Multi-Task Learning
* Alternating Structural Optimization
* Incoherent Low-Rank and Sparse Learning
* Robust Low-Rank Multi-Task Learning
* Clustered Multi-Task Learning
[Zhou, J., Chen, J., & Ye, J. (2011)]
Clustered multi-task learning via alternating structure optimization
Advances in Neural Information Processing Systems.
* Multi-Task Learning with Graph Structures
See also
*
Artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
*
Artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
*
Automated machine learning
Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready ...
(AutoML)
*
Evolutionary computation
In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, they ...
*
General game playing
General game playing (GGP) is the design of artificial intelligence programs to be able to play more than one game successfully. For many games like chess, computers are programmed to play these games using a specially designed algorithm, which ca ...
*
Human-based genetic algorithm In evolutionary computation, a human-based genetic algorithm (HBGA) is a genetic algorithm that allows humans to contribute solution suggestions to the evolutionary process. For this purpose, a HBGA has human interfaces for initialization, mutation, ...
*
Kernel methods for vector output Kernel methods are a well-established tool to analyze the relationship between input data and the corresponding output of a function. Kernels encapsulate the properties of functions in a Kernel trick, computationally efficient way and allow algorith ...
*
Multitask optimization
Multi-task optimization is a paradigm in the optimization literature that focuses on solving multiple self-contained tasks simultaneously.Gupta, A., Ong, Y. S., & Feng, L. (2018)Insights on transfer optimization: Because experience is the best t ...
*
Robot learning Robot learning is a research field at the intersection of machine learning and robotics. It studies techniques allowing a robot to acquire novel skills or adapt to its environment through learning algorithms. The embodiment of the robot, situated in ...
*
Transfer learning
Transfer learning (TL) is a research problem in machine learning (ML) that focuses on storing knowledge gained while solving one problem and applying it to a different but related problem. For example, knowledge gained while learning to recognize ...
References
{{Reflist
External links
The Biosignals Intelligence Group at UIUC
Software
*
ttps://web.archive.org/web/20131224113826/http://klcl.pku.edu.cn/member/sunxu/code.htm Online Multi-Task Learning Toolkit (OMT)A general-purpose online multi-task learning toolkit based on
conditional random field
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without consid ...
models and
stochastic gradient descent
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of ...
training (
C#,
.NET)
Machine learning