Verifying Event Salience Component Weights

As noted in Section 5.2, attention and learning are mediated by a set of cognitive models that model social influences (authority, conformity, ingroups, reference groups, similarity, valence), action characteristics (motivated attention, transferability), and general attentional factors (novelty, selection) that affect the likelihood that an agent will learn from an observed event. Each of these factors was chosen because it was based upon an empirical study which showed that the factor had a positive correlation with the probability of being able to recall a message or event. This analysis verifies that the components of the cognitive model capture the relationships they are intended to model.

Table 7.10: Event Salience Component Weights (Copy of Table 5.7)

Component Assumed Weight Source Process

Authority 0.33 Mantell(1971) Peripheral

Conformity 0.34 Tanford and Penrod(1984) Peripheral

In-Group 0.30 Tajfel(1982) Peripheral

Motivation (central) 0.47 Roskos-Ewoldsen and Fazio(1992) Central

Novelty 0.21 Johnston et al.(1990) Mixed

Reference Group 0.30 Kameda et al.(1997) Peripheral

Selective Attention 0.32 Simons and Chabris(1999) Mixed

Similarity 0.47 Platow et al.(2005) Peripheral

Transferability 0.10 Bandura(1986) Central

Valence/Halo 0.38 Hilmert et al.(2006) Peripheral

Earlier in Chapter 5, the cognitive components were described which are used to determine if an agent learns from an event that they can physically observe. Learning from an event requires that an agent must pay attention to the event, after which learning occurs probabilistically. As noted, under the current settings all attended events result in learning. As such, attention is the key factor that controls which events are learned. Attention to an event is determined probabilistically as a function of the attentional salience of that event. Table7.10 displays the assumed importance of each cognitive component in determining if an event is attended. Attentional salience for an event is a weighted sum of each of those inputs, as weighted by the displayed weight.

As mentioned earlier, these weights are not necessarily empirically true but are modeling assumptions that form the “best guess” from examining the stated studies. As noted in Section 5.2.5, no empirical study has examined all these factors simultaneously. As such, the linear structure of the attentional salience calculation and the weights must be considered as modeling assumptions. The true structure and relative importances of these factors in determining attention

and learning still has considerable ambiguity. This is an area where more empirical research could significantly improve the model quality.

However, the calculation of attentional salience does capture some important information. This analysis is intended to test for the following:

1. Firstly, according to the empirical studies, all of the factors in Table 7.10 should have a positive relationship with learning from an event.

2. Secondly, the computational agent cognitive model components should affect attention with these relative weights. This is an important sanity check that the cognitive model is wired correctly.

3. Finally, this analysis should demonstrate that relative weights can be calculated based upon observable data without needing to know their values a priori. This is important because it shows that an empirical study could be designed that would improve these weights, if attentional salience could be approximated by a sum of linearly weighted components.

Separate from the simulation runs, a test was made using the attention model alone. Events were passed to an agent for which each salience component was selected from a uniformly random distribution in [0,1]. A set of one hundred thousand randomly generated events were passed to the attention model, with the outcome recorded (attended vs. not attended). This attention model used an inattention salience of 8.0 (same as Hamariyah) and presented one event at a time.

A test system was implemented which examined an individual agent’s attention by passing it events with randomized salience component inputs. Figure 7.1displays the system that was used to test that the agent’s cognitive model was handling attention correctly. The attention model was shown a series of individual events, each of which was specifically designed to have a particular value for Novelty, Similarity, and all other components used for calculating attention salience as noted in Table 7.10. A data set was generated by presenting one hundred thousand events to the attention model, where each event had random and independent inputs to the salience calculation.

Attended(e) =β0·Novelty(e) +β1·MotivatedAttention(e)+

β2·SelectiveAttention(e) +β3·Transferability(e)+

β4·Authority(e) +β5·Conformity(e) +β6·Similarity(e)+

β7·Valence(e) +β8·InGroup(e) +β9·ReferenceGroup(e) +m+

(7.7) The data set was processed using a logistic regression, shown for reference in Equation 7.7 (a copy of Equation 7.3). This regression returns raw regression

Figure 7.1: Event Salience Test Setup

β weights. These raw β weights do not directly correspond to the true salience coefficient weights shown in Table 7.10because attention is the output variable, rather than attentional salience. As noted in Section 7.2.2, attention is a probabilistic function of the sum of salience terms for observed events as well as inattention salience. While the rawβ weights will not match the true salience weights, if each set of weights is normalized to sum to 1, then they should match up.

For example, the maximum attention salience occurs when all inputs are equal to 1 and sums to 3.22 (the sum of the weights in Table 7.10), with the contribution from novelty being 0.21. If the rawβweights sum to 6.44 (excluding the intercept), then the β weight from novelty should be 0.42. If the cognitive model is working properly, then Equation 7.8should hold for the salience input weights whereβi represents a rawβ regression weight andwi represents the true salience input weight for the input i. If this holds, the test has demonstrated that the agent pays attention to events because of the factors in Table 7.10and that the relative importance of each factor corresponds to its salience weight.

βi P iβi ≈ _Pwi iwi ∀i∈ {SalienceInputs} (7.8) To make this easier to examine, the raw regression weights for attention are multiplied by a factor of

P

wi|wi|

P

βi|βi|. While not changing the importance of the

weights relative to each other, it allows them to be directly compared against the underlying weights in the attention salience model (True Coefficients). The results of the regression are presented in Table 7.11. This table shows the raw β coefficients, the rescaled β coefficients, the true model coefficients, and the difference between the rescaledβ weights and the true salience weights.

Table 7.11: Component Weights for Attention (Random, Indep. Components)

Raw Rescaled True Model

Salience Input Coefficients (βi) Coefficients Coefficients (wi) Rescaled - Actual

Authority 0.21 0.34 0.33 0.01 Conformity 0.22 0.36 0.34 0.02 InGroup 0.18 0.29 0.30 -0.01 Motivation 0.27 0.44 0.47 -0.03 Novelty 0.13 0.22 0.21 0.01 Reference Group 0.19 0.31 0.30 0.01 Selection 0.20 0.31 0.31 0.00 Similarity 0.30 0.48 0.47 0.01 Transferability 0.07 0.11 0.10 0.01 Valence 0.23 0.37 0.38 -0.01

This verifies that the attention model integrates the attention salience components as designed. Each component has a measurably positive contribution toward learning, meaning that the cognitive components are correctly implemented. It also shows that, given the model design, a logistic regression can tease out the relative impact of different inputs to the attentional salience despite its low predictive utility. This means that if human attention was directed by such a process, the relative weights could be inferred.