Datasets:
Amogh1221
/
ML_Dataset

Dataset card Data Studio Files
xet
Community
1
text
stringlengths
0
4.09k
Abstract: Good old on-line back-propagation for plain multi-layer perceptrons yields a very low 0.35% error rate on the famous MNIST handwritten digits benchmark. All we need to achieve this best result so far are many hidden layers, many neurons per layer, numerous deformed training images, and graphics cards to greatly speed up learning.
Title: Modelling and Verification of Multiple UAV Mission Using SMV
Abstract: Model checking has been used to verify the correctness of digital circuits, security protocols, communication protocols, as they can be modelled by means of finite state transition model. However, modelling the behaviour of hybrid systems like UAVs in a Kripke model is challenging. This work is aimed at capturing the behaviour of an UAV performing cooperative search mission into a Kripke model, so as to verify it against the temporal properties expressed in Computation Tree Logic (CTL). SMV model checker is used for the purpose of model checking.
Title: Developing Experimental Models for NASA Missions with ASSL
Abstract: NASA's new age of space exploration augurs great promise for deep space exploration missions whereby spacecraft should be independent, autonomous, and smart. Nowadays NASA increasingly relies on the concepts of autonomic computing, exploiting these to increase the survivability of remote missions, particularly when human tending is not feasible. Autonomic computing has been recognized as a promising approach to the development of self-managing spacecraft systems that employ onboard intelligence and rely less on control links. The Autonomic System Specification Language (ASSL) is a framework for formally specifying and generating autonomic systems. As part of long-term research targeted at the development of models for space exploration missions that rely on principles of autonomic computing, we have employed ASSL to develop formal models and generate functional prototypes for NASA missions. This helps to validate features and perform experiments through simulation. Here, we discuss our work on developing such missions with ASSL.
Title: Exploration Of The Dendritic Cell Algorithm Using The Duration Calculus
Abstract: As one of the newest members in Artificial Immune Systems (AIS), the Dendritic Cell Algorithm (DCA) has been applied to a range of problems. These applications mainly belong to the field of anomaly detection. However, real-time detection, a new challenge to anomaly detection, requires improvement on the real-time capability of the DCA. To assess such capability, formal methods in the research of rea-time systems can be employed. The findings of the assessment can provide guideline for the future development of the algorithm. Therefore, in this paper we use an interval logic based method, named the Duration Calculus (DC), to specify a simplified single-cell model of the DCA. Based on the DC specifications with further induction, we find that each individual cell in the DCA can perform its function as a detector in real-time. Since the DCA can be seen as many such cells operating in parallel, it is potentially capable of performing real-time detection. However, the analysis process of the standard DCA constricts its real-time capability. As a result, we conclude that the analysis process of the standard DCA should be replaced by a real-time analysis component, which can perform periodic analysis for the purpose of real-time detection.
Title: Free Energy Methods for Bayesian Inference: Efficient Exploration of Univariate Gaussian Mixture Posteriors
Abstract: Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure which originates from computational Statistical Physics. The principle is first to choose a "reaction coordinate", that is, a "direction" in which the target distribution is multimodal. In a second step, the marginal log-density of the reaction coordinate with respect to the posterior distribution is estimated; minus this quantity is called "free energy" in the computational Statistical Physics literature. To this end, we use adaptive biasing Markov chain algorithms which adapt their targeted invariant distribution on the fly, in order to overcome sampling barriers along the chosen reaction coordinate. Finally, we perform an importance sampling step in order to remove the bias and recover the true posterior. The efficiency factor of the importance sampling step can easily be estimated once the bias is known, and appears to be rather large for the test cases we considered. A crucial point is the choice of the reaction coordinate. One standard choice (used for example in the classical Wang-Landau algorithm) is minus the log-posterior density. We discuss other choices. We show in particular that the hyper-parameter that determines the order of magnitude of the variance of each component is both a convenient and an efficient reaction coordinate. We also show how to adapt the method to compute the evidence (marginal likelihood) of a mixture model. We illustrate our approach by analyzing two real data sets.
Title: Unsupervised Supervised Learning II: Training Margin Based Classifiers without Labels
Abstract: Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing a margin-based risk function. Traditionally, these risk functions are computed based on a labeled dataset. We develop a novel technique for estimating such risks using only unlabeled data and the marginal label distribution. We prove that the proposed risk estimator is consistent on high-dimensional datasets and demonstrate it on synthetic and real-world data. In particular, we show how the estimate is used for evaluating classifiers in transfer learning, and for training classifiers with no labeled data whatsoever.
Title: Scalable Large-Margin Mahalanobis Distance Metric Learning
Abstract: For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis distance metric. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (psd) matrix is the unknown variable. a specialized gradient descent method is proposed. our algorithm is much more efficient and has a better performance in scalability compared with existing methods. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.
Title: Model Selection with the Loss Rank Principle
Abstract: A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) - for model selection in regression and classification. It is based on the loss rank, which counts how many other (fictitious) data would be fitted better. LoRP selects the model that has minimal loss rank. Unlike most penalized maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the regression functions and the loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN.
Title: A Unified Algorithmic Framework for Multi-Dimensional Scaling
Abstract: In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is ; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods, in comparable time. We expect that this framework will be useful for a number of \mds variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a compliment to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, where projecting to a random $O((1/\eps^2) \log n)$-dimensional sphere causes $\eps$-distortion.
Title: A new model for solution of complex distributed constrained problems
Abstract: In this paper we describe an original computational model for solving different types of Distributed Constraint Satisfaction Problems (DCSP). The proposed model is called Controller-Agents for Constraints Solving (CACS). This model is intended to be used which is an emerged field from the integration between two paradigms of different nature: Multi-Agent Systems (MAS) and the Constraint Satisfaction Problem paradigm (CSP) where all constraints are treated in central manner as a black-box. This model allows grouping constraints to form a subset that will be treated together as a local problem inside the controller. Using this model allows also handling non-binary constraints easily and directly so that no translating of constraints into binary ones is needed. This paper presents the implementation outlines of a prototype of DCSP solver, its usage methodology and overview of the CACS application for timetabling problems.
Title: Agent Based Approaches to Engineering Autonomous Space Software
Abstract: Current approaches to the engineering of space software such as satellite control systems are based around the development of feedback controllers using packages such as MatLab's Simulink toolbox. These provide powerful tools for engineering real time systems that adapt to changes in the environment but are limited when the controller itself needs to be adapted. We are investigating ways in which ideas from temporal logics and agent programming can be integrated with the use of such control systems to provide a more powerful layer of autonomous decision making. This paper will discuss our initial approaches to the engineering of such systems.
Title: Linguistic Geometries for Unsupervised Dimensionality Reduction
Abstract: Text documents are complex high dimensional objects. To effectively visualize such data it is important to reduce its dimensionality and visualize the low dimensional embedding as a 2-D or 3-D scatter plot. In this paper we explore dimensionality reduction methods that draw upon domain knowledge in order to achieve a better low dimensional embedding and visualization of documents. We consider the use of geometries specified manually by an expert, geometries derived automatically from corpus statistics, and geometries computed from linguistic resources.
Title: Text Region Extraction from Business Card Images for Mobile Devices
Abstract: Designing a Business Card Reader (BCR) for mobile devices is a challenge to the researchers because of huge deformation in acquired images, multiplicity in nature of the business cards and most importantly the computational constraints of the mobile devices. This paper presents a text extraction method designed in our work towards developing a BCR for mobile devices. At first, the background of a camera captured image is eliminated at a coarse level. Then, various rule based techniques are applied on the Connected Components (CC) to filter out the noises and picture regions. The CCs identified as text are then binarized using an adaptive but light-weight binarization technique. Experiments show that the text extraction accuracy is around 98% for a wide range of resolutions with varying computation time and memory requirements. The optimum performance is achieved for the images of resolution 1024x768 pixels with text extraction accuracy of 98.54% and, space and time requirements as 1.1 MB and 0.16 seconds respectively.
Title: Binarizing Business Card Images for Mobile Devices
Abstract: Business card images are of multiple natures as these often contain graphics, pictures and texts of various fonts and sizes both in background and foreground. So, the conventional binarization techniques designed for document images can not be directly applied on mobile devices. In this paper, we have presented a fast binarization technique for camera captured business card images. A card image is split into small blocks. Some of these blocks are classified as part of the background based on intensity variance. Then the non-text regions are eliminated and the text ones are skew corrected and binarized using a simple yet adaptive technique. Experiment shows that the technique is fast, efficient and applicable for the mobile devices.
Title: Particle Filtering on the Audio Localization Manifold
Abstract: We present a novel particle filtering algorithm for tracking a moving sound source using a microphone array. If there are N microphones in the array, we track all $N \choose 2$ delays with a single particle filter over time. Since it is known that tracking in high dimensions is rife with difficulties, we instead integrate into our particle filter a model of the low dimensional manifold that these delays lie on. Our manifold model is based off of work on modeling low dimensional manifolds via random projection trees [1]. In addition, we also introduce a new weighting scheme to our particle filtering algorithm based on recent advancements in online learning. We show that our novel TDOA tracking algorithm that integrates a manifold model can greatly outperform standard particle filters on this audio tracking task.
Title: Statistical and Computational Tradeoffs in Stochastic Composite Likelihood
Abstract: Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of the estimators resolve the computation-accuracy tradeoff differently, and taken together they span a continuous spectrum of computation-accuracy tradeoff resolutions. We prove the consistency of the estimators, provide formulas for their asymptotic variance, statistical robustness, and computational complexity. We discuss experimental results in the context of Boltzmann machines and conditional random fields. The theoretical and experimental studies demonstrate the effectiveness of the estimators when the computational resources are insufficient. They also demonstrate that in some cases reduced computational complexity is associated with robustness thereby increasing statistical accuracy.
Title: Exponential Family Hybrid Semi-Supervised Learning
Abstract: We present an approach to semi-supervised learning based on an exponential family characterization. Our approach generalizes previous work on coupled priors for hybrid generative/discriminative models. Our model is more flexible and natural than previous approaches. Experimental results on several data sets show that our approach also performs better in practice.
Title: Securing Interactive Sessions Using Mobile Device through Visual Channel and Visual Inspection
Abstract: Communication channel established from a display to a device's camera is known as visual channel, and it is helpful in securing key exchange protocol. In this paper, we study how visual channel can be exploited by a network terminal and mobile device to jointly verify information in an interactive session, and how such information can be jointly presented in a user-friendly manner, taking into account that the mobile device can only capture and display a small region, and the user may only want to authenticate selective regions-of-interests. Motivated by applications in Kiosk computing and multi-factor authentication, we consider three security models: (1) the mobile device is trusted, (2) at most one of the terminal or the mobile device is dishonest, and (3) both the terminal and device are dishonest but they do not collude or communicate. We give two protocols and investigate them under the abovementioned models. We point out a form of replay attack that renders some other straightforward implementations cumbersome to use. To enhance user-friendliness, we propose a solution using visual cues embedded into the 2D barcodes and incorporate the framework of "augmented reality" for easy verifications through visual inspection. We give a proof-of-concept implementation to show that our scheme is feasible in practice.
Title: Automatically Discovering Hidden Transformation Chaining Constraints
Abstract: Model transformations operate on models conforming to precisely defined metamodels. Consequently, it often seems relatively easy to chain them: the output of a transformation may be given as input to a second one if metamodels match. However, this simple rule has some obvious limitations. For instance, a transformation may only use a subset of a metamodel. Therefore, chaining transformations appropriately requires more information. We present here an approach that automatically discovers more detailed information about actual chaining constraints by statically analyzing transformations. The objective is to provide developers who decide to chain transformations with more data on which to base their choices. This approach has been successfully applied to the case of a library of endogenous transformations. They all have the same source and target metamodel but have some hidden chaining constraints. In such a case, the simple metamodel matching rule given above does not provide any useful information.
Title: Asymptotic Results on Adaptive False Discovery Rate Controlling Procedures Based on Kernel Estimators
Abstract: The False Discovery Rate (FDR) is a commonly used type I error rate in multiple testing problems. It is defined as the expected False Discovery Proportion (FDP), that is, the expected fraction of false positives among rejected hypotheses. When the hypotheses are independent, the Benjamini-Hochberg procedure achieves FDR control at any pre-specified level. By construction, FDR control offers no guarantee in terms of power, or type II error. A number of alternative procedures have been developed, including plug-in procedures that aim at gaining power by incorporating an estimate of the proportion of true null hypotheses. In this paper, we study the asymptotic behavior of a class of plug-in procedures based on kernel estimators of the density of the $p$-values, as the number $m$ of tested hypotheses grows to infinity. In a setting where the hypotheses tested are independent, we prove that these procedures are asymptotically more powerful in two respects: (i) a tighter asymptotic FDR control for any target FDR level and (ii) a broader range of target levels yielding positive asymptotic power. We also show that this increased asymptotic power comes at the price of slower, non-parametric convergence rates for the FDP. These rates are of the form $m^-k/(2k+1)$, where $k$ is determined by the regularity of the density of the $p$-value distribution, or, equivalently, of the test statistics distribution. These results are applied to one- and two-sided tests statistics for Gaussian and Laplace location models, and for the Student model.
Title: Properties of the Discrete Pulse Transform for Multi-Dimensional Arrays
Abstract: This report presents properties of the Discrete Pulse Transform on multi-dimensional arrays introduced by the authors two or so years ago. The main result given here in Lemma 2.1 is also formulated in a paper to appear in IEEE Transactions on Image Processing. However, the proof, being too technical, was omitted there and hence it appears in full in this publication.
Title: Supervised Topic Models
Abstract: We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive an approximate maximum-likelihood procedure for parameter estimation, which relies on variational methods to handle intractable posterior expectations. Prediction problems motivate this research: we use the fitted model to predict response values for new documents. We test sLDA on two real-world problems: movie ratings predicted from reviews, and the political tone of amendments in the U.S. Senate based on the amendment text. We illustrate the benefits of sLDA versus modern regularized regression, as well as versus an unsupervised LDA analysis followed by a separate regression.
Title: Information Fusion for Anomaly Detection with the Dendritic Cell Algorithm
Abstract: Dendritic cells are antigen presenting cells that provide a vital link between the innate and adaptive immune system, providing the initial detection of pathogenic invaders. Research into this family of cells has revealed that they perform information fusion which directs immune responses. We have derived a Dendritic Cell Algorithm based on the functionality of these cells, by modelling the biological signals and differentiation pathways to build a control mechanism for an artificial immune system. We present algorithmic details in addition to experimental results, when the algorithm was applied to anomaly detection for the detection of port scans. The results show the Dendritic Cell Algorithm is sucessful at detecting port scans.
Title: Branch and Bound Algorithms for Maximizing Expected Improvement Functions
Abstract: Deterministic computer simulations are often used as a replacement for complex physical experiments. Although less expensive than physical experimentation, computer codes can still be time-consuming to run. An effective strategy for exploring the response surface of the deterministic simulator is the use of an approximation to the computer code, such as a Gaussian process (GP) model, coupled with a sequential sampling strategy for choosing design points that can be used to build the GP model. The ultimate goal of such studies is often the estimation of specific features of interest of the simulator output, such as the maximum, minimum, or a level set (contour). Before approximating such features with the GP model, sufficient runs of the computer simulator must be completed. Sequential designs with an expected improvement (EI) function can yield good estimates of the features with a minimal number of runs. The challenge is that the expected improvement function itself is often multimodal and difficult to maximize. We develop branch and bound algorithms for efficiently maximizing the EI function in specific problems, including the simultaneous estimation of a minimum and a maximum, and in the estimation of a contour. These branch and bound algorithms outperform other optimization strategies such as genetic algorithms, and over a number of sequential design steps can lead to dramatically superior accuracy in estimation of features of interest.
Title: Penalized maximum likelihood estimation for generalized linear point processes
Abstract: A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space and give results on Gateaux differentiability of the log-likelihood. Of particular interest is when the intensity is expressed in terms of a linear filter parametrized by a Sobolev space. Using that the Sobolev spaces are reproducing kernel Hilbert spaces we derive results on the representation of the penalized maximum likelihood estimator in a special case and the gradient of the negative log-likelihood in general. The latter is used to develop a descent algorithm in the Sobolev space. We conclude the paper by extensions to multivariate and additive model specifications. The methods are implemented in the R-package ppstat.
Title: Universality, Characteristic Kernels and RKHS Embedding of Measures
Abstract: A Hilbert space embedding for probability measures has recently been proposed, wherein any probability measure is represented as a mean element in a reproducing kernel Hilbert space (RKHS). Such an embedding has found applications in homogeneity testing, independence testing, dimensionality reduction, etc., with the requirement that the reproducing kernel is characteristic, i.e., the embedding is injective. In this paper, we generalize this embedding to finite signed Borel measures, wherein any finite signed Borel measure is represented as a mean element in an RKHS. We show that the proposed embedding is injective if and only if the kernel is universal. This therefore, provides a novel characterization of universal kernels, which are proposed in the context of achieving the Bayes risk by kernel-based classification/regression algorithms. By exploiting this relation between universality and the embedding of finite signed Borel measures into an RKHS, we establish the relation between universal and characteristic kernels.
Title: Approaches for multi-step density forecasts with application to aggregated wind power
Abstract: The generation of multi-step density forecasts for non-Gaussian data mostly relies on Monte Carlo simulations which are computationally intensive. Using aggregated wind power in Ireland, we study two approaches of multi-step density forecasts which can be obtained from simple iterations so that intensive computations are avoided. In the first approach, we apply a logistic transformation to normalize the data approximately and describe the transformed data using ARIMA--GARCH models so that multi-step forecasts can be iterated easily. In the second approach, we describe the forecast densities by truncated normal distributions which are governed by two parameters, namely, the conditional mean and conditional variance. We apply exponential smoothing methods to forecast the two parameters simultaneously. Since the underlying model of exponential smoothing is Gaussian, we are able to obtain multi-step forecasts of the parameters by simple iterations and thus generate forecast densities as truncated normal distributions. We generate forecasts for wind power from 15 minutes to 24 hours ahead. Results show that the first approach generates superior forecasts and slightly outperforms the second approach under various proper scores. Nevertheless, the second approach is computationally more efficient and gives more robust results under different lengths of training data. It also provides an attractive alternative approach since one is allowed to choose a particular parametric density for the forecasts, and is valuable when there are no obvious transformations to normalize the data.
Title: Extending The Range of Application of Permutation Tests: the Expected Permutation p-value Approach
Abstract: The limitation of permutation tests is that they assume exchangeability. It is shown that in generalized linear models one can construct permutation tests from score statistics in particular cases. When under the null hypothesis the observations are not exchangeable, a representation in terms of Cox-Snell residuals allows to develop an approach based on an expected permutation p-value (Eppv); this is applied to the logistic regression model. A small simulation study and an illustration with real data are given.
Title: Learning by random walks in the weight space of the Ising perceptron
Abstract: Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the synaptic weight configuration is modified through a chain of single- or double-weight flips within the compatible weight configuration space of the earlier learned patterns. This process is able to reach a storage capacity of $\alpha \approx 0.63$ for pattern length N = 101 and $\alpha \approx 0.41$ for N = 1001. If in addition a relearning process is exploited, the learning performance is further improved to a storage capacity of $\alpha \approx 0.80$ for N = 101 and $\alpha \approx 0.42$ for N=1001. We found that, for a given learning task, the solutions constructed by the random walk learning process are separated by a typical Hamming distance, which decreases with the constraint density $\alpha$ of the learning task; at a fixed value of $\alpha$, the width of the Hamming distance distributions decreases with $N$.
Title: An Offline Technique for Localization of License Plates for Indian Commercial Vehicles
Abstract: Automatic License Plate Recognition (ALPR) is a challenging area of research due to its importance to variety of commercial applications. The overall problem may be subdivided into two key modules, firstly, localization of license plates from vehicle images, and secondly, optical character recognition of extracted license plates. In the current work, we have concentrated on the first part of the problem, i.e., localization of license plate regions from Indian commercial vehicles as a significant step towards development of a complete ALPR system for Indian vehicles. The technique is based on color based segmentation of vehicle images and identification of potential license plate regions. True license plates are finally localized based on four spatial and horizontal contrast features. The technique successfully localizes the actual license plates in 73.4% images.
Title: From Frequency to Meaning: Vector Space Models of Semantics
Abstract: Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are beginning to address these limits. This paper surveys the use of VSMs for semantic processing of text. We organize the literature on VSMs according to the structure of the matrix in a VSM. There are currently three broad classes of VSMs, based on term-document, word-context, and pair-pattern matrices, yielding three classes of applications. We survey a broad range of applications in these three categories and we take a detailed look at a specific open source project in each category. Our goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs for those who are already familiar with the area, and to provide pointers into the literature for those who are less familiar with the field.
Title: Integrating Innate and Adaptive Immunity for Intrusion Detection
Abstract: Network Intrusion Detection Systems (NDIS) monitor a network with the aim of discerning malicious from benign activity on that network. While a wide range of approaches have met varying levels of success, most IDS's rely on having access to a database of known attack signatures which are written by security experts. Nowadays, in order to solve problems with false positive alters, correlation algorithms are used to add additional structure to sequences of IDS alerts. However, such techniques are of no help in discovering novel attacks or variations of known attacks, something the human immune system (HIS) is capable of doing in its own specialised domain. This paper presents a novel immune algorithm for application to an intrusion detection problem. The goal is to discover packets containing novel variations of attacks covered by an existing signature base.
Title: Hitting and commute times in large graphs are often misleading
Abstract: Next to the shortest path distance, the second most popular distance function between vertices in a graph is the commute distance (resistance distance). For two vertices u and v, the hitting time H_uv is the expected time it takes a random walk to travel from u to v. The commute time is its symmetrized version C_uv = H_uv + H_vu. In our paper we study the behavior of hitting times and commute distances when the number n of vertices in the graph is very large. We prove that as n converges to infinty, hitting times and commute distances converge to expressions that do not take into account the global structure of the graph at all. Namely, the hitting time H_uv converges to 1/d_v and the commute time to 1/d_u + 1/d_v where d_u and d_v denote the degrees of vertices u and v. In these cases, the hitting and commute times are misleading in the sense that they do not provide information about the structure of the graph. We focus on two major classes of random graphs: random geometric graphs (k-nearest neighbor graphs, epsilon-graphs, Gaussian similarity graphs) and random graphs with given expected degrees (in particular, Erdos-Renyi graphs with and without planted partitions)
Title: A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data
Abstract: For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to $n$ data points requires the computation of the inverse and determinant of $n \times n$ correlation matrices, $R$, that are sometimes computationally unstable due to near-singularity of $R$. This happens if any pair of design points are very close together in the input space. The popular approach to overcome near-singularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this paper, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy. We also show that the proposed predictor converges to the GP interpolator.