Sistema konkurrenteak simulatzeko kernel bat: multiprozesadore sistemak

Jarraian, hainbat hilabetetan zehar garatutako proiektuaren deskribapena biltzen duen memoria dugu eskuragarri. Proiektu hau, sistema konkurrenteen simulazioan zentratzen da eta horretarako, mota honetako sistemen arloan hain erabiliak diren Petri Sareak lantzeaz gain, simulatzaile bat programatzeko informazio nahikoa ere barneratzen ditu. Gertaera diskretuko simulatzaile estatistiko batean oinarrituko da proiektuaren garapena, helburua izanik Petri Sareen bidez formalizatzen diren sistemak simulatzeko softwarea osatzea. Proiektuaren helburua da objektuetara zuzendutako hizkuntzaren bidez, Java hizkuntzaren bidez alegia, simulatzailearen programazioa erraztea eta ingurune honen baliabideak erabiltzea, bereziki XML teknologiari lotutakoak. Proiektu hau, bi zati nagusitan banatzen dela esan daiteke. Lehenengo zatiari dagokionez, konputazio munduan simulazioa aurkeztu eta honi buruzko behar adina informazio emango da. Hau, oso erabilgarria izango da programatuko den simulatzailearen nondik norakoak ulertu eta klase desberdinen inplementazioa egin ahal izateko. Horrez gain, zorizko aldagaiak eta hauen simulazioa ere islatzen dira, simulazio prozesu hori ahalik eta era errealean gauzatzeko helburuarekin. Ondoren, Petri Sareak aurkeztuko dira, hauen ezaugarri eta sailkapen desberdinak goraipatuz. Gainera, Petri Sareak definitzeko XML lengoaia erabiliko denez, mota honetako dokumentu eta eskemak aztertuko dira, hauek, garatuko den aplikazioaren oinarri izango direlarik. Bestalde, aplikazioaren muin izango diren klaseen diseinu eta inplementazioak bildu dira azken aurreko kapituluan. Alde batetik, erabili den DOM egituraren inguruko informazioa islatzen da eta bestetik, XML-tik habiatuz lortuko diren PetriNet instantziak maneiatzeko ezinbestekoak diren Java klaseen kodeak erakusten dira. Amaitzeko, egileak ateratako ondorioez gain, proiektuaren garapen prozesuan erabili den bibliografiaren berri ere ematen da.

Contributions to the efficient use of general purpose coprocessors: kernel density estimation as case study

142 p.

Copula-based Kernel Dependency Measures

The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous properties. Similarly to Shannon mutual information, the proposed dependence measure is invariant to any strictly increasing transformation of the marginal variables. This is important in many applications, for example in feature selection. The estimator is consistent, robust to outliers, and uses rank statistics only. We derive upper bounds on the convergence rate and propose independence tests too. We illustrate the theoretical contributions through a series of experiments in feature selection and low-dimensional embedding of distributions.

Structure Discovery in Nonparametric Regression through Compositional Kernel Search

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirrors the scientific discovery process. The learned structures can often decompose functions into interpretable components and enable long-range extrapolation on time-series datasets. Our structure search method outperforms many widely used kernels and kernel combination methods on a variety of prediction tasks.

Kernel conditional quantile estimation via reduction revisited

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches. © 2009 IEEE.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

The Random Forest Kernel and other kernels for big data from random partitions

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random Forest. To demonstrate the potential of this method, we propose two new kernels, the Random Forest Kernel and the Fast Cluster Kernel, and show that these kernels consistently outperform standard kernels on problems involving real-world datasets. Finally, we show how the form of these kernels lend themselves to a natural approximation that is appropriate for certain big data problems, allowing $O(N)$ inference in methods such as Gaussian Processes, Support Vector Machines and Kernel PCA.