*Thomas P. Trappenberg*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780198828044
- eISBN:
- 9780191883873
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828044.003.0005
- Subject:
- Neuroscience, Behavioral Neuroscience

This chapter returns to the more theoretical embedding of machine learning in regression. Prior chapters have shown that writing machine learning programs is easy using high-level computer languages ...
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This chapter returns to the more theoretical embedding of machine learning in regression. Prior chapters have shown that writing machine learning programs is easy using high-level computer languages and with the help of good machine learning libraries. However, applying such algorithms appropriately with superior performance requires considerable experience and a deeper knowledge of the underlying ideas and algorithms. This chapter takes a step back to consider basic regression in more detail, which in turn will form the foundation for discussing probabilistic models in following chapters. This includes the important discussion of gradient descent as a learning algorithm.Less

This chapter returns to the more theoretical embedding of machine learning in regression. Prior chapters have shown that writing machine learning programs is easy using high-level computer languages and with the help of good machine learning libraries. However, applying such algorithms appropriately with superior performance requires considerable experience and a deeper knowledge of the underlying ideas and algorithms. This chapter takes a step back to consider basic regression in more detail, which in turn will form the foundation for discussing probabilistic models in following chapters. This includes the important discussion of gradient descent as a learning algorithm.

*M. Hashem Pesaran*

- Published in print:
- 2015
- Published Online:
- March 2016
- ISBN:
- 9780198736912
- eISBN:
- 9780191800504
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198736912.003.0002
- Subject:
- Economics and Finance, Econometrics

This chapter extends the bivariate regression model discussed in Chapter 1 to the case where more than one variable is available to explain/predict y, the dependent variable. The topic is known as ...
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This chapter extends the bivariate regression model discussed in Chapter 1 to the case where more than one variable is available to explain/predict y, the dependent variable. The topic is known as multiple regression analysis, although only one relationship is in fact considered between y and the k explanatory variables, xit for j = 1, 2, ... , k. It covers standard techniques such as Ordinary Least Squares (OLS) and examines the properties of OLS estimators under classical assumption; discusses the Gauss-Markov theorem, multiple correlation coefficient, the multicollinearity problem, and partitioned regression; introduces regressions that are non-linear in variables; and discusses the interpretation of coefficients. Exercises are provided at the end of the chapter.Less

This chapter extends the bivariate regression model discussed in Chapter 1 to the case where more than one variable is available to explain/predict y, the dependent variable. The topic is known as multiple regression analysis, although only one relationship is in fact considered between y and the k explanatory variables, x_{it} for j = 1, 2, ... , k. It covers standard techniques such as Ordinary Least Squares (OLS) and examines the properties of OLS estimators under classical assumption; discusses the Gauss-Markov theorem, multiple correlation coefficient, the multicollinearity problem, and partitioned regression; introduces regressions that are non-linear in variables; and discusses the interpretation of coefficients. Exercises are provided at the end of the chapter.

*Thomas P. Trappenberg*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780198828044
- eISBN:
- 9780191883873
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828044.003.0001
- Subject:
- Neuroscience, Behavioral Neuroscience

This chapter provides a high-level overview of machine learning, in particular how it is related to building models from data. It starts with placing the basic concept in its historical context and ...
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This chapter provides a high-level overview of machine learning, in particular how it is related to building models from data. It starts with placing the basic concept in its historical context and phrases the learning problem in a simple mathematical term as function approximation as well as in a probabilistic context. In contrast to more traditional models, machine learning can be characterized as non-linear regression in high-dimensional spaces. This chapter points out how diverse subareas such as deep learning and Bayesian networks fit into the scheme of things and motivates further study with some examples of recent progress.Less

This chapter provides a high-level overview of machine learning, in particular how it is related to building models from data. It starts with placing the basic concept in its historical context and phrases the learning problem in a simple mathematical term as function approximation as well as in a probabilistic context. In contrast to more traditional models, machine learning can be characterized as non-linear regression in high-dimensional spaces. This chapter points out how diverse subareas such as deep learning and Bayesian networks fit into the scheme of things and motivates further study with some examples of recent progress.