Fast Recap:
Recap:
Density Estimation:
==MEANING of “Density Estimation” : Estimating PDFs from Unlabeled Data==
Has long been a major issue in patter recognition and machine learning. It is relevant to:
The problem is difficult and still open
“One cannot guarantee a good approximation using a limited number of observation”
Drawbacks of Statistical Approaches:
Parametric vs. Non-parametric techniques
ANN (Artificial Neural Networks) for Density Estimation:
(PNN) Parzen Neural Network:
Algorithm:
(The solution listed as are all solution to the problem)
Also in the PNN algorithm it is recommended to normalize data within a zero-centred meaningful range (meaningful range means not too little not to big, to be distinguished from the small zero-center range used in ANN with sigmoid activation function.
This is especially helpful to:
***If we know $X$ we can upgrade the PNN training algorithm***: ![[Pasted image 20220821195854.png]]
***Architecture Selection***: ![[Pasted image 20220907165230.png]]
TODO WHAT??
Use of PNNs for pattern classification:
Complexity:
TRAINING COMPLEXITY*:
TEST COMPLEXITY:
Comparison of training and testing complexity with SVMs (TODO ) and with PW (Parzen Window) and -NN (-Nearest Neighbour)
training comparison
testing comparison:
To sum it up:
Modelling Capabilities:
Definition of “Interesting PDFs”:
nonpaltry pdf:
Theorem:
Original Files:
(Not to study):
