Merge branch 'main' into main

Author: Aravind-11

README.md

@@ -1,3 +1,101 @@
 # Inductions-22
-##### Fork the repo and create a pull request of your solution to this repository for the corresponding tasks 
+
+##### Fork the repo and create a pull request of your solution to this repository for the corresponding tasks
+
 ##### Note : Do not send pull requests to the main repo. Make sure you are sending requests inside your tasks folder
+Sentimental
+
+> medium link:
+> [https://medium.com/@advaith142001/farmers-protest-twitter-sentiment-analysis-a8aca1e52f43](https://medium.com/@advaith142001/farmers-protest-twitter-sentiment-analysis-a8aca1e52f43)
+=======
+Parameter :
+A variable that is internal to the the model and whose value can be estimated from data.
+-They are required by the model when making predictions
+-They are often saved as part of the learned model 
+
+Hyperparameter :
+A variable that is external to the the model and whose value cannot be estimated from data.
+-They are often used in processes to help estimate model parameters.
+-They are often specified by the practitioner.
+
+Gaussian process:
+It's a powerful algorithm for both regression and classification 
+-Gaussian process is a probaility distribution over possible functions
+Kernal :
+The method of classifying linearly for the non-linear problems
+
+Surrogate method :
+A statistical model to accurately approximate the simulation output
+
+Probablistic model :
+Probabilistic modeling is a statistical approach that uses the effect of random occurrences or actions to forecast the possibility of future results
+-it provides a comprehensive understanding of the uncertainty associated with predictions. 
+-Using this method, we can quickly determine how confident any mobile learning model is and how accurate its prediction is.
+
+Nomenclatures:
+
+1. suurogate model (gaussian function in this case)
+It is the statistical/probabilistic modelling of the “blackbox” function. 
+It works as a proxy to the later. For experimenting with different parameters
+This model is used to simulate function output instead of calling the actual costly function
+
+2. Acquisition Function 
+It is a metric function which decides which parameter value that can return the optimal value from the function. 
+There are many variations of it. We will work with the one “Expected Improvement”
+
+
+
+Problem statement 
+To summarize  a research paper which talks about efficiency and implementation of bayesian optimaization 
+
+
+Pseudo code for Bayesian optimization  
+
+SURROGATE FUNCTION (Gaussian process)
+step1 Looping over all the samples values of input x, where the evaluatation takes place .
+  2. Building k and f vectors i.e the data 
+  3. Building matrices X and Y
+  4. Calculating mu and sigma.
+  5. Appending mu to predictedMu array and sigma to predictedSigma array
+step6 Calculation of Omega as the mean of blackbox function for sampled points
+step7 Calculation of Kappa =PredictedMu + Omega 
+step8 Returning values
+  Kappa(estimated mean of suurogate func.) and predictedSigma (estimated variance of surrogate func.)
+ I have used sklearn module to import gaussian Process in my model
+ACQUISITION FUNCTION
+Usually acquisition functiopn consist of :
+1.Upper confidence bound 
+2.Lower confidence bound 
+3.Probability of imbprovement 
+4.Expected Improvement 
+
+
+Mathematical inpretation
+
+let us take the actual function be f(x)
+bayesian function be y= f(x) + e(Etta) where e is small value to optimize the return value
+instead y can be represenated as gaussian distribution of (f(x), variance)
+GP is completely specified by its mean function mu(x) and its covariance k(x,x')
+
+Loss function can be representated by gaussian distribution of its mean and covariance as mentioned above
+
+Coming to acquisition function
+
+expected improvement EI(x)= E[max {0, f(x)-f(x")
+where x" isthe current potimal set of hyperparameters. Maximizingthis parameter will give
+us the point that improves upon function the most
+
+EI(x)= mu (x)- f(x"))psi(Z) + sigma (x)Pi(Z) if sigma (x) >0
+     = 0 if sigma (x) =0
+therffore, 
+  Z= (mu (x)- f(x") )/sigma (x)
+
+here, Psi (x) is cumulative function and pi(z) is probability density 
+
+
+Final points, 
+1.Given observed values f(x), update the posterior expectation of f using the GP model.
+2.Find xnew that maximises the EI: xnew=argmaxEI(x).
+3.Compute the value of f for the point xnew.
+
+by iterating for different values we can make a perfect model or function which suits the actual functionmain