Learning Agent-Based Models from Data

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Learning Agent-Based Models from Data Gianmarco De Francisci Morales Principal Researcher • CENTAI Team Lead • Social Algorithmics Team   [email protected] 1 SALT

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Learning Agent-Based Models from Data Models Gianmarco De Francisci Morales Principal Researcher • CENTAI Team Lead • Social Algorithmics Team   [email protected] 1 SALT

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Agent-based model 3

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Agent-based model Evolution over time of system of autonomous agents Agents interact according to prede fi ned rules Encode sociological assumptions 3

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Agent-based model Evolution over time of system of autonomous agents Agents interact according to prede fi ned rules Encode sociological assumptions System is simulated to draw conclusions 3

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Example: Schelling's segregation 2 types of agents: R and B Satisfaction: number of neighbors of same color Homophily parameter If τ Si < τ → relocate 4

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Example: Schelling's segregation 2 types of agents: R and B Satisfaction: number of neighbors of same color Homophily parameter If τ Si < τ → relocate 4

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Are ABMs scienti fi c models? 5

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Are ABMs scienti fi c models? Mechanistic models Explainable and causal by construction Counterfactual level of ladder of causality 5 𝔼 (Y ∣ X) 𝔼 (Y ∣ do(X)) 𝔼 (YX′ ∣ X, YX )

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Are ABMs scienti fi c models? Mechanistic models Explainable and causal by construction Counterfactual level of ladder of causality Data not a fi rst-class citizen No sound parameter- fi tting procedure 5

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Good tests kill fl awed theories — Karl Popper Falsi fi ability of ABMs 6

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ABMs and Data 7

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ABMs and Data ABM born as "theory development tool" Simulations generate implications of encoded assumptions 7

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ABMs and Data ABM born as "theory development tool" Simulations generate implications of encoded assumptions Now people use it as forecasting tool (epidemiology, economics, etc.) 7

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ABMs and Data ABM born as "theory development tool" Simulations generate implications of encoded assumptions Now people use it as forecasting tool (epidemiology, economics, etc.) Calibration to set parameters from data 7

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Calibration 8

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Calibration Run simulations with different parameters until model reproduces   summary statistics of data 8

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Calibration Run simulations with different parameters until model reproduces   summary statistics of data No parameter signi fi cance or model selection 8

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Calibration Run simulations with different parameters until model reproduces   summary statistics of data No parameter signi fi cance or model selection Arbitrary choice of summary statistics and distance measure 8

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Can we do better? 9

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Can we do better? Yes! 9

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Can we do better? Yes! Rewrite ABM as Probabilistic Generative Model   Xt ∼ Pt (Xt ∣ Θ, Xτ

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Can we do better? Yes! Rewrite ABM as Probabilistic Generative Model   Xt ∼ Pt (Xt ∣ Θ, Xτ

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Can we do better? Yes! Rewrite ABM as Probabilistic Generative Model   Xt ∼ Pt (Xt ∣ Θ, Xτ

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Historical Aside Maximum Likelihood Estimation invented by Fisher Dates back to Daniel Bernoulli and Lagrange in the eighteenth century Fisher introduced the method as alternative to method of moments Which he criticizes for its arbitrariness in the choice of moment equations 10

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Autodiff Set of techniques to evaluate the partial derivative of a computer program Chain rule to break complex expressions Originally created for neural networks and deep learning (backpropagation) Different from numerical and symbolic differentiation ∂f(g(x)) ∂x = ∂f ∂g ∂g ∂x 11

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Example Automatic Differentiation (autodiff) • Create computation graph for gradient computation ∗ "# + %# ∗ "& %& "' + ∗ −1 *%+ +1 , = 1 1 + *.(012034320545) 1/% 12

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Example Automatic Differentiation (autodiff) • Create computation graph for gradient computation ∗ "# + %# ∗ "& %& "' + ∗ −1 *%+ +1 1/% − 1 %& - = 1 1 + */(123145431656) - % = 1/% à 89 85 = −1/%& 13

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Example Automatic Differentiation (autodiff) • Create computation graph for gradient computation ∗ "# + %# ∗ "& %& "' + ∗ −1 *%+ +1 1/% − 1 %& - = 1 1 + */(123145431656) ∗ 1 - % = % + 1 à 89 85 = 1 14

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Example Automatic Differentiation (autodiff) • Create computation graph for gradient computation ∗ "# + %# ∗ "& %& "' + ∗ −1 *%+ +1 1/% − 1 %& - = 1 1 + */(123145431656) ∗ 1 ∗ - % = *5 à 89 85 = *5 15

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Example Automatic Differentiation (autodiff) • Create computation graph for gradient computation ∗ "# + %# ∗ "& %& "' + ∗ −1 *%+ +1 1/% − 1 %& - = 1 1 + */(123145431656) ∗ 1 ∗ ∗ −1 ∗ 89 814 - %, " = %" à 8; 81 = % 16

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Example Automatic Differentiation (autodiff) • Create computation graph for gradient computation ∗ "# + %# ∗ "& %& "' + ∗ −1 *%+ +1 1/% − 1 %& - = 1 1 + */(123145431656) ∗ 1 ∗ ∗ −1 ∗ 89 814 ∗ 89 816 17

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Problem Solution → 18

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Problem Solution → No parameter signi fi cance or model selection Probabilistic modeling   18 →

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Problem Solution → No parameter signi fi cance or model selection Arbitrary choice of summary statistics and distance measure Probabilistic modeling   Data likelihood   18 → →

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Problem Solution → No parameter signi fi cance or model selection Arbitrary choice of summary statistics and distance measure Manual, expensive, and   error-prone process Probabilistic modeling   Data likelihood   Automatic differentiation 18 → → →

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Likelihood vs Simulation 19

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Opinion dynamics How people's belief evolve Polarization, Radicalization, Echo Chambers Data from Social Media 20

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Opinion dynamics How people's belief evolve Polarization, Radicalization, Echo Chambers Data from Social Media 20

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Likelihood-Based Methods Improve Parameter Estimation in Opinion D XC X0 XC+1 B 4 n ) (a) BCM-F X: opinions s: interaction outcome e: interacting agents : bounded con fi dence interval ϵ Generative Model 21

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Macro-Parameter Inference 22

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Macro-Parameter Inference 22

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Macro-Parameter Inference 22

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Macro-Parameter Inference 22 RE=89%   (90th pctile) RE=22%   (90th pctile)

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More Accurate and Faster 23

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More Accurate and Faster 23

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More Accurate and Faster 23

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Micro-Parameter Inference 24

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Micro-Parameter Inference 24

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Micro-Parameter Inference 24

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Case Studies 1. Housing Market (HM) 2. Opinion Dynamics (OD) 25

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A B C n l 26

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A B C n l 26

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A B C n l 26

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0 1000 x=0 x=1 x=2 x=3 k=0 x=4 0 1000 k=1 0 1000 k=2 Number of agents Mt 0 100 k=0 0 100 k=1 100 k er of buyers DB t Learned trace Ground truth Latent Observable 0 1000 x=0 x=1 x=2 x=3 k=0 x=4 0 1000 k=1 0 1000 k=2 Number of agents Mt 0 100 k=0 0 100 k=1 100 k= ber of buyers DB t Learned trace Ground truth 0 1000 x=0 x=1 x=2 x=3 k=0 x=4 1000 k=1 f agents Mt Learned trace Ground truth Micro-State Inference

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Forecasting 28

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2 0 2 n+ = 0.4 n = 0.6 0 2 n+ = 1.2 n = 1.6 nthetic data traces generated in each scenario. Plots represent the opini Opinion Trajectories Parameter values encode different assumptions and   determine signi fi cantly different latent trajectories 29

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Reconstructing synthetic data Estimated x0 True x0 Estimated xt True xt 30

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Recovering parameters 31 Figure 4: Examples of synthetic data traces generated in each s 0 2 n+ = 0.6 n = 1.2 0 2 n+ = 0.4 n = 0.6 0 2 n+ = 1.2 n = 1.6 0 2 n+ = 0.2 n = 1.6 Figure 4: Examples of synthetic data traces generated in each scenario. Plots represent the opinion trajectories along time.

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Real data: 32

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Real data: Number of upvotes on comments 32

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Real data: Number of upvotes on comments Estimate position of users and subreddits in opinion space 32

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Real data: Number of upvotes on comments Estimate position of users and subreddits in opinion space Larger estimated distance of user from subreddit fewer upvotes of user on that subreddit → 32

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Variational Approach 33

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Likelihoods are hard 34

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Likelihoods are hard Writing the correct complete data likelihood can be challenging Easy to make mistakes Requires deep understanding of the data generating process 34

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Likelihoods are hard Writing the correct complete data likelihood can be challenging Easy to make mistakes Requires deep understanding of the data generating process Is there a way to avoid it? Variational approximation! 34

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Variational Inference 35

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Variational Inference Bayesian technique to approximate intractable probability integrals Alternative to Monte Carlo sampling (e.g., MCMC, Gibbs sampling) 35

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Variational Inference Bayesian technique to approximate intractable probability integrals Alternative to Monte Carlo sampling (e.g., MCMC, Gibbs sampling) approximation of the posterior = variational distribution, tractable parametric family Variational parameters optimized by minimizing the KL divergence between and P(Θ ∣ X) ≈ Qϕ (Θ) Qϕ ϕ P Q 35

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No Need to Write Likelihood 36 P( ∣ ) Original ABM Probabilistic Generative ABM Variational Inference Data Approximate posterior macro- and micro-parameters ˜ P(ε ∣ ) ˜ P(r 1 , …, r N ∣ ) t t+1 t+1 t

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Accurate Macro-Parameter Inference 37 SVI = Stochastic Variational Inference

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Accurate Micro-Parameter Inference 38

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Fast 39

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Model Thinking 40

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Model Thinking Always think about the Data-Generating Process 40

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Model Thinking Always think about the Data-Generating Process Model- fi rst thinking as justi fi cation for scienti fi c claims 40

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Model Thinking Always think about the Data-Generating Process Model- fi rst thinking as justi fi cation for scienti fi c claims Causal (possibly mechanistic) models (e.g., ABMs) 40

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Model Thinking Always think about the Data-Generating Process Model- fi rst thinking as justi fi cation for scienti fi c claims Causal (possibly mechanistic) models (e.g., ABMs) Use scienti fi cally signi fi cant models 40

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Conclusions 41

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Conclusions Fit ABMs as statistical models Rewrite as probabilistic models for the data-generating process 41

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Conclusions Fit ABMs as statistical models Rewrite as probabilistic models for the data-generating process Learn latent variables of models Forecasting and predictions Model selection 41

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Conclusions Fit ABMs as statistical models Rewrite as probabilistic models for the data-generating process Learn latent variables of models Forecasting and predictions Model selection Use data to fi gure out which models work (Ptolemy vs Kepler) Bring ABM in line with statistical models (and scienti fi c ones) 41

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C. Monti, G. De Francisci Morales, F. Bonchi   “Learning Opinion Dynamics From Social Traces”   KDD 2020 C. Monti, M. Pangallo, G. De Francisci Morales, F. Bonchi   “On Learning Agent-Based Models from Data”   Scienti fi c Reports 2023 J. Lenti, C. Monti, G. De Francisci Morales   “Likelihood-Based Methods Improve Parameter Estimation in Opinion Dynamics Models”   WSDM 2024 J. Lenti, F. Silvestri, G. De Francisci Morales   “Variational Inference of Parameters in Opinion Dynamics Models”   arXiv:2403.05358 2024 42 [email protected] https://gdfm.me @gdfm7