Deep Belief Nets and Ising Model-Based Network Construction

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Presentation transcript:

Deep Belief Nets and Ising Model-Based Network Construction Lecturer: Bo Chen

Network Construction Social , academic ,etc. Several users(nodes) A line means a connection between two users(nodes) Weights of the line indicates the strength of connection

What can it do? 1. Prediction: predict the information source 2. Recommendation: movie, paper , music 3. Other applications

How? 1. Information collection 2. Feature extraction 3. Construction based on features

Various Information Features How? Information Collection Various Information Feature Extraction Features Network Construction

Our Model Information Deep Belief Nets Features Weights Ising Model

Deep Belief Nets Constructed by Restricted Boltzmann Machine layer by layer greedily h3 h2 h1 data

Restricted Boltzmann Machine

Restricted Boltzmann Machine 1. Undirected or bidirected 2. One layer of visible units 3. One layer of hidden units 4. No connection between hidden units 5. No connection between visible units 6. The hidden units are conditionally independent given the visible units hidden j i visible

Terminology in RBM Weights and biases: weights refer to the connection between units and biases refer to each unit

Terminology in RBM Energy: v: visible units, vector, each usually take 1 or 0 h: hidden units, vector, each usually take 1 or 0 a: biases of visible units b: biases of hidden units w: weights

Terminology in RBM Probability: The probability of a configuration over both visible and hidden units: partition function

I & O in RBM Input: visible units Output: weights and biases (generative model)

Return to Deep Belief Nets Steps to train a DBN. 1. Use the parameters to extract a layer of features (the first hidden layer) from raw data 2. Treat the activations of the features as the input for the second hidden layer 3. Repeat step2 to train multiple layers of RBM

Return to Deep Belief Nets The third hidden layer h3 The third RBM The second hidden layer h2 The second RBM The first hidden layer h1 The first RBM data

A Brief Review Now we have a considerable number of features!!! 1. How to construct a network 2. Our model 3. The introduction of RBM 4. To train deep belief nets Now we have a considerable number of features!!!

Ising Model Ising Model User1 User2 User3 User4 User5 User6 Feature1 1 1 Feature2 Feature3 Feature4 Ising Model

Ising Model What will Ising Model do? 1. Treat every user as a node in an Ising Model 2. Treat every feature as one observation of their interaction 3. Infer the interaction between them from all the observations ( features )

Ising Model What is Ising Model? An energy-based model The energy of a configuration(Hamiltonian Function) Configuration σ (a set of users) Interaction 𝐽 𝑖𝑗 (connection strength between users) External field effect ℎ 𝑗

An Illustration External field effect Interaction Configuration

Ising Model The configuration probability given by Boltzmann Distribution is where and the normalization constant

Ising Model The conditional probability of 𝑋 𝑗 given all other nodes 𝑋 \j : Configuration Pairwise interaction Node parameter x1 x2 … xi xj t1 t2 ti tj Null … β1i β1j βi1 βij βj1 βji

How? Step1(lasso): Find possible neighbors for each Step2(EBIC): Choose the best set of neighbors Step3(AND rule or OR rule ): Determine the final edge Step4: Take the average of the weights

Experiment Not yet… BUT…

An Example An example of using Ising model to reconstruct a graph Sample Reconstruct

Thanks！

Q&A