SlideShare a Scribd company logo
Structured Dimensionality Reduction for Additive Model Regression
Abstract:
Additive models are regression methods which model the response variable as
the sum of univariate transfer functions of the input variables. Key benefits of
additive models are their accuracy and interpretability on many real-world tasks.
Additive models are however not adapted to problems involving a large number
(e.g., hundreds) of input variables, as they are prone to overfitting in addition to
losing interpretability. In this paper, we introduce a novel framework for applying
additive models to a large number of input variables. The key idea is to reduce the
task dimensionality by deriving a small number of new covariates obtained by
linear combinations of the inputs, where the linear weights are estimated with
regard to the regression problem at hand. The weights are moreover constrained
to prevent overfitting and facilitate the interpretation of the derived covariates.
We establish identifiability of the proposed model under mild assumptions and
present an efficient approximate learning algorithm. Experiments on synthetic
and real-world data demonstrate that our approach compares favorably to
baseline methods in terms of accuracy, while resulting in models of lower
complexity and yielding practical insights into high-dimensional real-world
regression tasks. Our framework broadens the applicability of additive models to
high-dimensional problems while maintaining their interpretability and potential
to provide practical insights.

More Related Content

Similar to Structured dimensionality reduction for additive model regression

GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATIONGENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
ijaia
 
result analysis for deep leakage from gradients
result analysis for deep leakage from gradientsresult analysis for deep leakage from gradients
result analysis for deep leakage from gradients
國騰 丁
 
A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...
A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...
A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...
Sheila Sinclair
 
CFM Challenge - Course Project
CFM Challenge - Course ProjectCFM Challenge - Course Project
CFM Challenge - Course Project
KhalilBergaoui
 
Modeling Chemical Datasets
Modeling Chemical DatasetsModeling Chemical Datasets
Modeling Chemical Datasets
Abhik Seal
 
Surrogate modeling for industrial design
Surrogate modeling for industrial designSurrogate modeling for industrial design
Surrogate modeling for industrial design
Shinwoo Jang
 
Machine Learning Unit 3 Semester 3 MSc IT Part 2 Mumbai University
Machine Learning Unit 3 Semester 3  MSc IT Part 2 Mumbai UniversityMachine Learning Unit 3 Semester 3  MSc IT Part 2 Mumbai University
Machine Learning Unit 3 Semester 3 MSc IT Part 2 Mumbai University
Madhav Mishra
 
Dimensionality Reduction for Classification with High-Dimensional Data
Dimensionality Reduction for Classification with High-Dimensional DataDimensionality Reduction for Classification with High-Dimensional Data
Dimensionality Reduction for Classification with High-Dimensional Data
International Journal of Engineering Inventions www.ijeijournal.com
 
Introduction-to-Non-Linear-Regression.pptx
Introduction-to-Non-Linear-Regression.pptxIntroduction-to-Non-Linear-Regression.pptx
Introduction-to-Non-Linear-Regression.pptx
ShriramKargaonkar
 
Machine learning session4(linear regression)
Machine learning   session4(linear regression)Machine learning   session4(linear regression)
Machine learning session4(linear regression)
Abhimanyu Dwivedi
 
Mixture Regression Model for Incomplete Data
Mixture Regression Model for Incomplete DataMixture Regression Model for Incomplete Data
Mixture Regression Model for Incomplete Data
Loc Nguyen
 
MF Presentation.pptx
MF Presentation.pptxMF Presentation.pptx
MF Presentation.pptx
HarshitSingh334328
 
Evaluation of Process Capability Using Fuzzy Inference System
Evaluation of Process Capability Using Fuzzy Inference SystemEvaluation of Process Capability Using Fuzzy Inference System
Evaluation of Process Capability Using Fuzzy Inference System
IOSR Journals
 
Chapter 18,19
Chapter 18,19Chapter 18,19
Chapter 18,19
heba_ahmad
 
IEEE Datamining 2016 Title and Abstract
IEEE  Datamining 2016 Title and AbstractIEEE  Datamining 2016 Title and Abstract
IEEE Datamining 2016 Title and Abstract
tsysglobalsolutions
 
Machine Learning.pdf
Machine Learning.pdfMachine Learning.pdf
Machine Learning.pdf
BeyaNasr1
 
LNCS 5050 - Bilevel Optimization and Machine Learning
LNCS 5050 - Bilevel Optimization and Machine LearningLNCS 5050 - Bilevel Optimization and Machine Learning
LNCS 5050 - Bilevel Optimization and Machine Learning
butest
 
graph_embeddings
graph_embeddingsgraph_embeddings
graph_embeddings
Armando Vieira
 
Qt unit i
Qt unit   iQt unit   i
Qt unit i
bhuvana ganesan
 
A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...
A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...
A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...
Martha Brown
 

Similar to Structured dimensionality reduction for additive model regression (20)

GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATIONGENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
 
result analysis for deep leakage from gradients
result analysis for deep leakage from gradientsresult analysis for deep leakage from gradients
result analysis for deep leakage from gradients
 
A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...
A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...
A Simulated Annealing Approach For Buffer Allocation In Reliable Production L...
 
CFM Challenge - Course Project
CFM Challenge - Course ProjectCFM Challenge - Course Project
CFM Challenge - Course Project
 
Modeling Chemical Datasets
Modeling Chemical DatasetsModeling Chemical Datasets
Modeling Chemical Datasets
 
Surrogate modeling for industrial design
Surrogate modeling for industrial designSurrogate modeling for industrial design
Surrogate modeling for industrial design
 
Machine Learning Unit 3 Semester 3 MSc IT Part 2 Mumbai University
Machine Learning Unit 3 Semester 3  MSc IT Part 2 Mumbai UniversityMachine Learning Unit 3 Semester 3  MSc IT Part 2 Mumbai University
Machine Learning Unit 3 Semester 3 MSc IT Part 2 Mumbai University
 
Dimensionality Reduction for Classification with High-Dimensional Data
Dimensionality Reduction for Classification with High-Dimensional DataDimensionality Reduction for Classification with High-Dimensional Data
Dimensionality Reduction for Classification with High-Dimensional Data
 
Introduction-to-Non-Linear-Regression.pptx
Introduction-to-Non-Linear-Regression.pptxIntroduction-to-Non-Linear-Regression.pptx
Introduction-to-Non-Linear-Regression.pptx
 
Machine learning session4(linear regression)
Machine learning   session4(linear regression)Machine learning   session4(linear regression)
Machine learning session4(linear regression)
 
Mixture Regression Model for Incomplete Data
Mixture Regression Model for Incomplete DataMixture Regression Model for Incomplete Data
Mixture Regression Model for Incomplete Data
 
MF Presentation.pptx
MF Presentation.pptxMF Presentation.pptx
MF Presentation.pptx
 
Evaluation of Process Capability Using Fuzzy Inference System
Evaluation of Process Capability Using Fuzzy Inference SystemEvaluation of Process Capability Using Fuzzy Inference System
Evaluation of Process Capability Using Fuzzy Inference System
 
Chapter 18,19
Chapter 18,19Chapter 18,19
Chapter 18,19
 
IEEE Datamining 2016 Title and Abstract
IEEE  Datamining 2016 Title and AbstractIEEE  Datamining 2016 Title and Abstract
IEEE Datamining 2016 Title and Abstract
 
Machine Learning.pdf
Machine Learning.pdfMachine Learning.pdf
Machine Learning.pdf
 
LNCS 5050 - Bilevel Optimization and Machine Learning
LNCS 5050 - Bilevel Optimization and Machine LearningLNCS 5050 - Bilevel Optimization and Machine Learning
LNCS 5050 - Bilevel Optimization and Machine Learning
 
graph_embeddings
graph_embeddingsgraph_embeddings
graph_embeddings
 
Qt unit i
Qt unit   iQt unit   i
Qt unit i
 
A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...
A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...
A General Purpose Exact Solution Method For Mixed Integer Concave Minimizatio...
 

Recently uploaded

How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17
Celine George
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Fajar Baskoro
 
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptxC1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
mulvey2
 
How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17
Celine George
 
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Celine George
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
Colégio Santa Teresinha
 
A Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdfA Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdf
Jean Carlos Nunes Paixão
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
adhitya5119
 
Smart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICTSmart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICT
simonomuemu
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
Priyankaranawat4
 
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Dr. Vinod Kumar Kanvaria
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
TechSoup
 
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat  Leveraging AI for Diversity, Equity, and InclusionExecutive Directors Chat  Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
TechSoup
 
World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024
ak6969907
 
How to Add Chatter in the odoo 17 ERP Module
How to Add Chatter in the odoo 17 ERP ModuleHow to Add Chatter in the odoo 17 ERP Module
How to Add Chatter in the odoo 17 ERP Module
Celine George
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
heathfieldcps1
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Akanksha trivedi rama nursing college kanpur.
 

Recently uploaded (20)

How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
 
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptxC1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
 
How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17
 
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
 
A Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdfA Independência da América Espanhola LAPBOOK.pdf
A Independência da América Espanhola LAPBOOK.pdf
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
 
Smart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICTSmart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICT
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
 
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
 
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat  Leveraging AI for Diversity, Equity, and InclusionExecutive Directors Chat  Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
 
World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024
 
How to Add Chatter in the odoo 17 ERP Module
How to Add Chatter in the odoo 17 ERP ModuleHow to Add Chatter in the odoo 17 ERP Module
How to Add Chatter in the odoo 17 ERP Module
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
 

Structured dimensionality reduction for additive model regression

  • 1. Structured Dimensionality Reduction for Additive Model Regression Abstract: Additive models are regression methods which model the response variable as the sum of univariate transfer functions of the input variables. Key benefits of additive models are their accuracy and interpretability on many real-world tasks. Additive models are however not adapted to problems involving a large number (e.g., hundreds) of input variables, as they are prone to overfitting in addition to losing interpretability. In this paper, we introduce a novel framework for applying additive models to a large number of input variables. The key idea is to reduce the task dimensionality by deriving a small number of new covariates obtained by linear combinations of the inputs, where the linear weights are estimated with regard to the regression problem at hand. The weights are moreover constrained to prevent overfitting and facilitate the interpretation of the derived covariates. We establish identifiability of the proposed model under mild assumptions and present an efficient approximate learning algorithm. Experiments on synthetic and real-world data demonstrate that our approach compares favorably to baseline methods in terms of accuracy, while resulting in models of lower complexity and yielding practical insights into high-dimensional real-world regression tasks. Our framework broadens the applicability of additive models to high-dimensional problems while maintaining their interpretability and potential to provide practical insights.