# Machine and Statistical Learning Fundamentals

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Machine and Statistical Learning Fundamentals

Dorit Hammerling

Department of Applied Mathematics and Statistics Colorado School of Mines(CSM)

Visiting Appointment: National Center for Atmospheric Research(NCAR)

Joint work with William Daniels (CSM) . . . and many other students and collaborators

June 22, 2020

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

1 / 42

Outline

Outline

1 General framework, inference vs prediction 2 Forms for f , cross-validation and model selection 3 Practical application combining concepts

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

2 / 42

General framework, inference vs prediction

Outline

1 General framework, inference vs prediction 2 Forms for f , cross-validation and model selection 3 Practical application combining concepts

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

3 / 42

General framework, inference vs prediction

Useful reference books:

• free and well-written • worked-out code examples

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

4 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Basic model formulation

The supervised model in its simplest form:

Y = f (X ) +

Model components: Y : some variable we are interested in, output f : some ﬁxed but unknown function of X X : variables X1, . . . , Xp we believe might have a relationship to Y, inputs

: random error term Main goal: estimate f

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

6 / 42

General framework, inference vs prediction

Basic model formulation

The supervised model in its simplest form:

Y = f (X ) +

Model components: Y : some variable we are interested in, output f : some ﬁxed but unknown function of X X : variables X1, . . . , Xp we believe might have a relationship to Y, inputs

: random error term Main goal: estimate f

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

6 / 42

Dorit Hammerling

Department of Applied Mathematics and Statistics Colorado School of Mines(CSM)

Visiting Appointment: National Center for Atmospheric Research(NCAR)

Joint work with William Daniels (CSM) . . . and many other students and collaborators

June 22, 2020

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

1 / 42

Outline

Outline

1 General framework, inference vs prediction 2 Forms for f , cross-validation and model selection 3 Practical application combining concepts

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

2 / 42

General framework, inference vs prediction

Outline

1 General framework, inference vs prediction 2 Forms for f , cross-validation and model selection 3 Practical application combining concepts

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

3 / 42

General framework, inference vs prediction

Useful reference books:

• free and well-written • worked-out code examples

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

4 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Some deﬁnitions for starters

Statistical learning: large set of tools to gain insights from data

Supervised versus unsupervised: • supervised: output and one or more inputs • classiﬁcation • regression • ... • unsupervised: only inputs, the structure of these inputs is of interest • clustering • association analysis • dimension reduction, e.g. principal components analysis • ...

⇒ We will focus on the supervised setting.

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

5 / 42

General framework, inference vs prediction

Basic model formulation

The supervised model in its simplest form:

Y = f (X ) +

Model components: Y : some variable we are interested in, output f : some ﬁxed but unknown function of X X : variables X1, . . . , Xp we believe might have a relationship to Y, inputs

: random error term Main goal: estimate f

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

6 / 42

General framework, inference vs prediction

Basic model formulation

The supervised model in its simplest form:

Y = f (X ) +

Model components: Y : some variable we are interested in, output f : some ﬁxed but unknown function of X X : variables X1, . . . , Xp we believe might have a relationship to Y, inputs

: random error term Main goal: estimate f

Hammerling (CSM)

ML/SL Fundamentals

June 22, 2020

6 / 42

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