Computational landscape of user behavior on social media

With the increasing abundance of “digital footprints” left by human interactions in online environments, e.g., social media and app use, the ability to model complex human behavior has become increasingly possible. Many approaches have been proposed, however, most previous model frameworks are fairly restrictive. We introduce a new social modeling approach that enables the creation of models directly from data with minimal a priori restrictions on the model class. In particular, we infer the minimally complex, maximally predictive representation of an individual's behavior when viewed in isolation and as driven by a social input. We then apply this framework to a heterogeneous catalog of human behavior collected from 15 000 users on the microblogging platform Twitter. The models allow us to describe how a user processes their past behavior and their social inputs. Despite the diversity of observed user behavior, most models inferred fall into a small subclass of all possible finite-state processes. Thus, our work demonstrates that user behavior, while quite complex, belies simple underlying computational structures.

Figure 1

A schematic representation of the classes of models that we consider in this paper. (a) The most general case, where the user's observed behavior is influenced by their social inputs and their own past behavior. (b) The self-driven case, where the user's behavior only depends on their past behavior. (c) The socially driven case, where the user's behavior only depends on their social inputs. (d) The seasonally driven case, where the user's behavior can largely be attributed to time.

Figure 2

(a) Rastergram representation of the activity of three users on Twitter over a 44-week period. (b) The expected activity of the same three users. Each panel corresponds to the expected activity by day-of-week, from Monday to Sunday. (c) The expected activity from (b) estimated using the GAM given by Eq. (4), laid out in the same format as the rastergram. Note that the color scale for each panel is taken from 0 to ${max}_t{p}_v\left(t\right)$ for each user $v$ to make the seasonality in the activity patterns more obvious.

Figure 3

Transitions between (a) $\epsilon$-machine causal states $s_i^{\epsilon M}$ and $s_j^{\epsilon M}$ and (b) $\epsilon$-transducer causal states $s_i^{\epsilon T}$ and $s_j^{\epsilon T}$. Each transition is labeled by (a) the marginal emission symbol $x$ and transition probability $p^{\epsilon \text{M}}$ and (b) the joint emission symbol $x|y$ and transition probability $p^{\epsilon \text{T}}$. Thus, the label $x:p^{\epsilon \text{M}}$ in (a) indicates that the output $x$ is emitted with probability $p^{\epsilon \text{M}}$, and the label $x|y:p^{\epsilon \text{T}}$ in (b) indicates that the output $x$ is emitted with probability $p^{\epsilon \text{T}}$ on an input of $y$.

Figure 4

The descriptive performance of the self-driven and socially driven models for each user on the test set data relative to the seasonally driven model (S) using the ETV-based score defined by Eq. (11). The diagonal entries show the marginal density of scores for the $\epsilon$-machine ($\epsilon \mathrm{M}$), self-memoryless $\epsilon$-transducer ($\epsilon \mathrm{T}$-ML), and self-memoryful $\epsilon$-transducer ($\epsilon \mathrm{T}\text{−}\mathrm{MF}$) across the users. The off-diagonal entries compare the scores between the nonseasonal models. A score greater than 1 indicates that the referenced model outperformed the seasonally driven model.

Figure 5

The $\epsilon$-machine representations of a renewal process of the eventually ${\mathrm{\Delta }}_0$-Poisson type with characteristic $(\tilde{n},{\mathrm{\Delta }}_0=1)$ (left) and of the reverse eventually ${\mathrm{\Delta }}_1$-Poisson type with characteristic $(\tilde{m},{\mathrm{\Delta }}_1=1)$ (right). The state label $s_i$ indicates the number of time steps $i$ away from the active state (left) or the quiescent state (right). 67.9% of users have $\epsilon$-machines of the renewal type, while only 0.59% have $\epsilon$-machines of the reverse-renewal type.

Figure 6

The $\epsilon$-machine representation of an alternating-renewal process of the eventually $({\mathrm{\Delta }}_1,{\mathrm{\Delta }}_0)$-Poisson type with characteristic $({\tilde{m}}_1,{\tilde{n}}_0,{\mathrm{\Delta }}_1=1,{\mathrm{\Delta }}_0=1)$. The state label $s_{i_x}$ indicates the number of time steps $i$ in the active chain ($x=1$) or the quiescent chain $(x=0)$. 8.7% of users have $\epsilon$-machines of the alternating-renewal type.

Figure 7

A schematic demonstrating the partitioning of the transducer state space associated with a renewal-like $\epsilon$-transducer. Each quadrant is determined by the input-output symbol pair being “counted,” and each third within a quadrant is determined by the input-output pair the count begins from. We only show outgoing transitions for the first third of the first quadrant, which correspond to transitions of $0|1$, $1|0$ or $1|1$ after observing $0|0$. 70.4% of users have $\epsilon$-transducers of this type.

Figure 8

The most common self-memoryful $\epsilon$-transducer architecture associated with 3376 of the 12 641 mentioned users (27%).

Figure 9

Pseudocode for the transCSSR algorithm. Arguments: $\mathcal{Y},\mathcal{X}$: the discrete alphabets for the input and output processes; $(y_1^N,x_1^N)$: the joint input-output sequence of length $N$ drawn from $\mathcal{Y}\times \mathcal{X}$; $L_{max}$: the maximum history length used when estimating candidate causal states; $\alpha$: the probability of falsely rejecting the null hypotheses Eqs. (A1) and (A2).