8818017
Using Model Trees for Classification
Model trees, which are a type of decision tree with linear regression functions at the leaves, form the basis of a recent successful technique for predicting continuous numeric values. They can be applied to classification problems by employing a standard method of transforming a classification problem into a problem of function approximation. Surprisingly, using this simple transformation the model tree inducer M5′, based on Quinlan's M5, generates more accurate classifiers than the state-of-the-art decision tree learner C5.0, particularly when most of the attributes are numeric.
5326806
Modeling for Optimal Probability Prediction
We present a general modeling method for optimal probability prediction over future observations, in which model dimensionality is determined as a natural by-product. This new method yields several estimators, and we establish theoretically that they are optimal (either overall or under stated restrictions) when the number of free parameters is infinite. As a case study, we investigate the problem of fitting logistic models in finite-sample situations. Simulation results on both artificial and practical datasets are supportive.
5074474
Maximum likelihood computation based on the Fisher scoring and Gauss-Newton quadratic approximations
The Fisher scoring and Gauss-Newton methods are two known methods for maximum likelihood computation. This paper provides a generalization for each method in a unified manner so that they can be used for some difficult maximum likelihood computation, when, for example, there exist constraints on the parameters. A generalized method does not use directly the Newton-type iteration formulas of these methods, but, instead, uses the corresponding quadratic functions transformed from them. It proceeds by repeatedly approximating the log-likelihood function with the quadratic functions in the neighborhoods of the current iterates and optimizing each quadratic function within the parameter space. It is shown that each quadratic function has a weighted linear regression formulation, which can be conveniently solved. This generalization also extends the applicability of the Fisher scoring method to situations when the expected Fisher information matrices are unavailable in closed form. Fast computation can generally be anticipated, owing to their small rates of convergence and a rapid solution of each linear regression problem. While the generalized Gauss-Newton method may sometimes suffer for the so-called large residual problem, the generalized Fisher scoring method has performed consistently well in the numerical experiments we conducted.
1436962
Predicting query times
We outline the need for search engines to provide user feedback on the expected time for a query, describe a scheme for learning a model of query time by observing sample queries, and discuss the results obtained for a set of actual user queries on a document collection using the MG search engine.
17202693
Multiobjective programming using uniform design and genetic algorithm
The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.
6142906
Multiple attribute decision making based on fuzzy preference information on alternatives: Ranking and weighting
This paper investigates the multiple attribute decision making (MADM) problem with fuzzy preference information on alternatives and proposes an eigenvector method to rank them. Three optimization models are introduced to assess the relative importance weights of attributes in a MADM problem, which integrate subjective fuzzy preference relations and objective information in different ways. Since the decisions these models lead to are based on both subjective and objective information, they are more balanced and credible than those that consider only one type of information. An example is provided to illustrate the application of the proposed models.
2456151
Subdivision Schemes and Refinement Equations with Nonnegative Masks
We consider the two-scale refinement equation f(x)=@?^N"n"="0c"nf(2x-n) with @?"nc"2"n=@?"nc"2"n"+"1=1 where c"0, c"N 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all c"n>=0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 00} is 1. We prove the conjecture for a large class of refinement equations.
509991
Brain Surface Conformal Parameterization with Algebraic Functions
In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.
15514608
Application of Relief-F feature filtering algorithm to selecting informative genes for cancer classification using microarray data
Numerous recent studies have shown that microarray gene expression data is useful for cancer classification. Classification based on microarray data is very different from previous classification problems in that the number of features (genes) greatly exceeds the number of instances (tissue samples). It has been shown that selecting a small set of informative genes can lead to improved classification accuracy. It is thus important to first apply feature selection methods prior to classification. In the machine learning field, one of the most successful feature filtering algorithms is the Relief-F algorithm. In this work, we empirically evaluate its performance on three published cancer classification data sets. We use the linear SVM and the k-NN as classifiers in the experiments, and compare the performance of Relief-F with other feature filtering methods, including Information Gain, Gain Ratio, and /spl chi//sup 2/-statistic. Using the leave-one-out cross validation, experimental results show that the performance of Relief-F is comparable with other methods.