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Regression and Model Fitting

Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, y, and a set of ... More

Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, y, and a set of independent variables, x, that describes the expectation value of y given x: E [y¦x]. The purpose of obtaining a “best-fit” model ranges from scientific interest in the values of model parameters (e.g., the properties of dark energy, or of a newly discovered planet) to the predictive power of the resulting model (e.g., predicting solar activity). This chapter starts with a general formulation for regression, list various simplified cases, and then discusses methods that can be used to address them, such as regression for linear models, kernel regression, robust regression and nonlinear regression.Less

Kernel-Based Machine Translation

Zhuoran Wang and John Shawe-Taylor

in Learning Machine Translation

This chapter presents a novel framework for machine translation based on kernel ridge regression. As a kernel method, the framework has the advantage of capturing the correspondences among the ... More

This chapter presents a novel framework for machine translation based on kernel ridge regression. As a kernel method, the framework has the advantage of capturing the correspondences among the features of inputs and outputs in a very high-dimensional space. But the drawback is that its computational complexities are much higher than probabilistic models. A solution is sparse approximation, which poses the problem of extracting a sufficient amount of relevant bilingual training samples for a given input. Other essential improvements to this model could be the integration of additional language models and the utilization of linguistic knowledge.Less

Robust Prediction Under Model Misspecification

Raymond L. Chambers and Robert G. Clark

in An Introduction to Model-Based Survey Sampling with Applications

Robust prediction under model misspecification focuses on the important topic of how to ensure unbiased prediction even when the assumed population model is not precisely specified. The general role ... More

Robust prediction under model misspecification focuses on the important topic of how to ensure unbiased prediction even when the assumed population model is not precisely specified. The general role of sample balance in ensuring this unbiasedness is explored in the context of the homogeneous and the ratio population models, and the problem of maintaining a suitable trade-off between prediction efficiency under a working model and unbiasedness under alternative population models is discussed. A general result that provides the necessary conditions for both unbiasedness and efficiency is provided and the extension of balanced sampling to the clustered population model is discussed. A misspecification-robust alternative to balanced sampling is flexible estimation, and the chapter concludes with a development of finite population prediction based on a non-parametric regression fit to the sample data.Less

Advanced Topics

Jeffrey S. Racine

in Reproducible Econometrics Using R

This chapter covers two advanced topics: a machine learning method (support vector machines useful for classification) and nonparametric kernel regression.