984 research outputs found
Otimização multi-objetivo em aprendizado de máquina
Orientador: Fernando José Von ZubenTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Regressão logística multinomial regularizada, classificação multi-rótulo e aprendizado multi-tarefa são exemplos de problemas de aprendizado de máquina em que objetivos conflitantes, como funções de perda e penalidades que promovem regularização, devem ser simultaneamente minimizadas. Portanto, a perspectiva simplista de procurar o modelo de aprendizado com o melhor desempenho deve ser substituída pela proposição e subsequente exploração de múltiplos modelos de aprendizado eficientes, cada um caracterizado por um compromisso (trade-off) distinto entre os objetivos conflitantes. Comitês de máquinas e preferências a posteriori do tomador de decisão podem ser implementadas visando explorar adequadamente este conjunto diverso de modelos de aprendizado eficientes, em busca de melhoria de desempenho. A estrutura conceitual multi-objetivo para aprendizado de máquina é suportada por três etapas: (1) Modelagem multi-objetivo de cada problema de aprendizado, destacando explicitamente os objetivos conflitantes envolvidos; (2) Dada a formulação multi-objetivo do problema de aprendizado, por exemplo, considerando funções de perda e termos de penalização como objetivos conflitantes, soluções eficientes e bem distribuídas ao longo da fronteira de Pareto são obtidas por um solver determinístico e exato denominado NISE (do inglês Non-Inferior Set Estimation); (3) Esses modelos de aprendizado eficientes são então submetidos a um processo de seleção de modelos que opera com preferências a posteriori, ou a filtragem e agregação para a síntese de ensembles. Como o NISE é restrito a problemas de dois objetivos, uma extensão do NISE capaz de lidar com mais de dois objetivos, denominada MONISE (do inglês Many-Objective NISE), também é proposta aqui, sendo uma contribuição adicional que expande a aplicabilidade da estrutura conceitual proposta. Para atestar adequadamente o mérito da nossa abordagem multi-objetivo, foram realizadas investigações mais específicas, restritas à aprendizagem de modelos lineares regularizados: (1) Qual é o mérito relativo da seleção a posteriori de um único modelo de aprendizado, entre os produzidos pela nossa proposta, quando comparado com outras abordagens de modelo único na literatura? (2) O nível de diversidade dos modelos de aprendizado produzidos pela nossa proposta é superior àquele alcançado por abordagens alternativas dedicadas à geração de múltiplos modelos de aprendizado? (3) E quanto à qualidade de predição da filtragem e agregação dos modelos de aprendizado produzidos pela nossa proposta quando aplicados a: (i) classificação multi-classe, (ii) classificação desbalanceada, (iii) classificação multi-rótulo, (iv) aprendizado multi-tarefa, (v) aprendizado com multiplos conjuntos de atributos? A natureza determinística de NISE e MONISE, sua capacidade de lidar adequadamente com a forma da fronteira de Pareto em cada problema de aprendizado, e a garantia de sempre obter modelos de aprendizado eficientes são aqui pleiteados como responsáveis pelos resultados promissores alcançados em todas essas três frentes de investigação específicasAbstract: Regularized multinomial logistic regression, multi-label classification, and multi-task learning are examples of machine learning problems in which conflicting objectives, such as losses and regularization penalties, should be simultaneously minimized. Therefore, the narrow perspective of looking for the learning model with the best performance should be replaced by the proposition and further exploration of multiple efficient learning models, each one characterized by a distinct trade-off among the conflicting objectives. Committee machines and a posteriori preferences of the decision-maker may be implemented to properly explore this diverse set of efficient learning models toward performance improvement. The whole multi-objective framework for machine learning is supported by three stages: (1) The multi-objective modelling of each learning problem, explicitly highlighting the conflicting objectives involved; (2) Given the multi-objective formulation of the learning problem, for instance, considering loss functions and penalty terms as conflicting objective functions, efficient solutions well-distributed along the Pareto front are obtained by a deterministic and exact solver named NISE (Non-Inferior Set Estimation); (3) Those efficient learning models are then subject to a posteriori model selection, or to ensemble filtering and aggregation. Given that NISE is restricted to two objective functions, an extension for many objectives, named MONISE (Many Objective NISE), is also proposed here, being an additional contribution and expanding the applicability of the proposed framework. To properly access the merit of our multi-objective approach, more specific investigations were conducted, restricted to regularized linear learning models: (1) What is the relative merit of the a posteriori selection of a single learning model, among the ones produced by our proposal, when compared with other single-model approaches in the literature? (2) Is the diversity level of the learning models produced by our proposal higher than the diversity level achieved by alternative approaches devoted to generating multiple learning models? (3) What about the prediction quality of ensemble filtering and aggregation of the learning models produced by our proposal on: (i) multi-class classification, (ii) unbalanced classification, (iii) multi-label classification, (iv) multi-task learning, (v) multi-view learning? The deterministic nature of NISE and MONISE, their ability to properly deal with the shape of the Pareto front in each learning problem, and the guarantee of always obtaining efficient learning models are advocated here as being responsible for the promising results achieved in all those three specific investigationsDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétrica2014/13533-0FAPES
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Positive Definite Kernels in Machine Learning
This survey is an introduction to positive definite kernels and the set of
methods they have inspired in the machine learning literature, namely kernel
methods. We first discuss some properties of positive definite kernels as well
as reproducing kernel Hibert spaces, the natural extension of the set of
functions associated with a kernel defined
on a space . We discuss at length the construction of kernel
functions that take advantage of well-known statistical models. We provide an
overview of numerous data-analysis methods which take advantage of reproducing
kernel Hilbert spaces and discuss the idea of combining several kernels to
improve the performance on certain tasks. We also provide a short cookbook of
different kernels which are particularly useful for certain data-types such as
images, graphs or speech segments.Comment: draft. corrected a typo in figure
Recovery under Side Constraints
This paper addresses sparse signal reconstruction under various types of
structural side constraints with applications in multi-antenna systems. Side
constraints may result from prior information on the measurement system and the
sparse signal structure. They may involve the structure of the sensing matrix,
the structure of the non-zero support values, the temporal structure of the
sparse representationvector, and the nonlinear measurement structure. First, we
demonstrate how a priori information in form of structural side constraints
influence recovery guarantees (null space properties) using L1-minimization.
Furthermore, for constant modulus signals, signals with row-, block- and
rank-sparsity, as well as non-circular signals, we illustrate how structural
prior information can be used to devise efficient algorithms with improved
recovery performance and reduced computational complexity. Finally, we address
the measurement system design for linear and nonlinear measurements of sparse
signals. Moreover, we discuss the linear mixing matrix design based on
coherence minimization. Then we extend our focus to nonlinear measurement
systems where we design parallel optimization algorithms to efficiently compute
stationary points in the sparse phase retrieval problem with and without
dictionary learning
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