A Fractional Programming Framework for Support Vector Machine-type Formulations

We develop a theoretical framework for relating various formulations of regularization problems through fractional programming. We focus on problems with objective functions of the type L + λ · P , where the parameter λ lacks intuitive interpretation. We observe that fractional programming is an elegant approach to obtain bounds on the range of the parameter, and then generalize this approach to show that different forms can be obtained from a common fractional program. Furthermore, we apply the proposed framework in two concrete settings; we consider support vector machines (SVMs), where the framework clarifies the relation between various existing soft-margin dual forms for classification, and the SVM+ algorithm (Vapnik and Vashist, 2009), where we use this methodology to derive a new dual formulation, and obtain bounds on the cost parameter

Conic SMO

We derive an SMO-like algorithm for the optimization problem arising from the Second Order Cone Programming formulation of support vector machines (SVMs) for classification. Due to the square root term in the objective of the form, we cannot easily compute the location of the extrema using Newton‘s formula. Instead we modify the analytic solution proposed for SMO (Platt, 1999), to account for the particular objective function and partial derivatives. We then establish some theoretical properties of the algorithm based on the results of (Bordes et al., 2005), and develop practical working set selection similar to (Fan et al., 2005). In addition, we propose an efficient implementation, and compare the convergence rate of Conic-SMO and SMO on synthetic data

Scenario-based approach to analysis of travel time reliability with traffic simulation models

This study established a conceptual framework for capturing the probabilistic nature of travel times with the use of existing traffic simulation models. The framework features three components: scenario manager, traffic simulation models, and trajectory processor. The scenario manager captures exogenous sources of variation in travel times through external scenarios consistent with real-world roadway disruptions. The traffic simulation models then produce individual vehicle trajectories for input scenarios while further introducing randomness that stems from endogenous sources of variation. Finally, the trajectory processor constructs distributions of travel time either for each scenario or for multiple scenarios to allow users to investigate scenario-specific impact on variability in travel times and overall system reliability. Within this framework, the paper discusses methodologies for performing scenario-based reliability analysis that focuses on (a) approaches to obtaining distributions of travel times from scenario-specific outputs and (b) issues and practices associated with designing and generating input scenarios. The proposed scenario-based approach was applied to a real-world network to show detailed procedures, analysis results, and their implications

Impact of Capacity, Crowding, and Vehicle Arrival Adherence on Public Transport Ridership: Los Angeles and Sydney Experience and Forecasting Approach

This paper describes innovative aspects in the development of regional travel models for both Sydney and Los Angeles. The overall approach was to incorporate the effects of capacity, crowding, and delayed vehicle arrivals in the network supply, mode choice, and assignment modules. Capacity and crowding modules were first developed and applied in Sydney. The Los Angeles effort has built upon that work and will also consider variations in vehicle arrivals. Most travel models ignore the fact that transit vehicles have limited capacity. The most behaviorally realistic way to implement this feature was through extra weight functions applied at the boarding station. A method was also developed to take into account crowding as a negative factor in the user perception of transit service quality. The work revealed that the probability of having a seat should be reflected in the segment in-vehicle time weight. There is a strong indication, from existing research and the Stated Preference surveys undertaken in Sydney, that in-vehicle time for a standing passenger should be weighted more onerously compared to a seating passenger. Ridership in heavily congested corridors in Los Angeles has been adversely impacted by delays in vehicle arrivals and severe bunching. Estimated wait and in-vehicle time functions will be incorporated in an integrated mode choice model and assignment procedures as part of the work reported in this paper. These methods can be used by modelers dealing with urban transport systems that have reached, or will reach, capacity and experience serious congestion related delays

Data pre-processing for the preterm prediction study MFMU dataset

Preterm birth is a major public health problem with profound implications on society. There would be extreme value in being able to identify women at risk of preterm birth during the course of their pregnancy. Previous research has largely focused on individual risk factors correlated with preterm birth (e.g. prior preterm birth, race, and infection) and less on combining these factors in a way to understand the complex etiologies of preterm birth. We attempt to address this gap by conducting a deeper analysis of the preterm prediction study data collected by the NICHD Maternal Fetal Medicine Units (MFMU) Network, a high-quality data for over 3,000 singleton pregnancies having detailed study visits and biospecimen collection at 24, 26, 28 and 30 weeks gestation. Reports from this dataset used relatively straightforward biostatitistical methodologies such as relative risk assessments to measure associations between risk factors and PTB (Maternal Fetal Medicine Units Net- work. Biostatistical Coordinating Center NICHD Networks, 1995). These methods include descriptive statistics, Pearson correlation, Fisher’s exact tests and linear/logistic regression where risk factors are studied independent of each other. In order to perform detailed experiments on this data using non-linear Support Vector Machines and other machine learning (ML) methodologies, it is necessary to complete several pre-processing steps that we describe in this report

Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user classes

This paper presents a formulation of the multiple user class, variable demand, probit stochastic user equilibrium model. Sufficient conditions are stated for differentiability of the equilibrium flows of this model. This justifies the derivation of sensitivity expressions for the equilibrium flows, which are presented in a format that can be implemented in commercially available software. A numerical example verifies the sensitivity expressions, and that this formulation is applicable to large networks

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported