Week 2: Working with ProbSpace Module

-

     This week I studied the existing Prob.py module which deals with the calculation of conditional probabilites, probability distributions and other functionalities. I also worked on understanding the paper dealing with Hilbert Space Embeddings of Conditional Distributions.  Here is a day-wise summary of my progress throughout the week:


Monday:

Continued to experiment with rkhsTest2.py script. Implemented a sawtooth kernel and evaluation function. Discussed results of the same with Roger sir in the weekly meeting. As it turns out, it doesn’t matter what kernel function we use, given enough data points and time, we can derive an accurate probability distribution curve. Using the right kernel to fit the dataset helps us to arrive at the desired accuracy of the curve much faster and with far lesser data points.


Tuesday:

Studied the paper (Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems ) to learn how to extract conditional probability distribution similar to how we obtained a regular PDF last week. Encountered difficulties with calculation of the beta(B) matrix which contains a list of weights(conditional probabilities) and is different for every testpoint. 


Wednesday:

Worked on understanding the Prob.py module and after some testing around with the probTest.py, figured out how to use some of the major functions( conditional probability estimation E(Y| X=x) ). After comparing it with an ideal curve, it is very accurate at high density portions of the distribution but becomes inaccurate upon moving away from the mean. The goal is to eliminate this problem with the help of RKHS embedding.

Thursday:

Discussed results with Roger sir on the regular weekly meeting, had a discussion about how to proceed with the paper as it contained some difficult to understand math equations. 


Friday:

  Understood the paper better after a mail sent by Roger Sir explaining some of the notations and importance. Did some tests specifically to calculate µhat(X) and mean(X) = f(µhat(X)) which is required to calculate the Covariance matrix equivalent in the Hilbert Space. However it appears we have reached the limit for the usefulness of this paper. 


Upcoming week plans:

Next week we will be focussing on a couple of easier to understand papers (Nonparametric Conditional Density Estimation and Fast Nonparametric Conditional Density Estimation)

Comments

Post a Comment

Popular posts from this blog

Week 1: RKHS Kernel Implementation

-
Image
      My first long term goal is to improve the existing conditional probability calculation module by making use of RKHS mapping to get rid of the curse of dimensionality problem that has been haunting the traditional method. Here is a day-wise summary of my progress throughout the week: Monday: My Internship officially started on this day, I had a 1 on 1 meeting with Roger Sir regarding this week’s assignment which would be to implement an RKHS kernel for the purpose of predicting a probability distribution function, given just a set of data points ( 1000 in my case) belonging to the said distribution. This would bolster my understanding of RKHS working and will come in use when implementing more complex kernels in the future. Tuesday: Implemented the RKHS kernel and the evaluation function. Dataset for the arbitrary function X = logistic(-2,1) if choice([0,1]) else logistic(2,1) was created using the synthDataGen.py script and used as the basis for the evaluation function. Made
Read more

Week 10: Implementing UPROB

-
Image
Week 10 Report This week, I developed the UPROB module (you can check out the code here ). Since this was the main focus throughout the week and I spent all my time developing, bug-fixing , testing and documenting results, I feel that a day-wise summary would not be the most effective method to show results. Instead I have opted to explain the functionalities, working and usage of this module. This will also serve as documentation for future reference. I have listed the results and conclusion towards the end of this report. UPROB Init: Initializing a UPROB Object is very similar to that of rkhsMV except for the final argument k , which denotes the % of variables to be filtered before applying JPROB methods on the remaining ones.  R1 and R2 are two separate rkhsMV instances, one for each of the UPROB methods, condE() and condP(). The idea is to store R1 and R2 such that if we are repeatedly performing operations on the same dataset, we need not initialize a new kernel each time thus sa
Read more

Week 12: Final Week

-
  These past 12 weeks have flown by so fast! It still feels like yesterday I started working on this project. There were highs and lows but at the end of the day we overcame our obstacles to create something to be proud of. It was a great learning experience and I had fun working with the team.  Monday: Implemented the prototype of the K decrement algorithm to reduce the number of filter variables in case of shortage of data points upon filtration. Here are some results: K decrement- condP() K = 100 rf = 0.8, minmin = 20 dims, datSize, tries, K =  3 1000 1 100 Average R2: JP, UP, PS =  0.67025996194      0.726423475099       0.7434199290171855 K=100 , rf = 0.8, minmin = 5 dims, datSize, tries, K =  3 1000 5 100 Average R2: JP, UP, PS =  0.70784384556      0.87296540935         0.764876980843549 K=100 , rf = 0.8, minmin = 4 dims, datSize, tries, K =  4 1000 1 100 Average R2: JP, UP, PS =  0.70162883565      0.80123074862         0.6089856810665888  K=100 in condP() function means that w
Read more