6,022 research outputs found
Optimized parameter search for large datasets of the regularization parameter and feature selection for ridge regression
In this paper we propose mathematical optimizations to select the optimal regularization parameter for ridge regression using cross-validation. The resulting algorithm is suited for large datasets and the computational cost does not depend on the size of the training set. We extend this algorithm to forward or backward feature selection in which the optimal regularization parameter is selected for each possible feature set. These feature selection algorithms yield solutions with a sparse weight matrix using a quadratic cost on the norm of the weights. A naive approach to optimizing the ridge regression parameter has a computational complexity of the order with the number of applied regularization parameters, the number of folds in the validation set, the number of input features and the number of data samples in the training set. Our implementation has a computational complexity of the order . This computational cost is smaller than that of regression without regularization for large datasets and is independent of the number of applied regularization parameters and the size of the training set. Combined with a feature selection algorithm the algorithm is of complexity and for forward and backward feature selection respectively, with the number of selected features and the number of removed features. This is an order faster than and for the naive implementation, with for large datasets. To show the performance and reduction in computational cost, we apply this technique to train recurrent neural networks using the reservoir computing approach, windowed ridge regression, least-squares support vector machines (LS-SVMs) in primal space using the fixed-size LS-SVM approximation and extreme learning machines
Kernel-Based Ranking. Methods for Learning and Performance Estimation
Machine learning provides tools for automated construction of predictive
models in data intensive areas of engineering and science. The family of
regularized kernel methods have in the recent years become one of the mainstream
approaches to machine learning, due to a number of advantages the
methods share. The approach provides theoretically well-founded solutions
to the problems of under- and overfitting, allows learning from structured
data, and has been empirically demonstrated to yield high predictive performance
on a wide range of application domains. Historically, the problems
of classification and regression have gained the majority of attention in the
field. In this thesis we focus on another type of learning problem, that of
learning to rank.
In learning to rank, the aim is from a set of past observations to learn
a ranking function that can order new objects according to how well they
match some underlying criterion of goodness. As an important special case
of the setting, we can recover the bipartite ranking problem, corresponding
to maximizing the area under the ROC curve (AUC) in binary classification.
Ranking applications appear in a large variety of settings, examples
encountered in this thesis include document retrieval in web search, recommender
systems, information extraction and automated parsing of natural
language. We consider the pairwise approach to learning to rank, where
ranking models are learned by minimizing the expected probability of ranking
any two randomly drawn test examples incorrectly. The development
of computationally efficient kernel methods, based on this approach, has in
the past proven to be challenging. Moreover, it is not clear what techniques
for estimating the predictive performance of learned models are the most
reliable in the ranking setting, and how the techniques can be implemented
efficiently.
The contributions of this thesis are as follows. First, we develop
RankRLS, a computationally efficient kernel method for learning to rank,
that is based on minimizing a regularized pairwise least-squares loss. In
addition to training methods, we introduce a variety of algorithms for tasks
such as model selection, multi-output learning, and cross-validation, based
on computational shortcuts from matrix algebra. Second, we improve the fastest known training method for the linear version of the RankSVM algorithm,
which is one of the most well established methods for learning to
rank. Third, we study the combination of the empirical kernel map and reduced
set approximation, which allows the large-scale training of kernel machines
using linear solvers, and propose computationally efficient solutions
to cross-validation when using the approach. Next, we explore the problem
of reliable cross-validation when using AUC as a performance criterion,
through an extensive simulation study. We demonstrate that the proposed
leave-pair-out cross-validation approach leads to more reliable performance
estimation than commonly used alternative approaches. Finally, we present
a case study on applying machine learning to information extraction from
biomedical literature, which combines several of the approaches considered
in the thesis. The thesis is divided into two parts. Part I provides the background
for the research work and summarizes the most central results, Part
II consists of the five original research articles that are the main contribution
of this thesis.Siirretty Doriast
Polynomial-Chaos-based Kriging
Computer simulation has become the standard tool in many engineering fields
for designing and optimizing systems, as well as for assessing their
reliability. To cope with demanding analysis such as optimization and
reliability, surrogate models (a.k.a meta-models) have been increasingly
investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging
are two popular non-intrusive meta-modelling techniques. PCE surrogates the
computational model with a series of orthonormal polynomials in the input
variables where polynomials are chosen in coherency with the probability
distributions of those input variables. On the other hand, Kriging assumes that
the computer model behaves as a realization of a Gaussian random process whose
parameters are estimated from the available computer runs, i.e. input vectors
and response values. These two techniques have been developed more or less in
parallel so far with little interaction between the researchers in the two
fields. In this paper, PC-Kriging is derived as a new non-intrusive
meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal
polynomials (PCE) approximates the global behavior of the computational model
whereas Kriging manages the local variability of the model output. An adaptive
algorithm similar to the least angle regression algorithm determines the
optimal sparse set of polynomials. PC-Kriging is validated on various benchmark
analytical functions which are easy to sample for reference results. From the
numerical investigations it is concluded that PC-Kriging performs better than
or at least as good as the two distinct meta-modeling techniques. A larger gain
in accuracy is obtained when the experimental design has a limited size, which
is an asset when dealing with demanding computational models
A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression
Many machine learning problems can be formulated as predicting labels for a
pair of objects. Problems of that kind are often referred to as pairwise
learning, dyadic prediction or network inference problems. During the last
decade kernel methods have played a dominant role in pairwise learning. They
still obtain a state-of-the-art predictive performance, but a theoretical
analysis of their behavior has been underexplored in the machine learning
literature.
In this work we review and unify existing kernel-based algorithms that are
commonly used in different pairwise learning settings, ranging from matrix
filtering to zero-shot learning. To this end, we focus on closed-form efficient
instantiations of Kronecker kernel ridge regression. We show that independent
task kernel ridge regression, two-step kernel ridge regression and a linear
matrix filter arise naturally as a special case of Kronecker kernel ridge
regression, implying that all these methods implicitly minimize a squared loss.
In addition, we analyze universality, consistency and spectral filtering
properties. Our theoretical results provide valuable insights in assessing the
advantages and limitations of existing pairwise learning methods.Comment: arXiv admin note: text overlap with arXiv:1606.0427
Sparse Learning Package with Stability Selection and Application to Alzheimer's Disease
abstract: Sparse learning is a technique in machine learning for feature selection and dimensionality reduction, to find a sparse set of the most relevant features. In any machine learning problem, there is a considerable amount of irrelevant information, and separating relevant information from the irrelevant information has been a topic of focus. In supervised learning like regression, the data consists of many features and only a subset of the features may be responsible for the result. Also, the features might require special structural requirements, which introduces additional complexity for feature selection. The sparse learning package, provides a set of algorithms for learning a sparse set of the most relevant features for both regression and classification problems. Structural dependencies among features which introduce additional requirements are also provided as part of the package. The features may be grouped together, and there may exist hierarchies and over- lapping groups among these, and there may be requirements for selecting the most relevant groups among them. In spite of getting sparse solutions, the solutions are not guaranteed to be robust. For the selection to be robust, there are certain techniques which provide theoretical justification of why certain features are selected. The stability selection, is a method for feature selection which allows the use of existing sparse learning methods to select the stable set of features for a given training sample. This is done by assigning probabilities for the features: by sub-sampling the training data and using a specific sparse learning technique to learn the relevant features, and repeating this a large number of times, and counting the probability as the number of times a feature is selected. Cross-validation which is used to determine the best parameter value over a range of values, further allows to select the best parameter value. This is done by selecting the parameter value which gives the maximum accuracy score. With such a combination of algorithms, with good convergence guarantees, stable feature selection properties and the inclusion of various structural dependencies among features, the sparse learning package will be a powerful tool for machine learning research. Modular structure, C implementation, ATLAS integration for fast linear algebraic subroutines, make it one of the best tool for a large sparse setting. The varied collection of algorithms, support for group sparsity, batch algorithms, are a few of the notable functionality of the SLEP package, and these features can be used in a variety of fields to infer relevant elements. The Alzheimer Disease(AD) is a neurodegenerative disease, which gradually leads to dementia. The SLEP package is used for feature selection for getting the most relevant biomarkers from the available AD dataset, and the results show that, indeed, only a subset of the features are required to gain valuable insights.Dissertation/ThesisM.S. Computer Science 201
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