Optimal estimation of direction in regression models with large number of parameters

We consider the problem of estimating the optimal direction in regression by maximizing the probability that the scalar product between the vector of unknown parameters and the chosen direction is positive. The estimator maximizing this probability is simple in form, and is especially useful for situations where the number of parameters is much larger than the number of observations. We provide examples which show that this estimator is superior to state-of-the-art methods such as the LASSO for estimating the optimal direction

Structured low-rank matrix completion for forecasting in time series analysis

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices and a convex relaxation based on the nuclear norm. Based on new theoretical results and a number of numerical and real examples, we investigate the cases when the proposed approach can work. Our results highlight the importance of choosing a proper weighting scheme for the known observations.Comment: 25 pages, 12 figure

Global optimization for structured low rank approximation

In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. Unlike many other methods described in the literature the family of algorithms we propose has the property of guaranteed convergence

Evolutionary dataset optimisation: learning algorithm quality through evolution

In this paper we propose a new method for learning how algorithms perform. Classically, algorithms are compared on a finite number of existing (or newly simulated) benchmark data sets based on some fixed metrics. The algorithm(s) with the smallest value of this metric are chosen to be the `best performing'. We offer a new approach to flip this paradigm. We instead aim to gain a richer picture of the performance of an algorithm by generating artificial data through genetic evolution, the purpose of which is to create populations of datasets for which a particular algorithm performs well. These data sets can be studied to learn as to what attributes lead to a particular progress of a given algorithm. Following a detailed description of the algorithm as well as a brief description of an open source implementation, a number of numeric experiments are presented to show the performance of the method which we call Evolutionary Dataset Optimisation

An initial analysis and reflection of the metrics used in the Teaching Excellence Framework in the UK

In this paper, we look at the results from the recent Teaching Excellence Framework (2017), which were made publicly available in June 2017. We offer some initial analysis and commentary, look at the primary reasons for providers being awarded Bronze, Silver and Gold, and look at some providers close to the borderline for their award. We demonstrate that the provider submissions, a narrative document prepared to accompany the submission would have had a significant effect upon the award bestowed

Method of moments estimation in linear regression with errors in both variables

Recently, in this journal, there has been revised attention on estimating the parameters of the errors in variables, linear structural model. For example, O’Driscoll and Ramirez (2011) used a geometric approach to give insight into the performance of various slope estimators for the linear structural model as introduced by the present author. This article aims to provide a unified method of moments approach for estimating the parameters in the linear structural model, concentrating attention on estimators using the higher moments, which to date has received only little attention in the literature