Inference Results

The results show that for a small sample of games and the moves therein, the inference is not as accurate compared to a large sample. This is logical, as maximum likelihood does not take into account prior beliefs and only works well by having lots of data. This means that as the amount of data grows the closer it will get to the normal distribution and the correct answer. The weight for the material balance attribute is given as $\lambda_{MAT}$ and the weight for the mobility attribute is given as $\lambda_{MOB}$ in the tables that follow.

 

Table 1: Inference results from two 1000 game databases using the simple model, with two $\lambda$ values.

	Data Set 1		Data Set 2
Attribute Weights	$\lambda_{MAT}$	$\lambda_{MOB}$	$\lambda_{MAT}$	$\lambda_{MOB}$
Actual Values	5.0	0.5	10.0	1.0
Inferred Values	5.1182	0.5000	9.9365	1.0000
Jansen's Values	5.15	0.51	10.23	1.02

The results in Table 1 are clearly quite similar to the Actual values and this demonstrates that this method of inference is solid and that it finds correct values. The next thing to note is that the inference from the strategy used through hill climbing could be a reason for the better approximations of the actual $\lambda$ values.

The next question is whether the results for the Grandmaster games were similar, and the answer is yes. The two grandmasters selected in Jansen et al.'s paper were Robert J. Fischer and Garry Kasparov [17][18]. As Jansen et al. used the entire database and since inference works better with more information, entire databases for each player were again used. The same particular games could not be found as they were not specified in the Jansen et al. paper but the most complete databases established were used. The results can be seen in Table 2, which shows the number of games in each grandmaster database, the inferred weights, and the past results of Jansen. The past results showed that the inference obtained with the simple model is not as accurate as it could be, but that a simple model can in fact have the capacity to model the play of Grandmasters. The results in duplicating these experiments verify these conclusions. The compression is measured as the percentage of the random game that the inferred game represents.

 

Table 2: Inference results from grandmaster databases using the simple model.

	No.
Results	Games	$\lambda_{MAT}$	$\lambda_{MOB}$	I-Random	I-Inferred	Comp (%)
Fischer	876	0.567	0.021	337857	319665	94.6
Jansen et al.'s Fischer	732	0.510	0.021	146047	138383	94.8
Kasparov	1879	0.526	0.021	340627	324108	95.2
Jansen et al.'s Kasparov	1030	0.458	0.025	191936	183021	95.4