Traffic density estimation of signalised arterials with stop line detector and probe data

This research aims to develop a reliable density estimation method for signalised arterials based on cumulative counts from upstream and downstream detectors. In order to overcome counting errors associated with urban arterials with mid-link sinks and sources, CUmulative plots and Probe Integration for Travel timE estimation (CUPRITE) is employed for density estimation. The method, by utilizing probe vehicles’ samples, reduces or cancels the counting inconsistencies when vehicles’ conservation is not satisfied within a section. The method is tested in a controlled environment, and the authors demonstrate the effectiveness of CUPRITE for density estimation in a signalised section, and discuss issues associated with the method.

Traffic density estimation of signalised arterials with stop line detector and probe data

This research aims to develop a reliable density estimation method for signalised arterials based on cumulative counts from upstream and downstream detectors. In order to overcome counting errors associated with urban arterials with mid-link sinks and sources, CUmulative plots and Probe Integration for Travel timE estimation (CUPRITE) is employed for density estimation. The method, by utilizing probe vehicles’ samples, reduces or cancels the counting inconsistencies when vehicles’ conservation is not satisfied within a section. The method is tested in a controlled environment, and the authors demonstrate the effectiveness of CUPRITE for density estimation in a signalised section, and discuss issues associated with the method.

Simulation-based density estimation for time series using covariate data

This paper proposes a simulation-based density estimation technique for time series that exploits information found in covariate data. The method can be paired with a large range of parametric models used in time series estimation. We derive asymptotic properties of the estimator and illustrate attractive finite sample properties for a range of well-known econometric and financial applications.

Computationally Efficient Methods for MDL-Optimal Density Estimation and Data Clustering

The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

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

142 p.

Extension of the Ye and Shreeve group contribution method for density estimation of ionic liquids in a wide range of temperatures and pressures

An extension of the Ye and Shreeve group contribution method [C. Ye, J.M. Shreeve, J. Phys. Chem. A 111 (2007) 1456–1461] for the estimation of densities of ionic liquids (ILs) is here proposed. The new version here presented allows the estimation of densities of ionic liquids in wide ranges of temperature and pressure using the previously proposed parameter table. Coefficients of new density correlation proposed were estimated using experimental densities of nine imidazolium-based ionic liquids. The new density correlation was tested against experimental densities available in literature for ionic liquids based on imidazolium, pyridinium, pyrrolidinium and phosphonium cations. Predicted densities are in good agreement with experimental literature data in a wide range of temperatures (273.15–393.15 K) and pressures (0.10–100 MPa). For imidazolium-based ILs, the mean percent deviation (MPD) is 0.45% and 1.49% for phosphonium-based ILs. A low MPD ranging from 0.41% to 1.57% was also observed for pyridinium and pyrrolidinium-based ILs.

Multivariate Density Estimation: An SVM Approach

We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters.

Risk Bounds for Mixture Density Estimation

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron. Approximation and estimation bounds are given for the above methods. We extend and improve upon the estimation results of Li and Barron, and in particular prove an $O(\\frac{1}{\\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination.

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

A sparse kernel density estimation algorithm using forward constrained regression

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward constrained regression manner. The leave-one-out (LOO) test score is used for kernel selection. The jackknife parameter estimator subject to positivity constraint check is used for the parameter estimation of a single parameter at each forward step. As such the proposed approach is simple to implement and the associated computational cost is very low. An illustrative example is employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to that of the classical Parzen window estimate.

An orthogonal forward regression technique for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the desired response, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density (SKD) estimates. The proposed algorithm incrementally minimises a leave-one-out test score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights of the selected sparse model are finally updated using the multiplicative nonnegative quadratic programming algorithm, which ensures the nonnegative and unity constraints for the kernel weights and has the desired ability to reduce the model size further. Except for the kernel width, the proposed method has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Several examples demonstrate the ability of this simple regression-based approach to effectively construct a SKID estimate with comparable accuracy to that of the full-sample optimised PW density estimate. (c) 2007 Elsevier B.V. All rights reserved.

A forward-constrained regression algorithm for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward-constrained regression (FCR) manner. The proposed algorithm selects significant kernels one at a time, while the leave-one-out (LOO) test score is minimized subject to a simple positivity constraint in each forward stage. The model parameter estimation in each forward stage is simply the solution of jackknife parameter estimator for a single parameter, subject to the same positivity constraint check. For each selected kernels, the associated kernel width is updated via the Gauss-Newton method with the model parameter estimate fixed. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate the efficacy of the proposed approach.