Patrick Michl, profile picture
Uploaded byPatrick Michl
PDF, PPTX25 views

Regulation Analysis using Restricted Boltzmann Machines

This document summarizes a presentation on using restricted Boltzmann machines to model the regulation of metabolism. It discusses using RBMs as a graphical model to represent topological network structures and preserve dependencies between transcription factors, signals, and enzymes in metabolic pathways. The document outlines how an RBM represents the network as visible and hidden units, learns the dependencies through an energy-based model and stochastic gradient descent, and validates the results on simulated data representing simple regulatory relationships.

Embed presentation

Download as PDF, PPTX
Regulation Analysis using Restricted Boltzmann Machines Network Modeling Seminar, 10/1/2013 Patrick Michl
Page 21/10/2013 | Author Department Agenda Biological Problem Analysing the regulation of metabolism Modeling Implementation & Results
Page 31/10/2013 | Author Department Biological Problem Analysing the regulation of metabolism Signal Regulation Metabolism A linear metabolic pathway of enzymes (E) …
Page 41/10/2013 | Author Department Biological Problem Analysing the regulation of metabolism Signal Regulation Metabolism … is regulated by transcription factors (TF) …
Page 51/10/2013 | Author Department Biological Problem Analysing the regulation of metabolism Signal Regulation Metabolism … which respond to signals (S)
Page 61/10/2013 | Author Department P 4 P 3 P 2 P 1 Biological Problem Analysing the regulation of metabolism Upregulated linear pathways …
Page 71/10/2013 | Author Department P 4 P 3 P 2 P 1 Biological Problem Analysing the regulation of metabolism … can appear in different patterns
Page 81/10/2013 | Author Department Biological Problem Analysing the regulation of metabolism Which transcription factors and signals cause this patterns … ? E ?
Page 91/10/2013 | Author Department Biological Problem Analysing the regulation of metabolism … and how do they interact? (topological structure) ? E ? ? ?
Page 101/10/2013 | Author Department Agenda Biological Problem Analysing the regulation of metabolism Network Modeling Restricted Boltzmann Machines (RBM) Validation & Implementation
Page 111/10/2013 | Author Department Network Modeling Restricted Boltzmann Machines (RBM) Lets start with some pathway of our interest … S E TF
Page 121/10/2013 | Author Department Network Modeling Restricted Boltzmann Machines (RBM) … and lists of interesting TFs and interesting SigMols S E TF
Page 131/10/2013 | Author Department Network Modeling Restricted Boltzmann Machines (RBM) How to model the topological structure? S E TF
Page 141/10/2013 | Author Department Graphical Models Graphical Models can preserve topological structures … Network Modeling Restricted Boltzmann Machines (RBM)
Page 151/10/2013 | Author Department Graphical Models Directed Graph Undirected Graph… … but there are many types of graphical models Network Modeling Restricted Boltzmann Machines (RBM)
Page 161/10/2013 | Author Department Graphical Models Directed Graph Bayesian Networks Undirected Graph… The most common type is the Bayesian Network (BN) … Network Modeling Restricted Boltzmann Machines (RBM)
Page 171/10/2013 | Author Department Bayesian Networks Bayesian Networks use joint probabilities … Network Modeling Restricted Boltzmann Machines (RBM) a b a b c P[a,b,c] 0 0 0 0.1 0 0 1 0.9 0 1 0 0.5 0 1 1 0.5 1 0 0 … … … … … c ?
Page 181/10/2013 | Author Department Bayesian Networks … to represents conditional dependencies in an acyclic graph … Network Modeling Restricted Boltzmann Machines (RBM) a b a b c P[a,b,c] 0 0 0 0.1 0 0 1 0.9 0 1 0 0.5 0 1 1 0.5 1 0 0 … … … … … c
Page 191/10/2013 | Author Department Bayesian Networks … but the regulation mechanism of a cell can be more complicated Network Modeling Restricted Boltzmann Machines (RBM) a b c d
Page 201/10/2013 | Author Department Graphical Models Directed Graph Bayesian Networks Undirected Graph Markov Random Fields … Another type of graphical models are Markov Random Fields (MRF)… Network Modeling Restricted Boltzmann Machines (RBM)
Page 211/10/2013 | Author Department Markov Random Fields Motivation (Ising Model) A set of magnetic dipoles (spins) is arranged in a graph (lattice) where neighbors are coupled with a given strengt ... which emerged with the Ising Model from statistical Physics … Network Modeling Restricted Boltzmann Machines (RBM)
Page 221/10/2013 | Author Department Markov Random Fields Motivation (Ising Model) A set of magnetic dipoles (spins) is arranged in a graph (lattice) where neighbors are coupled with a given strengt ... which uses local energies to calculate new states … Network Modeling Restricted Boltzmann Machines (RBM)
Page 231/10/2013 | Author Department Markov Random Fields Drawback By allowing cyclic dependencies the computational costs explode … the drawback are high computational costs … Network Modeling Restricted Boltzmann Machines (RBM) a b c d
Page 241/10/2013 | Author Department Graphical Models Directed Graph Bayesian Networks Undirected Graph Markov Random Fields Restricted Boltzmann Machines (RBM) … … … which can be avoided by using Restricted Boltzmann Machines Network Modeling Restricted Boltzmann Machines (RBM)
Page 251/10/2013 | Author Department RBMs are Artificial Neuronal Networks … Neuron like units Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines
Page 261/10/2013 | Author Department … with two layers: visible units (v) and hidden units (h) h1 v1 v2 v3 v4 h2 h3 Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines
Page 271/10/2013 | Author Department Visible units are strictly connected with hidden units h1 v1 v2 v3 v4 h2 h3 Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines
Page 281/10/2013 | Author Department In our model the visible units have continuous values … Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines 𝑉 ≔ set of visible units 𝑥 𝑣 ≔ value of unit 𝑣, ∀𝑣 ∈ 𝑉 𝑥 𝑣 ∈ 𝑅, ∀𝑣 ∈ 𝑉
Page 291/10/2013 | Author Department … and the hidden units binary values Network Modeling Restricted Boltzmann Machines (RBM) 𝑉 ≔ set of visible units 𝑥 𝑣 ≔ value of unit 𝑣, ∀𝑣 ∈ 𝑉 𝑥 𝑣 ∈ 𝑅, ∀𝑣 ∈ 𝑉 𝐻 ≔ set of hidden units 𝑥ℎ ≔ value of unit ℎ, ∀ℎ ∈ 𝐻 𝑥ℎ ∈ {0, 1}, ∀ℎ ∈ 𝐻 Restricted Boltzmann Machines
Page 301/10/2013 | Author Department Restricted Boltzmann Machines Visible units are modeled with gaussians to encode data … Network Modeling Restricted Boltzmann Machines (RBM) 𝑥 𝑣~𝑁 𝑏 𝑣 + 𝑤 𝑣ℎℎ 𝑥ℎ, 𝜎𝑣 , ∀𝑣 ∈ 𝑉 𝜎𝑣 ≔ std. dev. of unit 𝑣 𝑏 𝑣 ≔ bias of unit 𝑣 𝑤 𝑣ℎ ≔ weight of edge (𝑣, ℎ)
Page 311/10/2013 | Author Department … and hidden units with simoids to encode dependencies Network Modeling Restricted Boltzmann Machines (RBM) 𝑥 𝑣~𝑁 𝑏 𝑣 + 𝑤 𝑣ℎℎ 𝑥ℎ, 𝜎𝑣 , ∀𝑣 ∈ 𝑉 𝜎𝑣 ≔ std. dev. of unit 𝑣 𝑏 𝑣 ≔ bias of unit 𝑣 𝑤 𝑣ℎ ≔ weight of edge (𝑣, ℎ) 𝑥ℎ~sigmoid 𝑏ℎ + 𝑤 𝑣ℎ𝑣 𝑥 𝑣 𝜎 𝑣 , ∀ℎ ∈ 𝐻 𝑏ℎ ≔ bias of unit ℎ 𝑤 𝑣ℎ ≔ weight of edge (𝑣, ℎ) Restricted Boltzmann Machines
Page 321/10/2013 | Author Department The challenge is to find the configuration of the parameters … Network Modeling Restricted Boltzmann Machines (RBM) Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) Learning in Restricted Boltzmann Machines
Page 331/10/2013 | Author Department Like in the Ising model the units states correspond to local energies … Local Energy Network Modeling Restricted Boltzmann Machines (RBM) 𝐸ℎ ≔ - 𝑤 𝑣ℎ𝑣 𝑥 𝑣 𝜎 𝑣 𝑥ℎ + 𝑥ℎ 𝑏ℎ𝐸 𝑣 ≔ - 𝑤 𝑣ℎℎ 𝑥 𝑣 𝜎 𝑣 𝑥ℎ + (𝑥 𝑣−𝑏 𝑣)2 2𝜎 𝑣 2 Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) In RBMs configurations of parameters have probabilities, that can be defined by local energies 1 2 Learning in Restricted Boltzmann Machines
Page 341/10/2013 | Author Department … which sum to a global energy, which is our objective function Global Energy Network Modeling Restricted Boltzmann Machines (RBM) 𝐸 ≔ 𝐸 𝑣𝑣 + 𝐸ℎℎ = − 𝑤 𝑣ℎℎ𝑣 𝑥 𝑣 𝜎 𝑣 𝑥ℎ + (𝑥 𝑣−𝑏 𝑣)2 2𝜎 𝑣 2 +𝑣 𝑤 𝑣ℎ 𝑥 𝑣 𝜎 𝑣 𝑥ℎℎ Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) ↔ Minimize global energy (to data) Learning in Restricted Boltzmann Machines
Page 351/10/2013 | Author Department Learning in Restricted Boltzmann Machines The optimization can be done using stochastic gradient descent … Network Modeling Restricted Boltzmann Machines (RBM) Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) ↔ Minimize global energy (to data) ↔ Perform stochastic gradient descent on 𝜎𝑣, 𝑏 𝑣, 𝑏ℎ, 𝑤 𝑣ℎ (to data)
Page 361/10/2013 | Author Department … which has an efficient learning algorithmus Network Modeling Restricted Boltzmann Machines (RBM) Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) ↔ Minimize global energy (to data) ↔ Perform stochastic gradient descent on 𝜎𝑣, 𝑏 𝑣, 𝑏ℎ, 𝑤 𝑣ℎ (to data) Gradient Descent on RBMs The bipartite graph structure allows constrastive divergency learning, using Gibbs-sampling Learning in Restricted Boltzmann Machines
Page 371/10/2013 | Author Department How to model our initial structure as an RBM? Network Modeling Restricted Boltzmann Machines (RBM) S E TF
Page 381/10/2013 | Author Department We define S and E as visible Layer … S E TF Network Modeling Restricted Boltzmann Machines (RBM)
Page 391/10/2013 | Author Department S E We define S and E as visible Layer … TF Network Modeling Restricted Boltzmann Machines (RBM)
Page 401/10/2013 | Author Department S E … and TF as hidden Layer TF Network Modeling Restricted Boltzmann Machines (RBM)
Page 411/10/2013 | Author Department Agenda Biological Problem Analysing the regulation of metabolism Network Modeling Restricted Boltzmann Machines (RBM) Implementation & Results python::metapath
Page 421/10/2013 | Author Department Results Validation of the results • Information about the true regulation • Information about the descriptive power of the data
Page 431/10/2013 | Author Department Results Validation of the results • Information about the true regulation • Information about the descriptive power of the data Without this infomation validation can only be done, using simulated data!
Page 441/10/2013 | Author Department Results Simulation 1 First of all we need to understand how the modell handles dependencies and noise To demonstrate this we create very simple data with a simple structure
Page 451/10/2013 | Author Department Simulation 1 What can we expect from this model? S E TF
Page 461/10/2013 | Author Department Simulation 1 … as RBM we get 8 visible and 2 hidden units, fully connected S E TF
Page 471/10/2013 | Author Department Simulation 1 Let‘s feed the machine with samples … S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Data
Page 481/10/2013 | Author Department Simulation 1 .. to get the calculated parameters (especially the weight matrix) Weight matrix TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0
Page 491/10/2013 | Author Department Simulation 1 The weights are visualized by the intensity of the edges S E TF TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0 Weight matrix
Page 501/10/2013 | Author Department Simulation 1 Now we can compare the results with the samples S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Learning samples S E TF
Page 511/10/2013 | Author Department Simulation 1 There‘s a strong dependency between S3 an E1 S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Learning samples S E TF
Page 521/10/2013 | Author Department Simulation 1 S1, S2 and S4 do almost not affect the metabolism … S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Learning samples S E TF
Page 531/10/2013 | Author Department Simulation 1 … so we can forget them and get S1,TF1 for our regulation model S E TF
Page 541/10/2013 | Author Department Simulation 1 We can also take a look at the causal mechanism … TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0 Weight matrix
Page 551/10/2013 | Author Department Simulation 1 The edge (S3, TF1) dominates TF1 … TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0 Weight matrix
Page 561/10/2013 | Author Department Simulation 1 Also E1 seems to have an effect on S3 (fewer than S3 on E1) s3 e1 e2 e3 e4 TF1 TF1 TF1 TF1 TF1
Page 571/10/2013 | Author Department Results Comparing to Bayesian Networks For this purpose we simulate data in three steps Of course we want to compare the method with Bayesian Networks
Page 581/10/2013 | Author Department Results Comparing to Bayesian Networks Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Of course we want to compare the method with Bayesian Networks
Page 591/10/2013 | Author Department Results Comparing to Bayesian Networks Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Step 2 Manipulate data in a fixed order Of course we want to compare the method with Bayesian Networks
Page 601/10/2013 | Author Department Results Comparing to Bayesian Networks Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Step 2 Manipulate data in a fixed order Step 3 Add noise to manipulated data and normalize data Of course we want to compare the method with Bayesian Networks
Page 611/10/2013 | Author Department Results Comparing to Bayesian Networks Idea • ‚melt down‘ the bimodal distribution from very sharp to very noisy • Try to find the original causal structure with BN and RBM • Measure Accuracy by counting the right and wrong dependencies Of course we want to compare the method with Bayesian Networks
Page 621/10/2013 | Author Department Simulation 2 Results 𝑒1 = 0.5𝑠1 + 0.5𝑠2 + 𝑁(𝜇 = 0, 𝜎) 𝑒2 = 0.5𝑠2 + 0.5𝑠3 + 𝑁(𝜇 = 0, 𝜎) 𝑒3 = 0.5𝑠3 + 0.5𝑠4 + 𝑁(𝜇 = 0, 𝜎) 𝑒4 = 0.5𝑠4 + 0.5𝑠1 + 𝑁(𝜇 = 0, 𝜎) Of course we want to compare the method with Bayesian Networks Step 1: Number of visible nodes 8 (4E, 4S) Create intergradient datasets from sharp to noisy bimodal distribution 𝜎1 = 0.0, 𝜎1 = 0.3, 𝜎3 = 0.9, 𝜎4 = 1.2, 𝜎4 = 1.5 Step 2 + 3: Data Manipulation + add noise
Page 631/10/2013 | Author Department Results Simulation 2 RBM Model (𝜎 = 0.0)
Page 641/10/2013 | Author Department Results Simulation 2 Causal Mechanism (𝜎 = 0.0)
Page 651/10/2013 | Author Department Results Simulation 2 Comparison BN / RBM 0 0,2 0,4 0,6 0,8 1 1,2 RBM BN
Page 661/10/2013 | Author Department Conclusion Conclusion • RBMs are more stable against noise compared to BNs. It has to be assumed that RBMs have high predictive power regarding the regulation mechanisms of cells • The drawback are high computational costs Since RBMs are getting more popular (Face recognition / Voice recognition, Image transformation). Many new improvements in facing the computational costs have been made.
Page 671/10/2013 | Author Department Acknowledgement eilsLABS PD Dr. Rainer König Prof. Dr Roland Eils Network Modeling Group

More Related Content

PDF
Library aware-power-conscious-realization-of-complementary-boolean-functions-
byCemal Ardil
 
PDF
PERFORMANCE ANALYSIS OF SRAM CELL USING REVERSIBLE LOGIC GATES
byBUKYABALAJI
 
PDF
2012
bysubodh Singhal
 
PDF
Crdom cell re ordering based domino on-the-fly mapping
byVLSICS Design
 
DOCX
Assignement 3 ADV report (1)
byRiddhi Shah
 
PDF
A PROGRESSIVE MESH METHOD FOR PHYSICAL SIMULATIONS USING LATTICE BOLTZMANN ME...
byijdpsjournal
 
PDF
DUAL FIELD DUAL CORE SECURE CRYPTOPROCESSOR ON FPGA PLATFORM
byVLSICS Design
 
PDF
DSP IEEE paper
byprreiya
 
Library aware-power-conscious-realization-of-complementary-boolean-functions-
byCemal Ardil
 
PERFORMANCE ANALYSIS OF SRAM CELL USING REVERSIBLE LOGIC GATES
byBUKYABALAJI
 
2012
bysubodh Singhal
 
Crdom cell re ordering based domino on-the-fly mapping
byVLSICS Design
 
Assignement 3 ADV report (1)
byRiddhi Shah
 
A PROGRESSIVE MESH METHOD FOR PHYSICAL SIMULATIONS USING LATTICE BOLTZMANN ME...
byijdpsjournal
 
DUAL FIELD DUAL CORE SECURE CRYPTOPROCESSOR ON FPGA PLATFORM
byVLSICS Design
 
DSP IEEE paper
byprreiya
 

What's hot

PDF
logical effort based dual mode logic gates by mallika
byMallika Naidu
 
PDF
Research of 64-bits RISC Dual-core Microprocessor with High Performance and L...
byTELKOMNIKA JOURNAL
 
PDF
Adaptive Training of Radial Basis Function Networks Based on Cooperative
byESCOM
 
PDF
Final Project Report
byRiddhi Shah
 
PDF
IRJET-RFID Based Book Tracking in Libraries: Using Bicam
byIRJET Journal
 
PDF
Local Binary Fitting Segmentation by Cooperative Quantum Particle Optimization
byTELKOMNIKA JOURNAL
 
DOCX
Flexible dsp accelerator architecture exploiting carry save arithmetic
byNexgen Technology
 
PDF
Parallel Processor for Graphics Acceleration
bySandip Jassar (sandipjassar@hotmail.com)
 
DOCX
Flexible dsp accelerator architecture exploiting carry save arithmetic
byIeee Xpert
 
PPTX
Floor planning
byshaik sharief
 
PDF
Implementation of Efficient Ternary Content Addressable Memory by Using Butte...
byInternational journal of scientific and technical research in engineering (IJSTRE)
 
PDF
Bn26425431
byIJERA Editor
 
PPTX
PLA Minimization -Testing
byDr.YNM
 
PDF
Ijetcas14 400
byIasir Journals
 
PPT
Protein structure alignment beyond spatial proximity 3 dsig_2012
bySheng Wang
 
DOC
Report-Implementation of Quantum Gates using Verilog
byShashank Kumar
 
PDF
IRJET- Design of Memristor based Multiplier
byIRJET Journal
 
DOCX
ADS Lab 5 Report
byRiddhi Shah
 
PDF
DESIGN OF DELAY COMPUTATION METHOD FOR CYCLOTOMIC FAST FOURIER TRANSFORM
bysipij
 
logical effort based dual mode logic gates by mallika
byMallika Naidu
 
Research of 64-bits RISC Dual-core Microprocessor with High Performance and L...
byTELKOMNIKA JOURNAL
 
Adaptive Training of Radial Basis Function Networks Based on Cooperative
byESCOM
 
Final Project Report
byRiddhi Shah
 
IRJET-RFID Based Book Tracking in Libraries: Using Bicam
byIRJET Journal
 
Local Binary Fitting Segmentation by Cooperative Quantum Particle Optimization
byTELKOMNIKA JOURNAL
 
Flexible dsp accelerator architecture exploiting carry save arithmetic
byNexgen Technology
 
Parallel Processor for Graphics Acceleration
bySandip Jassar (sandipjassar@hotmail.com)
 
Flexible dsp accelerator architecture exploiting carry save arithmetic
byIeee Xpert
 
Floor planning
byshaik sharief
 
Implementation of Efficient Ternary Content Addressable Memory by Using Butte...
byInternational journal of scientific and technical research in engineering (IJSTRE)
 
Bn26425431
byIJERA Editor
 
PLA Minimization -Testing
byDr.YNM
 
Ijetcas14 400
byIasir Journals
 
Protein structure alignment beyond spatial proximity 3 dsig_2012
bySheng Wang
 
Report-Implementation of Quantum Gates using Verilog
byShashank Kumar
 
IRJET- Design of Memristor based Multiplier
byIRJET Journal
 
ADS Lab 5 Report
byRiddhi Shah
 
DESIGN OF DELAY COMPUTATION METHOD FOR CYCLOTOMIC FAST FOURIER TRANSFORM
bysipij
 

Similar to Regulation Analysis using Restricted Boltzmann Machines

PDF
Concept of Regulation Analysis using Restricted Boltzmann Machines
byPatrick Michl
 
PDF
rbm_hls
byDavid Lau
 
PPTX
Boltzmann Machines in Deep learning and machine learning also used for traini...
byvenkatasaisumanth74
 
PDF
Restricted Boltzmann Machine - A comprehensive study with a focus on Deep Bel...
byIndraneel Pole
 
PPTX
Restricted boltzmann machine
by강민국 강민국
 
PDF
Deep Generative Models
byMijung Kim
 
PPTX
MODULE V_REINFORCEMENT LEARNING _Machine Learning.pptx
byarchanaonlineexam
 
PPTX
ANN - UNIT 4.pptx
bySRM Institute of Science and Technology
 
PPTX
Deep Belief nets
bybutest
 
PDF
Dl1 deep learning_algorithms
byArmando Vieira
 
PPTX
DNN and RBM
byMasayuki Tanaka
 
PPTX
Introsuction to restricted boltzman machine
byRajanRock3
 
PDF
Restricted Boltzmann Machine | Neural Network Tutorial | Deep Learning Tutori...
byEdureka!
 
PPTX
Presentation on Deep Learning lecture_30.pptx
bymasudcse1
 
PPT
Deep Beleif Networks
byDeepak Singh
 
PDF
Convolutional Neural Networks square measure terribly kind of like n.pdf
bypoddaranand1
 
PPTX
Generative models
byAvner Gidron
 
PPTX
22PCOAM16 Unit 2 Session 14 RBF Network.pptx
byGuru Nanak Technical Institutions
 
PPTX
unit 4_1-SC.pptxfgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg...
byRajeshT305412
 
PDF
Relational machine-learning
byBhushan Kotnis
 
Concept of Regulation Analysis using Restricted Boltzmann Machines
byPatrick Michl
 
rbm_hls
byDavid Lau
 
Boltzmann Machines in Deep learning and machine learning also used for traini...
byvenkatasaisumanth74
 
Restricted Boltzmann Machine - A comprehensive study with a focus on Deep Bel...
byIndraneel Pole
 
Restricted boltzmann machine
by강민국 강민국
 
Deep Generative Models
byMijung Kim
 
MODULE V_REINFORCEMENT LEARNING _Machine Learning.pptx
byarchanaonlineexam
 
ANN - UNIT 4.pptx
bySRM Institute of Science and Technology
 
Deep Belief nets
bybutest
 
Dl1 deep learning_algorithms
byArmando Vieira
 
DNN and RBM
byMasayuki Tanaka
 
Introsuction to restricted boltzman machine
byRajanRock3
 
Restricted Boltzmann Machine | Neural Network Tutorial | Deep Learning Tutori...
byEdureka!
 
Presentation on Deep Learning lecture_30.pptx
bymasudcse1
 
Deep Beleif Networks
byDeepak Singh
 
Convolutional Neural Networks square measure terribly kind of like n.pdf
bypoddaranand1
 
Generative models
byAvner Gidron
 
22PCOAM16 Unit 2 Session 14 RBF Network.pptx
byGuru Nanak Technical Institutions
 
unit 4_1-SC.pptxfgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg...
byRajeshT305412
 
Relational machine-learning
byBhushan Kotnis
 

More from Patrick Michl

PDF
Attention Please! 2022
byPatrick Michl
 
PDF
Spec2Vec - Energy based non-linear Calibration in NIRS
byPatrick Michl
 
PDF
Attention please! Attention Mechanism in Neural Networks
byPatrick Michl
 
PDF
Structure learning with Deep Neural Networks
byPatrick Michl
 
PDF
Structure learning with Deep Neural Networks
byPatrick Michl
 
PDF
Structure learning with Deep Autoencoders
byPatrick Michl
 
PDF
Synchronization and Collective Dynamics
byPatrick Michl
 
PDF
Epidemic Spreading
byPatrick Michl
 
Attention Please! 2022
byPatrick Michl
 
Spec2Vec - Energy based non-linear Calibration in NIRS
byPatrick Michl
 
Attention please! Attention Mechanism in Neural Networks
byPatrick Michl
 
Structure learning with Deep Neural Networks
byPatrick Michl
 
Structure learning with Deep Neural Networks
byPatrick Michl
 
Structure learning with Deep Autoencoders
byPatrick Michl
 
Synchronization and Collective Dynamics
byPatrick Michl
 
Epidemic Spreading
byPatrick Michl
 

Recently uploaded

PPT
Ch04uiuuuuuuuuuuuuuuuuuuuuuukkkkkkklh.ppt
bykarzanberdawood
 
PPTX
F4 chapter 2.1-Cpr-Powerpoint Cardiopulmonary resuscitation use for emergency...
byYeohLeemoi48
 
PDF
Basic Principles of Plant Pathology; Entomology & Nematology in Plant Patholo...
byNistarini College, Purulia (W.B) India
 
PPTX
Aerobic-and-Anaerobic-Digesters-Biological-Waste-Treatment-Technologies.pptx
byShanmugaPriya168919
 
PDF
PHYTOREMEDIATION OF HEAVY METALS IN SOIL
byswethaviji2005
 
PPTX
ORGANIC CHEMISTRY PRESENTATION WEEK 3 and 4
byJohnRenier1
 
PDF
S. Dharshini ( Msc. Microbiology) Microbial aspects and Metabolic aspects.
bydharshinisampath6
 
PPTX
Bioremediation anaerobic process, sulphur, nitrate, iron reduction, hydrocarb...
byNandhiniV90
 
PDF
Bioremedation - Dechlorination ,Types and process , advantage and disadvantage
byswathijagadeesan1402
 
PPTX
Q4- MUSIC AND ARTS_Week 1-Week 2_LC 1 (B).pptx
byAizaRazonado
 
PPTX
Unit_49_Class_1_Systems_Integration.pptx
bynehaijaz13
 
PDF
Origin Of Life & Evolution || BIOLOGY || CBSE & CHSE
byVivek Kola
 
PPTX
Phytoextraction , Bioremediation . pptx
byswathin2411
 
PPTX
TOPIC - DROUGHT PRIMING AND STRESS MEMORY
byAbhishekkumawat67
 
PPTX
Week 3 - Microbes - Pathogens & Infection (1).pptx
byEnas813292
 
PDF
Hematology-1-Lesson_About_Hematopoiesis_and_erythropoetin
byyunahilnaya
 
PDF
Machine Learning Lectures --- Likelihood
byZahra Sadeghi
 
PDF
谷歌留痕技术 [ 𝙩𝙤𝙥 𝟮𝟯𝟯. 𝙘 𝙤𝙢 ]
by6stynggfo
 
PPTX
Rolling with Science: Perfecting the Joint and Vaporizing the Competition
byMarkus Roggen
 
PPTX
Annual Report of CMC filed in the USFDA for NDA & ANDA
byPHARMA IQ EDUCATION
 
Ch04uiuuuuuuuuuuuuuuuuuuuuuukkkkkkklh.ppt
bykarzanberdawood
 
F4 chapter 2.1-Cpr-Powerpoint Cardiopulmonary resuscitation use for emergency...
byYeohLeemoi48
 
Basic Principles of Plant Pathology; Entomology & Nematology in Plant Patholo...
byNistarini College, Purulia (W.B) India
 
Aerobic-and-Anaerobic-Digesters-Biological-Waste-Treatment-Technologies.pptx
byShanmugaPriya168919
 
PHYTOREMEDIATION OF HEAVY METALS IN SOIL
byswethaviji2005
 
ORGANIC CHEMISTRY PRESENTATION WEEK 3 and 4
byJohnRenier1
 
S. Dharshini ( Msc. Microbiology) Microbial aspects and Metabolic aspects.
bydharshinisampath6
 
Bioremediation anaerobic process, sulphur, nitrate, iron reduction, hydrocarb...
byNandhiniV90
 
Bioremedation - Dechlorination ,Types and process , advantage and disadvantage
byswathijagadeesan1402
 
Q4- MUSIC AND ARTS_Week 1-Week 2_LC 1 (B).pptx
byAizaRazonado
 
Unit_49_Class_1_Systems_Integration.pptx
bynehaijaz13
 
Origin Of Life & Evolution || BIOLOGY || CBSE & CHSE
byVivek Kola
 
Phytoextraction , Bioremediation . pptx
byswathin2411
 
TOPIC - DROUGHT PRIMING AND STRESS MEMORY
byAbhishekkumawat67
 
Week 3 - Microbes - Pathogens & Infection (1).pptx
byEnas813292
 
Hematology-1-Lesson_About_Hematopoiesis_and_erythropoetin
byyunahilnaya
 
Machine Learning Lectures --- Likelihood
byZahra Sadeghi
 
谷歌留痕技术 [ 𝙩𝙤𝙥 𝟮𝟯𝟯. 𝙘 𝙤𝙢 ]
by6stynggfo
 
Rolling with Science: Perfecting the Joint and Vaporizing the Competition
byMarkus Roggen
 
Annual Report of CMC filed in the USFDA for NDA & ANDA
byPHARMA IQ EDUCATION
 

Regulation Analysis using Restricted Boltzmann Machines

  • 1.
    Regulation Analysis using RestrictedBoltzmann Machines Network Modeling Seminar, 10/1/2013 Patrick Michl
  • 2.
    Page 21/10/2013 | Author Department Agenda BiologicalProblem Analysing the regulation of metabolism Modeling Implementation & Results
  • 3.
    Page 31/10/2013 | Author DepartmentBiological Problem Analysing the regulation of metabolism Signal Regulation Metabolism A linear metabolic pathway of enzymes (E) …
  • 4.
    Page 41/10/2013 | Author DepartmentBiological Problem Analysing the regulation of metabolism Signal Regulation Metabolism … is regulated by transcription factors (TF) …
  • 5.
    Page 51/10/2013 | Author DepartmentBiological Problem Analysing the regulation of metabolism Signal Regulation Metabolism … which respond to signals (S)
  • 6.
    Page 61/10/2013 | Author Department P4 P 3 P 2 P 1 Biological Problem Analysing the regulation of metabolism Upregulated linear pathways …
  • 7.
    Page 71/10/2013 | Author Department P4 P 3 P 2 P 1 Biological Problem Analysing the regulation of metabolism … can appear in different patterns
  • 8.
    Page 81/10/2013 | Author DepartmentBiological Problem Analysing the regulation of metabolism Which transcription factors and signals cause this patterns … ? E ?
  • 9.
    Page 91/10/2013 | Author DepartmentBiological Problem Analysing the regulation of metabolism … and how do they interact? (topological structure) ? E ? ? ?
  • 10.
    Page 101/10/2013 | Author Department Agenda BiologicalProblem Analysing the regulation of metabolism Network Modeling Restricted Boltzmann Machines (RBM) Validation & Implementation
  • 11.
    Page 111/10/2013 | Author DepartmentNetwork Modeling Restricted Boltzmann Machines (RBM) Lets start with some pathway of our interest … S E TF
  • 12.
    Page 121/10/2013 | Author DepartmentNetwork Modeling Restricted Boltzmann Machines (RBM) … and lists of interesting TFs and interesting SigMols S E TF
  • 13.
    Page 131/10/2013 | Author DepartmentNetwork Modeling Restricted Boltzmann Machines (RBM) How to model the topological structure? S E TF
  • 14.
    Page 141/10/2013 | Author Department GraphicalModels Graphical Models can preserve topological structures … Network Modeling Restricted Boltzmann Machines (RBM)
  • 15.
    Page 151/10/2013 | Author Department GraphicalModels Directed Graph Undirected Graph… … but there are many types of graphical models Network Modeling Restricted Boltzmann Machines (RBM)
  • 16.
    Page 161/10/2013 | Author Department GraphicalModels Directed Graph Bayesian Networks Undirected Graph… The most common type is the Bayesian Network (BN) … Network Modeling Restricted Boltzmann Machines (RBM)
  • 17.
    Page 171/10/2013 | Author Department BayesianNetworks Bayesian Networks use joint probabilities … Network Modeling Restricted Boltzmann Machines (RBM) a b a b c P[a,b,c] 0 0 0 0.1 0 0 1 0.9 0 1 0 0.5 0 1 1 0.5 1 0 0 … … … … … c ?
  • 18.
    Page 181/10/2013 | Author Department BayesianNetworks … to represents conditional dependencies in an acyclic graph … Network Modeling Restricted Boltzmann Machines (RBM) a b a b c P[a,b,c] 0 0 0 0.1 0 0 1 0.9 0 1 0 0.5 0 1 1 0.5 1 0 0 … … … … … c
  • 19.
    Page 191/10/2013 | Author Department BayesianNetworks … but the regulation mechanism of a cell can be more complicated Network Modeling Restricted Boltzmann Machines (RBM) a b c d
  • 20.
    Page 201/10/2013 | Author Department GraphicalModels Directed Graph Bayesian Networks Undirected Graph Markov Random Fields … Another type of graphical models are Markov Random Fields (MRF)… Network Modeling Restricted Boltzmann Machines (RBM)
  • 21.
    Page 211/10/2013 | Author Department MarkovRandom Fields Motivation (Ising Model) A set of magnetic dipoles (spins) is arranged in a graph (lattice) where neighbors are coupled with a given strengt ... which emerged with the Ising Model from statistical Physics … Network Modeling Restricted Boltzmann Machines (RBM)
  • 22.
    Page 221/10/2013 | Author Department MarkovRandom Fields Motivation (Ising Model) A set of magnetic dipoles (spins) is arranged in a graph (lattice) where neighbors are coupled with a given strengt ... which uses local energies to calculate new states … Network Modeling Restricted Boltzmann Machines (RBM)
  • 23.
    Page 231/10/2013 | Author Department MarkovRandom Fields Drawback By allowing cyclic dependencies the computational costs explode … the drawback are high computational costs … Network Modeling Restricted Boltzmann Machines (RBM) a b c d
  • 24.
    Page 241/10/2013 | Author Department GraphicalModels Directed Graph Bayesian Networks Undirected Graph Markov Random Fields Restricted Boltzmann Machines (RBM) … … … which can be avoided by using Restricted Boltzmann Machines Network Modeling Restricted Boltzmann Machines (RBM)
  • 25.
    Page 251/10/2013 | Author Department RBMsare Artificial Neuronal Networks … Neuron like units Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines
  • 26.
    Page 261/10/2013 | Author Department …with two layers: visible units (v) and hidden units (h) h1 v1 v2 v3 v4 h2 h3 Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines
  • 27.
    Page 271/10/2013 | Author Department Visibleunits are strictly connected with hidden units h1 v1 v2 v3 v4 h2 h3 Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines
  • 28.
    Page 281/10/2013 | Author Department Inour model the visible units have continuous values … Network Modeling Restricted Boltzmann Machines (RBM) Restricted Boltzmann Machines 𝑉 ≔ set of visible units 𝑥 𝑣 ≔ value of unit 𝑣, ∀𝑣 ∈ 𝑉 𝑥 𝑣 ∈ 𝑅, ∀𝑣 ∈ 𝑉
  • 29.
    Page 291/10/2013 | Author Department …and the hidden units binary values Network Modeling Restricted Boltzmann Machines (RBM) 𝑉 ≔ set of visible units 𝑥 𝑣 ≔ value of unit 𝑣, ∀𝑣 ∈ 𝑉 𝑥 𝑣 ∈ 𝑅, ∀𝑣 ∈ 𝑉 𝐻 ≔ set of hidden units 𝑥ℎ ≔ value of unit ℎ, ∀ℎ ∈ 𝐻 𝑥ℎ ∈ {0, 1}, ∀ℎ ∈ 𝐻 Restricted Boltzmann Machines
  • 30.
    Page 301/10/2013 | Author Department RestrictedBoltzmann Machines Visible units are modeled with gaussians to encode data … Network Modeling Restricted Boltzmann Machines (RBM) 𝑥 𝑣~𝑁 𝑏 𝑣 + 𝑤 𝑣ℎℎ 𝑥ℎ, 𝜎𝑣 , ∀𝑣 ∈ 𝑉 𝜎𝑣 ≔ std. dev. of unit 𝑣 𝑏 𝑣 ≔ bias of unit 𝑣 𝑤 𝑣ℎ ≔ weight of edge (𝑣, ℎ)
  • 31.
    Page 311/10/2013 | Author Department …and hidden units with simoids to encode dependencies Network Modeling Restricted Boltzmann Machines (RBM) 𝑥 𝑣~𝑁 𝑏 𝑣 + 𝑤 𝑣ℎℎ 𝑥ℎ, 𝜎𝑣 , ∀𝑣 ∈ 𝑉 𝜎𝑣 ≔ std. dev. of unit 𝑣 𝑏 𝑣 ≔ bias of unit 𝑣 𝑤 𝑣ℎ ≔ weight of edge (𝑣, ℎ) 𝑥ℎ~sigmoid 𝑏ℎ + 𝑤 𝑣ℎ𝑣 𝑥 𝑣 𝜎 𝑣 , ∀ℎ ∈ 𝐻 𝑏ℎ ≔ bias of unit ℎ 𝑤 𝑣ℎ ≔ weight of edge (𝑣, ℎ) Restricted Boltzmann Machines
  • 32.
    Page 321/10/2013 | Author Department Thechallenge is to find the configuration of the parameters … Network Modeling Restricted Boltzmann Machines (RBM) Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) Learning in Restricted Boltzmann Machines
  • 33.
    Page 331/10/2013 | Author Department Likein the Ising model the units states correspond to local energies … Local Energy Network Modeling Restricted Boltzmann Machines (RBM) 𝐸ℎ ≔ - 𝑤 𝑣ℎ𝑣 𝑥 𝑣 𝜎 𝑣 𝑥ℎ + 𝑥ℎ 𝑏ℎ𝐸 𝑣 ≔ - 𝑤 𝑣ℎℎ 𝑥 𝑣 𝜎 𝑣 𝑥ℎ + (𝑥 𝑣−𝑏 𝑣)2 2𝜎 𝑣 2 Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) In RBMs configurations of parameters have probabilities, that can be defined by local energies 1 2 Learning in Restricted Boltzmann Machines
  • 34.
    Page 341/10/2013 | Author Department …which sum to a global energy, which is our objective function Global Energy Network Modeling Restricted Boltzmann Machines (RBM) 𝐸 ≔ 𝐸 𝑣𝑣 + 𝐸ℎℎ = − 𝑤 𝑣ℎℎ𝑣 𝑥 𝑣 𝜎 𝑣 𝑥ℎ + (𝑥 𝑣−𝑏 𝑣)2 2𝜎 𝑣 2 +𝑣 𝑤 𝑣ℎ 𝑥 𝑣 𝜎 𝑣 𝑥ℎℎ Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) ↔ Minimize global energy (to data) Learning in Restricted Boltzmann Machines
  • 35.
    Page 351/10/2013 | Author Department Learningin Restricted Boltzmann Machines The optimization can be done using stochastic gradient descent … Network Modeling Restricted Boltzmann Machines (RBM) Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) ↔ Minimize global energy (to data) ↔ Perform stochastic gradient descent on 𝜎𝑣, 𝑏 𝑣, 𝑏ℎ, 𝑤 𝑣ℎ (to data)
  • 36.
    Page 361/10/2013 | Author Department …which has an efficient learning algorithmus Network Modeling Restricted Boltzmann Machines (RBM) Task: Find dependencies in data ↔ Find configuration of parameters with maximum likelihood (to data) ↔ Minimize global energy (to data) ↔ Perform stochastic gradient descent on 𝜎𝑣, 𝑏 𝑣, 𝑏ℎ, 𝑤 𝑣ℎ (to data) Gradient Descent on RBMs The bipartite graph structure allows constrastive divergency learning, using Gibbs-sampling Learning in Restricted Boltzmann Machines
  • 37.
    Page 371/10/2013 | Author Department Howto model our initial structure as an RBM? Network Modeling Restricted Boltzmann Machines (RBM) S E TF
  • 38.
    Page 381/10/2013 | Author Department Wedefine S and E as visible Layer … S E TF Network Modeling Restricted Boltzmann Machines (RBM)
  • 39.
    Page 391/10/2013 | Author Department SE We define S and E as visible Layer … TF Network Modeling Restricted Boltzmann Machines (RBM)
  • 40.
    Page 401/10/2013 | Author Department SE … and TF as hidden Layer TF Network Modeling Restricted Boltzmann Machines (RBM)
  • 41.
    Page 411/10/2013 | Author Department Agenda BiologicalProblem Analysing the regulation of metabolism Network Modeling Restricted Boltzmann Machines (RBM) Implementation & Results python::metapath
  • 42.
    Page 421/10/2013 | Author Department Results Validationof the results • Information about the true regulation • Information about the descriptive power of the data
  • 43.
    Page 431/10/2013 | Author Department Results Validationof the results • Information about the true regulation • Information about the descriptive power of the data Without this infomation validation can only be done, using simulated data!
  • 44.
    Page 441/10/2013 | Author Department Results Simulation1 First of all we need to understand how the modell handles dependencies and noise To demonstrate this we create very simple data with a simple structure
  • 45.
    Page 451/10/2013 | Author Department Simulation1 What can we expect from this model? S E TF
  • 46.
    Page 461/10/2013 | Author Department Simulation1 … as RBM we get 8 visible and 2 hidden units, fully connected S E TF
  • 47.
    Page 471/10/2013 | Author Department Simulation1 Let‘s feed the machine with samples … S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Data
  • 48.
    Page 481/10/2013 | Author Department Simulation1 .. to get the calculated parameters (especially the weight matrix) Weight matrix TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0
  • 49.
    Page 491/10/2013 | Author Department Simulation1 The weights are visualized by the intensity of the edges S E TF TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0 Weight matrix
  • 50.
    Page 501/10/2013 | Author Department Simulation1 Now we can compare the results with the samples S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Learning samples S E TF
  • 51.
    Page 511/10/2013 | Author Department Simulation1 There‘s a strong dependency between S3 an E1 S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Learning samples S E TF
  • 52.
    Page 521/10/2013 | Author Department Simulation1 S1, S2 and S4 do almost not affect the metabolism … S E 1,0,0,1 1,0,0,0 1,0,0,1 1,1,0,0 1,0,0,1 1,0,1,0 1,0,0,1 1,0,0,1 1,0,1,1 0,0,0,0 1,0,1,1 0,1,0,0 1,0,1,1 0,0,1,0 1,0,1,1 0,0,0,1 Learning samples S E TF
  • 53.
    Page 531/10/2013 | Author Department Simulation1 … so we can forget them and get S1,TF1 for our regulation model S E TF
  • 54.
    Page 541/10/2013 | Author Department Simulation1 We can also take a look at the causal mechanism … TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0 Weight matrix
  • 55.
    Page 551/10/2013 | Author Department Simulation1 The edge (S3, TF1) dominates TF1 … TF1 TF2 S1 0,3 0,8 S2 0,5 0,6 S3 1,0 0,1 S4 0,3 0,8 E1 0,8 0,0 E2 0,1 0,0 E3 0,1 0,0 E4 0,2 0,0 Weight matrix
  • 56.
    Page 561/10/2013 | Author Department Simulation1 Also E1 seems to have an effect on S3 (fewer than S3 on E1) s3 e1 e2 e3 e4 TF1 TF1 TF1 TF1 TF1
  • 57.
    Page 571/10/2013 | Author Department Results Comparingto Bayesian Networks For this purpose we simulate data in three steps Of course we want to compare the method with Bayesian Networks
  • 58.
    Page 581/10/2013 | Author Department Results Comparingto Bayesian Networks Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Of course we want to compare the method with Bayesian Networks
  • 59.
    Page 591/10/2013 | Author Department Results Comparingto Bayesian Networks Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Step 2 Manipulate data in a fixed order Of course we want to compare the method with Bayesian Networks
  • 60.
    Page 601/10/2013 | Author Department Results Comparingto Bayesian Networks Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Step 2 Manipulate data in a fixed order Step 3 Add noise to manipulated data and normalize data Of course we want to compare the method with Bayesian Networks
  • 61.
    Page 611/10/2013 | Author Department Results Comparingto Bayesian Networks Idea • ‚melt down‘ the bimodal distribution from very sharp to very noisy • Try to find the original causal structure with BN and RBM • Measure Accuracy by counting the right and wrong dependencies Of course we want to compare the method with Bayesian Networks
  • 62.
    Page 621/10/2013 | Author Department Simulation2 Results 𝑒1 = 0.5𝑠1 + 0.5𝑠2 + 𝑁(𝜇 = 0, 𝜎) 𝑒2 = 0.5𝑠2 + 0.5𝑠3 + 𝑁(𝜇 = 0, 𝜎) 𝑒3 = 0.5𝑠3 + 0.5𝑠4 + 𝑁(𝜇 = 0, 𝜎) 𝑒4 = 0.5𝑠4 + 0.5𝑠1 + 𝑁(𝜇 = 0, 𝜎) Of course we want to compare the method with Bayesian Networks Step 1: Number of visible nodes 8 (4E, 4S) Create intergradient datasets from sharp to noisy bimodal distribution 𝜎1 = 0.0, 𝜎1 = 0.3, 𝜎3 = 0.9, 𝜎4 = 1.2, 𝜎4 = 1.5 Step 2 + 3: Data Manipulation + add noise
  • 63.
  • 64.
  • 65.
    Page 651/10/2013 | Author Department Results Simulation2 Comparison BN / RBM 0 0,2 0,4 0,6 0,8 1 1,2 RBM BN
  • 66.
    Page 661/10/2013 | Author Department Conclusion Conclusion •RBMs are more stable against noise compared to BNs. It has to be assumed that RBMs have high predictive power regarding the regulation mechanisms of cells • The drawback are high computational costs Since RBMs are getting more popular (Face recognition / Voice recognition, Image transformation). Many new improvements in facing the computational costs have been made.
  • 67.
    Page 671/10/2013 | Author Department Acknowledgement eilsLABS PDDr. Rainer König Prof. Dr Roland Eils Network Modeling Group