This section provides Table 5.12, a summary table of results. The summary table lists p-value for each experiment for each architecture.
This Results chapter has presented data and statistical analysis of embodied architectures. Having now shown the quantitative measures, the next chapter will give insight into implications of these measures.
Discussion
In this chapter, the empirical analysis of the behavior of the embodied neural ar- chitecture is discussed. First, statistical analysis of the basic embodied architecture performing distal reward, persistence to goal, and rapid transfer learning tasks is discussed. Then the statistical analysis of the categorical limits supporting embod- ied architecture during the same task performance is considered. Following that, the original architecture is compared to the limits architecture. Finally, results are discussed in the context of behavior observed in biological rats.
6.1
Statistical Analysis of Baseline Architecture
Statistical Analysis is employed to provide evidence that observed behavior is not a product of chance. Rather, the neural architecture itself is showing significant learning of distal reward behavior.
6.1.1
Distal Reward Learning
Using analysis of variance (ANOVA) to test the statistical difference between the data for the individual release pathlength for the individual rats between the static platform group and the random platform location group yields a p-value of 0.0001955,
indicating that there is a less than a 0.02 percent chance that the observed results were observed in a system where the null hypothesis is valid. A p-value of 0.05 is generally accepted as the cut off for statistical significance [106]. The null hypothesis was that learning to a fixed platform location would be performed no better than learning to a random platform location. Since there is effectively no learning to a random platform location, were the null hypothesis true, it would mean that no learning had occurred in the experiment. Table 5.3 in Section 5.1.1 shows sum pathlenth over the last half of releases of the experiment for each rat. It is seen that for most rats, sum pathlength for the releases making up the last half of each trial is lower in the fixed platform case than the random platform case. The average over all subjects was 14774 with fixed platform and 20268 with random platform. Shorter pathlengths to the fixed platform indicate that the platform location was learned. Based on a significant result against the null hypothesis, along with the data in Table 5.3 which shows evidence of learning, it is concluded that embodiments of the computational model will learn to navigate to a fixed platform.
6.1.2
Persistence to Goal
As shown in results section 5.1.2, the average percent time spent near reward for untrained rats is 5.51. The average percent time spent near reward for trained rats
is 6.19. A p-value of 4.79x10−15 is observed for ANOVA between the two groups.
This indicates that for the two groups of twenty simulated rats observed, there is
a probability of 4.79x10−15 that the behavioral difference, as measured between the
two groups, could have occurred given a true null hypothesis. In this case, the null hypothesis was that trained rats will spend an equal amount of time searching around the location of reward in the water maze as will untrained rats. Therefore the trained rats did, with statistical significance, spend more time swimming within the platform region.
Initial N E S W N 5786 5892 5075 5708 E 2160 1481 1219 1195 S 8102 6834 8290 6485 W 7903 7266 7843 7019 Differences N -106 711 78 E 679 941 965 S 1268 -188 1618 W 637 60 884
Table 6.1: Differences of pathlenths between naive release and releases with potential transfer learning.
Table 5.10. PctInThresh records the percent of total tank time which the rat spent within a constant distance from the center of the platform location. It can be ob- served that there is no overlap between the fractions of time which the two popula- tion samples spent in the platform region. On an absolute scale, there is not a large magnitude in the difference between measured group behaviors, but the analysis of variance allows us to none the less assign meaningful statistical significance to the measures.
Therefore, it can be said that the embodied computational neural architecture is capable of performing the persistence to goal behavior. This same persistence to goal is observed in biological rats, as will be discussed in a later section.
6.1.3
Rapid Transfer Learning
Results section 5.1.3 reports the average across rats of the sum across releases for each trial of the experiment. The top half of table 6.1 shows the same values in a new format. The format of this table shows naive release points on the row headers and potential transfer learning release points on the column headers. The bottom half shows the difference in pathlength between naive releases and releases with the potential for transfer learning. Naive releases occur with the computational rat having not prior experience. Releases with the potential for transfer learning occur
when a rat has previously been trained from a different release point. Across potential transfer learning releases from the north release point, there is an average pathlength difference of 228 from the naive values minus the potential transfer learning values. For the east release point, the average difference was 862. The south difference was 899. The west difference was 527. These differences indicate that on average, transfer learning occurred as a positive difference indicates that the transfer learning average pathlengths were lower. A p-value of 0.04026 for the observed rapid transfer learning behavior. Recall that the null hypothesis for rapid transfer learning is that given a rat will be released from point X, a rat trained from some release point other than X will show no increased performance as compared to a rat with no morris water tank training at all. 0.04026 is the weakest p-value observed for the three experiments. None the less, it is low enough to be considered statistically significant by most criteria. The embodied neural architecture therefore demonstrates reasonably sound rapid transfer learning behavior.