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Popularity Prediction with Reinforced Poisson Process

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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

  • 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

    2

  • 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

    3

  • 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.

    4

  • 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

    5

  • 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.

    6

  • 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 .

    7

  • 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

  • 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.

    9

  • 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

    10

  • 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.

    11

  • 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.

    12

  • TYPES OF POINT PROCESS

    Simple Point Process

    Temporal Point Process

    Marked Point Process

    13

  • 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.

    14

  • 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.

    15

  • 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:

    16

  • 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

    17

  • 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:

    18

  • 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

    19

  • CONTD

    The log-likelihood for the retweeting dynamics {tk} up to Ti is

    where

    20

  • 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

    21

  • PREDICTION

    To predict the expected number of retweets N(t) for message m at any

    given time moment.

    Solving this,

    22

  • 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

    23

  • 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

    24

  • FIN

    25