Leveraging Multiple Linear Regression for Wavelength Selection

In multivariate calibration, wavelengths selection is often used to lower prediction errors of sample properties. As a result, many methods have been created to select wavelengths. Several of the wavelength selection methods involve many tuning parameters that are typically complex or difficult to work with. The purpose of this poster is to show an easy way to select wavelengths while using few simple tuning parameters. The proposed method uses multiple linear regression (MLR) as an indicator to which wavelengths should be used to create a model. From a collection of random MLR models, those models with an acceptable bias/variance balance are evaluated to determine the wavelengths most frequently used. Portions of the most frequently selected wavelengths are chosen as the final MLR selected wavelengths. These MLR selected wavelengths are used to produce a calibration model by the method of partial least squares (PLS). This proposed wavelength selection method is compared to PLS models containing all wavelengths using several near infrared data sets. The PLS models with the selected wavelengths show an improvement in prediction error, suggesting this method as a simple way to select wavelengths

Leveraging Equivariant Features for Absolute Pose Regression

While end-to-end approaches have achieved state-of-the-art performance in many perception tasks, they are not yet able to compete with 3D geometry-based methods in pose estimation. Moreover, absolute pose regression has been shown to be more related to image retrieval. As a result, we hypothesize that the statistical features learned by classical Convolutional Neural Networks do not carry enough geometric information to reliably solve this inherently geometric task. In this paper, we demonstrate how a translation and rotation equivariant Convolutional Neural Network directly induces representations of camera motions into the feature space. We then show that this geometric property allows for implicitly augmenting the training data under a whole group of image plane-preserving transformations. Therefore, we argue that directly learning equivariant features is preferable than learning data-intensive intermediate representations. Comprehensive experimental validation demonstrates that our lightweight model outperforms existing ones on standard datasets.Comment: 11 pages, 8 figures, CVPR202

Three Essays on Clean Water State Revolving Funds: Determinants of State Leveraging and Measurement of Debt Affordability

Leveraging is a popular option among Clean Water State Revolving Funds (CWSRFs). Most states choose to issue bonds to meet the requirement of the state match contribution, and to provide additional funding into the pool of funds available for community loan assistance. Leveraging offers short-term remedies to fill a financial resources gap; however, this raises concern about any costs associated with leveraging that might negatively influence the sustainability of CWSRFs in the long run. This dissertation comprises three essays that examine the different factors that motivate CWSRFs to leverage, and it offers a look at how they measure their affordability leveraging. Chapter Two borrows the assumptions of pecking order theory to build CWSRF’s leverage model. It focuses on the internal set of factors, and it analyses how the entity’s size, profitability, growth, reserve, and risk affect its leveraging. Chapter Three examines the relationship between leveraging and an external set of indicators, including socioeconomic, demographic, political, and institutional factors. The findings suggest that, in leveraging, internal factors appear to be more influential than external ones. The entity’s size and growth (entity-based factors) are found to be significant with both total and annual leveraging, while state wealth, state politics, and environmental needs also indicate some connection to debt share or debt per capita. Chapter Four particularly scrutinizes how leveraged states measure their debt affordability; it replicates the regression method and predicts the future debt service for New York state. The findings suggest that the regression method can be a good tool for predicting the debt affordability level for CWSRFs. The predicted values from that method can also serve as a supplemental reference source for states before they consider additional leveraging

A Statistical Perspective on Algorithmic Leveraging

One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales rows/columns of data matrices to reduce the data size before performing computations on the subproblem. This method has been successful in improving computational efficiency of algorithms for matrix problems such as least-squares approximation, least absolute deviations approximation, and low-rank matrix approximation. Existing work has focused on algorithmic issues such as worst-case running times and numerical issues associated with providing high-quality implementations, but none of it addresses statistical aspects of this method. In this paper, we provide a simple yet effective framework to evaluate the statistical properties of algorithmic leveraging in the context of estimating parameters in a linear regression model with a fixed number of predictors. We show that from the statistical perspective of bias and variance, neither leverage-based sampling nor uniform sampling dominates the other. This result is particularly striking, given the well-known result that, from the algorithmic perspective of worst-case analysis, leverage-based sampling provides uniformly superior worst-case algorithmic results, when compared with uniform sampling. Based on these theoretical results, we propose and analyze two new leveraging algorithms. A detailed empirical evaluation of existing leverage-based methods as well as these two new methods is carried out on both synthetic and real data sets. The empirical results indicate that our theory is a good predictor of practical performance of existing and new leverage-based algorithms and that the new algorithms achieve improved performance.Comment: 44 pages, 17 figure