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Simon Ciranka
BayesianLearning
Commits
1e6050b8
Commit
1e6050b8
authored
Sep 07, 2018
by
Simon Ciranka
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1e6050b8
Marbles in Roberts data
#
Marbles in Roberts data
=======================
Here I introduce the three possible learing models that i implemented. I
...
...
@@ -7,19 +7,20 @@ Reinforcement learning like belief updating with a delta rule. Then i
implement a sequential Beta updating model and later the Exponential
Discount factor model which we discussed in todays mails.
HGF like updating with only one free paramter.
##
HGF like updating with only one free paramter.
==============================================
I did this before our mails, so i thought i just leave it here. I am
trying something new
here t
he probability of the Binomial Outcome
trying something new
. T
he probability of the Binomial Outcome
distribution in not assumed to be beta, but normally distributed.
Binomal and Normals are not Conjugate so Neural population encoding also
encodes via approximate normals, so if we want to find neural correlates
of uncertainty maybe such a model would be more adequate. Mathys
proposed the HGF as a learning model under uncertainty which i slightly
modify here to only have two levels. I will also use the delta like
The good thing here is, that we dont rely on the assumption that at some point in the information processing
the bits are made discrete, then somehow updated into a probability distribution.
We have a continous representation and Reenforcement learning like update rules.
Mathys proposed the HGF as a learning model under uncertainty which i slightly
modify here to only have two levels and no coupling parameter. I will also use the delta like
learning rules where uncertainty about the true outcome distribution can
be interpreted as a learning rate.
be interpreted as a
n adaptive
learning rate.
```
r
...
...
@@ -32,8 +33,6 @@ be interpreted as a learning rate.
priorMu
=
0.5
;
priorSig
=
1
;
obs
=
NA
;
# make an array
#hazard=1;
# here i need to make my outcomes sequential.
red
<-
strsplit
(
subjectLevel
$
sequence.marbles.color2
[
i
],
""
)
red
<-
as.numeric
(
unlist
(
red
))
#prepre the array
...
...
@@ -75,7 +74,7 @@ be interpreted as a learning rate.
}
```
Sequential Updating
##
Sequential Updating
-------------------
In this model each piece of evidence is weighted sequentially in the
...
...
@@ -144,7 +143,7 @@ estimate of the participants to create logliks.
}
```
Exponential Discount Factor.
##
Exponential Discount Factor.
----------------------------
This is the model as I understood it from your mail. Insted having a
...
...
@@ -191,7 +190,7 @@ amount of time.
```
Ok. so far so good. In the Following i am going to fit these models the the Behavioral data of the "Entscheidungs" experiment.
Data Loading
###
Data Loading
------------
In this Chunk of Code i load the Data which i made with first loading
...
...
@@ -209,7 +208,7 @@ data and run the script [01\_makeDataFrame.R](01_makeDataFrame.R)
```
Model Fitting
###
Model Fitting
-------------
In the Following I fit the Model with Rs Optim function and store the
...
...
@@ -245,7 +244,7 @@ fitted Parameters in the same dataFrame
```
Here i Fit the Simple LearningRate Model.
####
Here i Fit the Simple LearningRate Model.
-----------------------------------------
```
r
...
...
@@ -278,7 +277,7 @@ Here i Fit the Simple LearningRate Model.
```
Here i Fit the Discount LearningRate Model.
####
Here i Fit the Discount LearningRate Model.
-------------------------------------------
```
r
...
...
@@ -310,7 +309,7 @@ Here i Fit the Discount LearningRate Model.
```
Model Comparison
####
Model Comparison
----------------
Here i judge via G^2 which model is the best. I compare the “HGF Like
...
...
@@ -335,7 +334,7 @@ Seqential Updating is bad.
```
![](
HalfHGF_files/figure-markdown_strict/unnamed-chunk-1-1.png
)
So now lets look at the learning rates.
#
So now lets look at the learning rates.
---------------------------------------
### Marble Estimate Distribution
...
...
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