retweet dynamics
DESCRIPTION
Popularity Prediction with Reinforced Poisson ProcessTRANSCRIPT
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M o d e l i n g a n d P re d i c t i n g R e t we e t i n g
D y n a m i c s o n
M i c ro b l og g i n g P l a t fo r m s
S h u a i G a o
Ju n M a
Z h u m i n C h e n
WSDM 15
Sankarshan Mridha
Abir De
Reading Group
11/06/2015 1
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
1. Model Formulation
2. Parameter Estimation
3. Prediction
6. Result
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
1. Model Formulation
2. Parameter Estimation
3. Prediction
6. Result
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INTRODUCTION
Popularity prediction is a trending research topic in current times.
Existing works focuses only on effective features.
It ignores the underlying arrival process of the event.
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
1. Model Formulation
2. Parameter Estimation
3. Prediction
6. Result
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PROBLEM STATEMENT
To model the retweeting dynamics of a message using training period
data
To use the above model to predict the popularity of that message in the
future.
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CONTD
The retweeting dynamics of a message m upto Ti is characterized by a
set of time moments when each retweet
arrives.
Prediction Problem: For a message m, given its retweeting dynamics
{tkm} upto the indicator time Ti , Predict its popularity at the reference
time Tr .
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
6. Experiment
1. Model Formulation
2. Parameter Estimation
3. Prediction
4. Result
7. Conclusion8
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DATA SET
Two dataset of Weibo message for the month July 2013.
Random: 0.8 million original message from 10K random users. 10K
random messages with retweeting count [50,20K] from this set.
News: All original message from 25 news account. 18K messages
with retweeting count [50,20K] from that set.
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
1. Model Formulation
2. Parameter Estimation
3. Prediction
6. Result
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POINT PROCESS ( BASIC IDEA )
A point process is a random collection of points.
Each point represents time and/or location of an event
Eg: lightning strike or earthquake.
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POINT PROCESS ( BASIC IDEA )
A point process is a random collection of points.
Each point represents time and/or location of an event
Eg: lightning strike or earthquake.
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TYPES OF POINT PROCESS
Simple Point Process
Temporal Point Process
Marked Point Process
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POISSON PROCESS
Its a simple point process.
N(t) is a Poisson process if the number of events in [0,t] follows a Poisson distribution.
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POISSON PROCESS
Its a simple point process.
N(t) is a Poisson process if the number of events in [0,t] follows a Poisson distribution.
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REINFORCED POISSON PROCESS [shen et al 14 ]
Generative probabilistic model.
Salient Features:
Item fitness
Aging effect
Reinforcement mechanism (rich-gets-richer phenomenon)
[Shen et al 2014] Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes,
Huawei Shen , Dashun Wang , Chaoming Song , Albert-Laszl o Barab asi (AAAI 2014)
Rate Equation:
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
1. Model Formulation
2. Parameter Estimation
3. Prediction
6. Result
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EXTENDED REINFORCED POISSON PROCESS
Gao et all 15 extends the RFP process (Shen et al 14) for retweeting dynamics
Power Law Temporal relaxation function instead of log-nomal relaxation function
Exponential reinforcement function instead of linear reinforcement function
Rate equation:
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MODEL FORMULATION
Given the (k 1)th retweet arrives at tk-1m, the probability that the kth retweet
arrives at tkm follows:
The probability that no retweet arrives between tmnm and Ti is
The likelihood of the observing retweeting dynamics {tmk } up to Ti follows
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CONTD
The log-likelihood for the retweeting dynamics {tk} up to Ti is
where
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PARAMETER ESTIMATION (c*, *, *)
Maximizing log-likelihood function:
For parameters and , the optimal values can be foundby maximizing the log-likelihood using the gradient ascent method.
where 1 and 2 are the learning rate at each iteration
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PREDICTION
To predict the expected number of retweets N(t) for message m at any
given time moment.
Solving this,
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1. Introduction
2. Problem Statement
3. Data Set
4. Point Process
1. Basic Idea
2. Different Types of Point Process
3. Poisson Process
4. Reinforced Poisson Process
5. Extended Reinforced Poisson Process
1. Model Formulation
2. Parameter Estimation
3. Prediction
6. Result
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OUTPUT
SH: Linear Regression For Logarithmic Popularity, ML: Multivariate Linear Regression Method , LL: RPF model with log normal relaxation,
PL: RPF with power law relaxation and linear Reinforcement function, PE: RPF model with power law relaxation and exponential reinforcement function
RESULT
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FIN
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