CurrDayChange input discretization

01Dec10

We have only 1 input now, the currDayChange. We try to discretize the input into different equal sample size bins. For example, the 2 bins version discretize the currDayChange according to its sign, mapping negative numbers to -1 and positive numbers to +1. We pursue this, because we suspect that there is inherently something difficult to learn in a continuous Gaussian function. Presenting the data in a nice simple way, we increase the chance that the ANN can learn it. For example, this is the function for the first day prediction (the aggregation of the first 200 days) that the ANN should memorize in case we discretize the input into 10 equal size bins:

This is the function if we discretize it to 4 bins (but using the same 10 bins visualization as before)

The parameters of the experiments:
nNeurons = 2;
nEpoch = 5;
lookbackWindowSize = 200;
outlierFixLimit = 0.04;
nEnsembleMembers = [1, 0, 0];

We made 8 different random experiments per bin version:

the non-discretized experiment:

Note the STD here. The 2bins case is very stable. Almost all the experiments give the same result. This is the beauty of discretization. We made the objective function simple. The ANN can learn it easily and consistently. Compare that STD with the STD of the continuous case.

The performance numbers:

And we make a plot of these performance numbers.

Conclusions:
the 8.7% CAGR of the continuous case can be doubled to 15.38% CAGR in the 4 bins case. So, this test revealed that it is advantageous to discretize the input. We should decide we want to us the 2 bins or 4 bins or 6 bins version.

our most important measure is the D_stat. And the highest D_stat (52.24%) is in the 6 bins case. (however, note the high 0.58% STD that shows high randomness)

– Personally, I would like to use the 6 bins version (maybe with more nNeurons). Intuitively it feels right to discretize the today change as very oversold, oversold, slightly oversold, slightly overbought, overbought, very overbought. I like these 6 categories. However, the tests show unusually high STD in the 6 bins case. So, I hesitate.

The 2 bins case has the lowest randomness. If that is important: stability, low nEnsembleMembers, use the 2 bins case. That is very stable even with only 1 ensemble member.

– Note that the volatility = randomness can be attacked by increasing the members of the ensemble. So our decision should be:
if we have 1 ensembleMembers, use 2 bins.
if we have 2-5 ensembleMembers, use 4 bins
if we have 6+ ensembleMembers, use 6 bins.

– We may repeat the same experiment with 10 ensembleMembers. If the volatility can be decreased, we would like to use 6 bins further on.

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