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Data Science for Networked Data, Lecture notes of Algorithms and Programming

Key problems in network modeling, including how to estimate the network, model dynamic processes over a network, and perform efficient search over a network. The author presents methods for estimating graphical models for discrete data and discusses statistical inference, resource allocation, and local algorithms. mathematical analysis derived for Gaussian data and methods for constructing connectivity networks from matrix data. The author also discusses confidence sets for source estimation and graph hypothesis testing.

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2021/2022

Uploaded on 05/11/2023

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Data science for networked data
Po-Ling Loh
University of Wisconsin-Madison
Department of Statistics
AISTATS
Okinawa, Japan
April 16, 2019
Joint work with:
Justin Khim (UPenn), Varun Jog (UW-Madison), Ashley Hou (UW-Madison),
Wen Yan (Southeast University), and Muni Pydi (UW-Madison)
Po-Ling Loh (UW-Madison) Data science for networked data Apr 16, 2019 1 / 45
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Data science for networked data

Po-Ling Loh

University of Wisconsin-Madison

Department of Statistics

AISTATS Okinawa, Japan April 16, 2019 Joint work with: Justin Khim (UPenn), Varun Jog (UW-Madison), Ashley Hou (UW-Madison), Wen Yan (Southeast University), and Muni Pydi (UW-Madison)

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Key problems in network modeling

1 Given data from a network, how do we estimate the network?

2 How do we model dynamic processes over a network?

3 How do we perform efficient search over a network?

Graphical models

Method for constructing connectivity network from matrix of data

Graphical models

Method for constructing connectivity network from matrix of data

entries of the covariance inverse and due to the geometry of this penalty, the resulting covariance inverse contains entries being exactly zero. The corresponding network is thus sparse. This is an attractive feature of the graphical Lasso, as many of the cell metabolic or enzymatic process networks are known to be sparse [12]. Networks which are very densely connected are unlikely to represent the true biochemical processes within a cell. containing in total 100 genes. The multifactoria were induced by slightly increasing or decrea activation of all the genes in the network sim different random amounts [5]. If we think of the d format, the data set for each network (Fig. 1) con with 100 rows and 100 columns. Each row of this the 100 genes expression measurements for the

gene expression (mRNA) data E. coli network

Graphical models

Mathematical analysis derived for Gaussian data

In practice, transform data to Gaussian before applying algorithm

Graphical models

But not all data are transformable!

Graphical models

But not all data are transformable!

We have developed new methods for estimating graphical models for

discrete (count) data

However, life is more than network estimation...

Outline

1 Statistical inference

Confidence sets for source estimation

Graph hypothesis testing

2 Resource allocation

Influence maximization

Budget allocation

Network immunization

3 Local algorithms