Diffusion limits of the random walk Metropolis algorithm in high dimensions

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring high-dimensional measures found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.Comment: Published in at http://dx.doi.org/10.1214/10-AAP754 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entropic measures of individual mobility patterns

Understanding human mobility from a microscopic point of view may represent a fundamental breakthrough for the development of a statistical physics for cognitive systems and it can shed light on the applicability of macroscopic statistical laws for social systems. Even if the complexity of individual behaviors prevents a true microscopic approach, the introduction of mesoscopic models allows the study of the dynamical properties for the non-stationary states of the considered system. We propose to compute various entropy measures of the individual mobility patterns obtained from GPS data that record the movements of private vehicles in the Florence district, in order to point out new features of human mobility related to the use of time and space and to define the dynamical properties of a stochastic model that could generate similar patterns. Moreover, we can relate the predictability properties of human mobility to the distribution of time passed between two successive trips. Our analysis suggests the existence of a hierarchical structure in the mobility patterns which divides the performed activities into three different categories, according to the time cost, with different information contents. We show that a Markov process defined by using the individual mobility network is not able to reproduce this hierarchy, which seems the consequence of different strategies in the activity choice. Our results could contribute to the development of governance policies for a sustainable mobility in modern cities

A new perspective to measure delayed recognition in a simple way

The phenomenon of delayed recognition in scientific discoveries is enjoying an ever increasing attention, as it is seen of potential scientific and even commercial values. This poster firstly reviews the performance of existing approaches in measuring the phenomenon of delayed recognition, and then tries to find a new perspective to better understand it. Literature review shows defects in terms of applicability, reasonability and complexity in currently existing approaches, as well as the usefulness of two measures in this study. Specifically, correlation analysis on the two measures suggests a high positive correlation between them, and formula derivation further uncovers a decisive common term in their equations. Based on the logic behind this common term, the idea of weighted summation of yearly citations is suggested to quantify how much a single paper’s citations are delayed, but there still lacks empirical studies

An Approach for the Empirical Validation of Software Complexity Measures

Software metrics are widely accepted tools to control and assure software quality. A large number of software metrics with a variety of content can be found in the literature; however most of them are not adopted in industry as they are seen as irrelevant to needs, as they are unsupported, and the major reason behind this is due to improper empirical validation. This paper tries to identify possible root causes for the improper empirical validation of the software metrics. A practical model for the empirical validation of software metrics is proposed along with root causes. The model is validated by applying it to recently proposed and well known metrics

Evaluation Criteria for Object-oriented Metrics

In this paper an evaluation model for object-oriented (OO) metrics is proposed. We have evaluated the existing evaluation criteria for OO metrics, and based on the observations, a model is proposed which tries to cover most of the features for the evaluation of OO metrics. The model is validated by applying it to existing OO metrics. In contrast to the other existing criteria, the proposed model is simple in implementation and includes the practical and important aspects of evaluation; hence it suitable to evaluate and validate any OO complexity metric

Extensions of SNOMED taxonomy abstraction networks supporting auditing and complexity analysis

The Systematized Nomenclature of Medicine – Clinical Terms (SNOMED CT) has been widely used as a standard terminology in various biomedical domains. The enhancement of the quality of SNOMED contributes to the improvement of the medical systems that it supports. In previous work, the Structural Analysis of Biomedical Ontologies Center (SABOC) team has defined the partial-area taxonomy, a hierarchical abstraction network consisting of units called partial-areas. Each partial-area comprises a set of SNOMED concepts exhibiting a particular relationship structure and being distinguished by a unique root concept. In this dissertation, some extensions and applications of the taxonomy framework are considered. Some concepts appearing in multiple partial-areas have been designated as complex due to the fact that they constitute a tangled portion of a hierarchy and can be obstacles to users trying to gain an understanding of the hierarchy’s content. A methodology for partitioning the entire collection of these so-called overlapping complex concepts into singly-rooted groups was presented. A novel auditing methodology based on an enhanced abstraction network is described. In addition, the existing abstraction network relies heavily on the structure of the outgoing relationships of the concepts. But some of SNOMED hierarchies (or subhierarchies) serve only as targets of relationships, with few or no outgoing relationships of their own. This situation impedes the applicability of the abstraction network. To deal with this problem, a variation of the above abstraction network, called the converse abstraction network (CAN) is defined and derived automatically from a given SNOMED hierarchy. An auditing methodology based on the CAN is formulated. Furthermore, a preliminary study of the complementary use of the abstraction network in description logic (DL) for quality assurance purposes pertaining to SNOMED is presented. Two complexity measures, a structural complexity measure and a hierarchical complexity measure, based on the abstraction network are introduced to quantify the complexity of a SNOMED hierarchy. An extension of the two measures is also utilized specifically to track the complexity of the versions of the SNOMED hierarchies before and after a sequence of auditing processes

Applicability of Weyuker’s Properties on OO Metrics: Some Misunderstandings

Weyuker’s properties have been suggested as a guiding tool in identification of a good and comprehensive complexity measure by several researchers. Weyuker proposed nine properties to evaluate complexity measure for traditional programming. However, they are extensively used for evaluating object-oriented (OO) metrics, although the object-oriented features are entirely different in nature. In this paper, two recently reported OO metrics were evaluated and, based on it; the usefulness and relevance of these properties for evaluation purpose for object-oriented systems is discussed

Software Measurement Activities in Small and Medium Enterprises: an Empirical Assessment

An empirical study for evaluating the proper implementation of measurement/metric programs in software companies in one area of Turkey is presented. The research questions are discussed and validated with the help of senior software managers (more than 15 years’ experience) and then used for interviewing a variety of medium and small scale software companies in Ankara. Observations show that there is a common reluctance/lack of interest in utilizing measurements/metrics despite the fact that they are well known in the industry. A side product of this research is that internationally recognized standards such as ISO and CMMI are pursued if they are a part of project/job requirements; without these requirements, introducing those standards to the companies remains as a long-term target to increase quality

The rationale of e-health evaluation: The case of NHS Direct

An important area of research is that of the evaluation of e-health services. A holistic e-health evaluation framework should address the aspects that are hampering healthcare services from embracing the full potential of information and communication technologies towards successful e-health initiatives. Towards building a holistic evaluation framework for e-health services, this paper is intended to examine the rationale of e-health evaluation, as the paper argues that this aspect should be addressed first in the development of such a framework. NHS Direct which is one of the largest e-health services in the world has been chosen to discuss and validate a set of evaluation rationales and their applicability in practice