26,290 research outputs found
Model Selection Techniques for Kernel-Based Regression Analysis Using Information Complexity Measure and Genetic Algorithms
In statistical modeling, an overparameterized model leads to poor generalization on unseen data points. This issue requires a model selection technique that appropriately chooses the form, the parameters of the proposed model and the independent variables retained for the modeling. Model selection is particularly important for linear and nonlinear statistical models, which can be easily overfitted.
Recently, support vector machines (SVMs), also known as kernel-based methods, have drawn much attention as the next generation of nonlinear modeling techniques. The model selection issues for SVMs include the selection of the kernel, the corresponding parameters and the optimal subset of independent variables. In the current literature, k-fold cross-validation is the widely utilized model selection method for SVMs by the machine learning researchers. However, cross-validation is computationally intensive since one has to fit the model k times.
This dissertation introduces the use of a model selection criterion based on information complexity (ICOMP) measure for kernel-based regression analysis and its applications. ICOMP penalizes both the lack-of-fit and the complexity of the model to choose the optimal model with good generalization properties. ICOMP provides a simple index for each model and does not require any validation data. It is computationally efficient and it has been successfully applied to various linear model selection problems. In this dissertation, we introduce ICOMP to the nonlinear kernel-based modeling areas. Specifically, this dissertation proposes ICOMP and its various forms in the area of kernel ridge regression; kernel partial least squares regression; kernel principal component analysis; kernel principal component regression; relevance vector regression; relevance vector logistic regression and classification problems. The model selection tasks achieved by our proposed criterion include choosing the form of the kernel function, the parameters of the kernel function, the ridge parameter, the number of latent variables, the number of principal components and the optimal subset of input variables in a simultaneous fashion for intelligent data mining.
The performance of the proposed model selection method is tested on simulation bench- mark data sets as well as real data sets. The predictive performance of the proposed model selection criteria are comparable to and even better than cross-validation, which is too costly to compute and not efficient.
This dissertation combines the Genetic Algorithm with ICOMP in variable subsetting, which significantly decreases the computational time as compared to the exhaustive search of all possible subsets. GA procedure is shown to be robust and performs well in our repeated simulation examples.
Therefore, this dissertation provides researchers an alternative computationally efficient model selection approach for data analysis using kernel methods
Bounded Coordinate-Descent for Biological Sequence Classification in High Dimensional Predictor Space
We present a framework for discriminative sequence classification where the
learner works directly in the high dimensional predictor space of all
subsequences in the training set. This is possible by employing a new
coordinate-descent algorithm coupled with bounding the magnitude of the
gradient for selecting discriminative subsequences fast. We characterize the
loss functions for which our generic learning algorithm can be applied and
present concrete implementations for logistic regression (binomial
log-likelihood loss) and support vector machines (squared hinge loss).
Application of our algorithm to protein remote homology detection and remote
fold recognition results in performance comparable to that of state-of-the-art
methods (e.g., kernel support vector machines). Unlike state-of-the-art
classifiers, the resulting classification models are simply lists of weighted
discriminative subsequences and can thus be interpreted and related to the
biological problem
Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification
We propose a high dimensional classification method that involves
nonparametric feature augmentation. Knowing that marginal density ratios are
the most powerful univariate classifiers, we use the ratio estimates to
transform the original feature measurements. Subsequently, penalized logistic
regression is invoked, taking as input the newly transformed or augmented
features. This procedure trains models equipped with local complexity and
global simplicity, thereby avoiding the curse of dimensionality while creating
a flexible nonlinear decision boundary. The resulting method is called Feature
Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by
generalizing the Naive Bayes model, writing the log ratio of joint densities as
a linear combination of those of marginal densities. It is related to
generalized additive models, but has better interpretability and computability.
Risk bounds are developed for FANS. In numerical analysis, FANS is compared
with competing methods, so as to provide a guideline on its best application
domain. Real data analysis demonstrates that FANS performs very competitively
on benchmark email spam and gene expression data sets. Moreover, FANS is
implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure
Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States
Motivated by the problem of predicting sleep states, we develop a mixed
effects model for binary time series with a stochastic component represented by
a Gaussian process. The fixed component captures the effects of covariates on
the binary-valued response. The Gaussian process captures the residual
variations in the binary response that are not explained by covariates and past
realizations. We develop a frequentist modeling framework that provides
efficient inference and more accurate predictions. Results demonstrate the
advantages of improved prediction rates over existing approaches such as
logistic regression, generalized additive mixed model, models for ordinal data,
gradient boosting, decision tree and random forest. Using our proposed model,
we show that previous sleep state and heart rates are significant predictors
for future sleep states. Simulation studies also show that our proposed method
is promising and robust. To handle computational complexity, we utilize Laplace
approximation, golden section search and successive parabolic interpolation.
With this paper, we also submit an R-package (HIBITS) that implements the
proposed procedure.Comment: Journal of Classification (2018
Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages
We propose an efficient nonparametric strategy for learning a message
operator in expectation propagation (EP), which takes as input the set of
incoming messages to a factor node, and produces an outgoing message as output.
This learned operator replaces the multivariate integral required in classical
EP, which may not have an analytic expression. We use kernel-based regression,
which is trained on a set of probability distributions representing the
incoming messages, and the associated outgoing messages. The kernel approach
has two main advantages: first, it is fast, as it is implemented using a novel
two-layer random feature representation of the input message distributions;
second, it has principled uncertainty estimates, and can be cheaply updated
online, meaning it can request and incorporate new training data when it
encounters inputs on which it is uncertain. In experiments, our approach is
able to solve learning problems where a single message operator is required for
multiple, substantially different data sets (logistic regression for a variety
of classification problems), where it is essential to accurately assess
uncertainty and to efficiently and robustly update the message operator.Comment: accepted to UAI 2015. Correct typos. Add more content to the
appendix. Main results unchange
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