class: center, middle, inverse, title-slide # ABM-MAS Project<br> ## <em>Algorithmic Bias in<br> Echo Chamber Formation</em> <br><br> ### 2020-12-21 | <em>University of Turin</em> --- name: overview class: center # Overview .left[ **Goal**: to assess the impact of the recommendation algorithm on Twitter echo chambers. #### 1. [*Definitions*](#definitions) #### 2. [*Data*](#data) #### 3. [*Model*](#model) #### 4. [*Exploratory Data Analysis*](#exploratory-data-analysis) #### 5. [*Future Developments*](#future) ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: definitions class: center ## Definitions .left[ ### Recommendation algorithm A parametric feed-ranking system which is said to be * *free* if completely determined by the follower graph topology and users activity chronology; * *biased* otherwise.] .left[ ### Echo Chamber Let's consider a metagraph `\(G\)`, a measure of node attribute homogeneity `\(\xi:2^G \to \mathbb{R}\)` and a clustering algorithm `\(\mathcal{C}\)`. We define a `\((\mathcal{C}, p)\)`-*echo chamber* as a subgraph `\(H \subseteq G\)` such that 1. `\(H\)` is a `\(\mathcal{C}\)`-cluster. 2. `\(\xi(H) \geq p\)`. ] --- name: data class: center # Data .left[ ### 2012 collection 1. **Tweets mining**: all relevant tweet objects from 2012 data. 2. **Hashtag-based users mining**: U.S. election related hashtags have been searched and the users who adopted them selected. 3. **Subscription-based users mining**: the set `\(X\)` of users who survived from 2012 to 2020 has been considered ( `\(\sim 100,000\)` ). ### 2020 collection 1. **Interaction network scraping**: user timeline-aggregated interaction network has been extracted `\(\forall x \in X\)` in order to filter the subset `\(Y \subset X\)` of those who are still active and sufficiently connected ( `\(\sim 10,000\)` ). 2. **Users activity monitoring**: A detailed temporal activity monitoring pipeline has been launched `\(\forall y \in Y\)`. ] --- name: exploratory-data-analysis class: center # Exploratory Data Analysis .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: tweet-dynamics class: center ## Tweet Dynamics: *X vs. Y* .pull-left[ ### Year     ] .pull-right[ ### Election Period     ] --- name: retweet-dynamics class: center ## Retweet Dynamics: *X vs. Y* .pull-left[ ### Year     ] .pull-right[ ### Election Period     ] --- name: hashtag-dynamics class: center ## Hashtag Dynamics: *X vs. Y* .pull-left[ ### Year     ] .pull-right[ ### Election Period     ] --- name: activity-ensemblesx class: center ## Activity Ensembles: *X* .pull-left[ ### Year  ] .pull-right[ ### Election Period  ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: activity-ensemblesy class: center ## Activity Ensembles: *Y* .pull-left[ ### Year  ] .pull-right[ ### Election Period  ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: favorite-activity class: center ## Favorite Activity: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: hashtag-activity class: center ## Hashtag Activity: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: friend-activity class: center ## Friend Activity: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: friend-activity class: center ## Mention Activity: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] --- name: hashtag-frequency class: center ## Hashtag Frequency: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] --- name: hashtag-heterogeneity class: center ## Hashtag Heterogeneity: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] --- name: interacting-user-heterogeneity class: center ## Interaction Heterogeneity: *X vs. Y* .pull-left[ ### Year   ] .pull-right[ ### Election Period   ] --- name: activity-correlogram-X class: center ## Activity Correlations: *X* .pull-left[ ### Year  ] .pull-right[ ### Election Period  ] --- name: activity-correlation-matrix-X class: center ## Activity Correlations: *X* .pull-left[ ### Year  ] .pull-right[ ### Election Period  ] --- name: activity-correlogram-Y class: center ## Activity Correlations: *Y* .pull-left[ ### Year  ] .pull-right[ ### Election Period  ] --- name: activity-correlation-matrix-Y class: center ## Activity Correlations: *Y* .pull-left[ ### Year  ] .pull-right[ ### Election Period  ] --- name: CCDF-Y-year class: center  --- name: CCDF-Y-election class: center ## Election CCDF: *Y*  --- name: timespan-users class: center ### Activity Timespan Distributions: *X vs. Y* .pull-left[ ### Year  ] .pull-right[ ### Election Period   ] --- name: timespan-users-Y class: center ### Hashtag Timespan Distributions: *X vs. Y* .pull-left[ ### Year  ] .pull-right[ ### Election Period   ] --- name: model-architecture class: center ## Model Architecture .small[ #### Ambient Space A **multiplex graph** `\((V,(E_{\text{follow}}, E_{\text{retweet}}, E_{\text{favorite}}, E_{\text{mention}}))\)` .pull-left[ .left[ #### Tweet * `id` `\(\in \mathbb{N}\)` * `user_id` `\(\in \mathbb{N}\)` * `retweet_status` `\(\in \{T,F\}\)` * `content` `\(\in \mathbb{R}\)` * ... #### User * `id` `\(\in \mathbb{N}\)` * `opinion` `\(\in \mathbb{R}\)` * `activity_rate` `\(\in \mathbb{R}\)` * ... ]] .pull-right[ .left[ #### Micro-dynamics * `Tweet!` * `Update!`: opinion dynamics * `Follow!`: social dynamics * `Unfollow!`: social dynamics * ... #### Macro-dynamics * Centrality metrics * Clustering metrics * ... ]] ] --- name: model-simple1 class: center ## Minimal Model .small[ .pull-left[ .left[ #### Tweet Type * `id` `\(\in V \subset \mathbb{N}\)` * `user_id` `\(\in \mathbb{N}\)` * `retweet_status` `\(\in \mathbb{B}\)` * `retweeted_id` `\(\in \mathbb{N}\)` * `retweeted_user_id` `\(\in \mathbb{N}\)` * `content` `\(\in \mathbb{R}\)` * `favorite_count` `\(\in \mathbb{N}\)` * `retweet_count` `\(\in \mathbb{N}\)` * `step` `\(\in \mathbb{N}\)` #### User Type * `id` `\(\in \mathbb{N}\)` * `pos` `\(\in \mathbb{N}\)` * `feed` `\(\subset \mathcal{T}\)` * `tweets` `\(\subset \mathcal{T}\)` * `favorites` `\(\subset \mathcal{T}\)` * `opinion` `\(\in \mathbb{R}\)` * `tweet_rate` `\(\in \mathbb{R}\)` * `retweet_rate` `\(\in \mathbb{R}\)` * `favorite_rate` `\(\in \mathbb{R}\)` * `follow_rate` `\(\in \mathbb{R}\)` * `unfollow_rate` `\(\in \mathbb{R}\)` ] ] .pull-right[ .left[ #### Data * Degree distributions * Activity distributions * Tweet * Favourite * Follow #### Parameters * Population size `\(N\)` * Number of replicates `\(R\)` * Number of time steps `\(T\)` * Controversialness `\(\alpha\)` * Follow threshold `\(f\)` * Unfollow threshold `\(u\)` #### Properties * Population size `N` * Time step `step` * Tweet ID counter `tweet_id` * Tweet objects `tweets` * Controversialness `α` * Follow threshold `follow_threshold` * Unfollow threshold `unfollow_threshold` ] ] ] --- name: model-simple2 class: center ## Minimal Model .small[ .pull-left[ .left[ #### Initialization * `id`: sequentially initialized * `pos`: sequentially initialized * `feed`: initialized as an empty array * `tweets`: initialized as an empty array * `favorites`: initialized as an empty array * `opinion`: drawn from `\(\mathcal{U}(-1,1)\)` * `tweet_rate` and `retweet_rate`: sampled from 2012 activity data * `favorite_rate`: sampled from 2012 activity data * `follow_rate` and `unfollow_rate`: sampled from 2012 activity data * `follower_graph`: friends (outneighbors) of each user (node) have been drawn from a `\(\Gamma(2,1)\)` #### Calibration Not discussed yet. #### Validation Not discussed yet. ]] .pull-right[ .left[ #### Micro-Dynamics * Opinion dynamics (`Update!`): governed by the equation in [Baumann et al. (2020)](https://doi.org/10.1103/PhysRevLett.124.048301) * Follow dynamics (`Follow!`): uniform sampling from the complement of set of friends according to `follow_rate` and `follow_threshold` * Unfollow dynamics (`Unfollow!`): uniform sampling from the set of friends according to the user's `unfollow_rate` and `unfollow_threshold` #### Macro-Dynamics * Time step `step` is incremented by one at each iteration * Tweet ID counter `tweet_id` is incremented by one every time a tweet is authored (or retweeted) * Tweet objects `tweets` is enriched with every tweet object authored (or retweeted) ]] ] --- name: model-simple3 class: center ## Minimal Model .small[ .pull-left[ .left[ ### Thoughts & Doubts * How to define distinct time scales ? `$$T_{F} \gg T_{RT} > T_{L}$$` * Choose `nsteps` taking into account the constraints induced by Monitor resolution. * Highlight the latency of the opinion variable: users do not have direct access to the *cognitive opinion* of others but they have indirect access to *behavioral opinion* leading to a non-zero probability of misinterpretation (we may model it via probability distributions centered around the true value) * Think about how to implement possible polarization/segregation mitigation strategies (e.g. *homophily-induced heterophily*) * How to reliably mine temporal behavioral opinion and reaction mechanisms (e.g. net positive interaction rate: net of T,RTs,L of known polarity / total number of interactions) ]] .pull-right[ .left[ ### To-Do List * Overwrite all graph-related functions in `Agents.jl` to ensure compatibility with `MultiplexGraphs.jl` (e.g. `get_node_agents()`,...) * Think about all elementary variables, parameters and timing distributions * Explore the portfolio of possible recommendation systems (e.g. GNN, bipartite, centrality-based, simple weighted sum,...) * Implement `Read!`, `Tweet!`, `Like!`, `RT!` behaviors * Implement the simplest recommendation system (in `model_step!`) * Implement non-trivial interpretation distribution `\(\rho_i\)` * Think of the best parametrization that allows effective calibration ]] ] --- name: future class: center # Future Developments .left[ ### Initialization, calibration & validation * A time step is selected so that it encompasses a statistically significant portion of 2012 data. The distributions extracted from the first temporal slice is used to initialize the model. * The rest, except for the last slice, is instead adopted to calibrate the model (parameters such as changes in activity rates) * The last slice will be used for validation. .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] ] --- name: future class: center # Future Developments .left[ ### Recommendation algorithm * Training and validation of a model able to perform link prediction on the multiplex graph of the ABM from the monitor data. * Fit the parametric algorithm on the dynamics predicted by the link prediction model on the multiplex graph. * Predicted feeds of all users will let us draw a temporal directed **tweet network**, whose nodes are users and edges encode reading relationships. This new network encodes the actual information flow on Twitter, the one where the concept of echo chambers makes sense. .footnote[ .left[.small[For further details, please read the [report](https://inphyt.github.io/ABM_MAS/Report/report.html).]]] ]