Lottery prediction using Python's Numpy (Some one pitch in?)

Hi,

As of late I have been learning much about machine learning, basically trying to rehearse how computers learn and possibly use this method to gain an "achievement" with the lottery!!? lol - Thus far I wanted to present what I currently have figured out in terms of coding using python to predict a vector of 5 dimensions or a pick 5 game. What I have, is very simple - however complex if you're not familiar with programming and machine learning. I thought to share my code and see if there's any one here whom would like to contribute in this project and make it complete.

So far the following functions have been called;

One and only one input training sample for X (Multiple batches are needed to predict better), likewise, only one sample for y.

There are 5 inputs, 5 outputs and 4 hidden layers.

5 random weights per neuron connection w^l_jk.

The sigmoid function is assigned to each activation layer.

And sigmoid prime which depicts the amount of error for the output y-hat.

import numpy as np
 #Sample training input
X = np.array(([3,5,20,23,26]), dtype=float)
y = np.array(([3,20,25,28,30]), dtype=float)

X = X/np.amax(X, axis=0)
y = y/36 #Max number size is 36

class Neural_Network(object):
       def __init__(self):
      #define Hyperparameters
          self.inputLayerSize = 5
          self.outputLayerSize = 5
          self.hiddenLayerSize_1 = 7
          self.hiddenLayerSize_2 = 7
          self.hiddenLayerSize_3 = 7
          self.hiddenLayerSize_4 = 7
 
  #weights (parameters)
 
         self.W1 = np.random.randn(self.inputLayerSize, self.hiddenLayerSize_1)
         self.W2 = np.random.randn(self.hiddenLayerSize_1, self.hiddenLayerSize_2)
         self.W3 = np.random.randn(self.hiddenLayerSize_2, self.hiddenLayerSize_3)
         self.W4 = np.random.randn(self.hiddenLayerSize_3, self.hiddenLayerSize_4)
         self.W5 = np.random.randn(self.hiddenLayerSize_4, self.outputLayerSize)
 
     def forward(self, X):
     #propagate inputs through network
         self.z2 = np.dot(X, self.W1)
        self.a2 = self.sigmoid(self.z2)
        self.z3 = np.dot(self.a2, self.W2)
        self.a3 = self.sigmoid(self.z3)
        self.z4 = np.dot(self.a3, self.W3)
        self.a4 = self.sigmoid(self.z4)
        self.z5 = np.dot(self.a4, self.W5)
        yHat = self.sigmoid(self.z5)
 
     return yHat
 
     def sigmoid(z):
      #Apply sigmoid activation function to scalar, vector or matrix
      return 1/(1+np.exp(-z))
 
     def sigmoidPrime(z):
      #Derivative of sigmoid function
     return np.exp(-z)/((1+np.exp(-z))**2)
 
NN = Neural_Network()

yHat = NN.forward(X)

print yHat

print y

Still, what's missing is adding;

Backpropagation,

Computing the cost function with respect to each derivatives weight,

Numerical gradient checking,

training the network,

Testing and overfitting.

Any one interested in adding information is welcome. This is a software to get a visual sense in how Neural Networks can perform predictions in the background.

Adding backprop and the cost function to the above code;

def costFunction(self, X, y):
#compute cost for given x,y, use weights already stored in class
self.yHat = self.forward(X)
J = 0.5*sum((y-self.yHat)**2)
return J

def costFunctionPrime(self, X, y):
#compute derivative with respect to W's for a given x and y
self.yHat = self.forward(X)

delta6 = np.multiply(-(y-self.yHat), self.sigmoidPrime(self.z5))
dJdW5 = np.dot(self.a4.T, delta6)

delta5 = np.multiply(-(y-self.yHat), self.sigmoidPrime(self.z4))
dJdW4 = np.dot(self.a3.T, delta5)

delta4 = np.multiply(-(y-self.yHat), self.sigmoidPrime(self.z3))
dJdW3 = np.dot(self.a2.T, delta4)

delta3 = np.multiply(-(y-self.yHat), self.sigmoidPrime(self.z2))
dJdW2 = np.dot(self.a4.T, delta3)

delta2 = np.dot(delta3, self.W5.T)*self.sigmoidPrime(self.z2)
dJdW1 = np.dot(X.T, delta2)

return dJdW1, dJdW2, dJdW3, dJdW4, dJdW5

NN = Neural_Network()
cost1 = NN.costFunctionPrime(X,y)
dJdW1, dJdW2, dJdW3, dJdW4, dJdW5 = NN.costFunctionPrime(X,y)

print dJdW1, dJdW2, dJdW3, dJdW4, dJdW5

 You use random. Are you on qpicks?

No. Random is simply used to initialize the value of "weights" in order to run gradient descent. Without random values, it is very complex to choose your own weight values - mathematically speaking, it could take more than the universe has existed to find all possible values for a 3 dimensional vector, for example.

Adding numerical Gradient checking to the above code. Adding code as I am testing it works for me;

#helper functions for interacting with other classes
def getParams(self):
#get w's unrolled into vector
params = np.concatenate((self.W1.ravel(), self.W2.ravel(), self.W3.ravel(), self.W4.ravel(), self.W5.ravel()))
#params_1 = np.concatenate((self.W3.ravel(), self.W4.ravel(), self.W5.ravel()))
return params#, params_1

def setParams(self, params):
#Set W1 and W2 using single paramater vector.
W1_start=0

W1_end=self.hiddenLayerSize_1 * self.inputLayerSize

self.W1=np.reshape(params[W1_start:W1_end], (self.inputLayerSize , self.hiddenLayerSize_1))

W2_end=W1_end + self.hiddenLayerSize_1*self.hiddenLayerSize_2

self.W2=np.reshape(params[W1_end:W2_end], (self.hiddenLayerSize_2, self.hiddenLayerSize_3))

W3_end = W2_end + self.hiddenLayerSize_2*self.hiddenLayerSize_3

self.W3=np.reshape(params[W2_end:W3_end], (self.hiddenLayerSize_3, self.hiddenLayerSize_4))

W4_end=W3_end + self.hiddenLayerSize_3*self.hiddenLayerSize_4

self.W4=np.reshape(params[W3_end:W4_end], (self.hiddenLayerSize_4, self.outputLayerSize))

#W5_end=W4_end + self.hiddenLayerSize_5*self.outputLayerSize

#self.W5 = np.reshape(params[W4_end:W5_end], (self.hiddenLayerSize_5, self.outputLayerSize))

def computeGradients(self, X, y):
dJdW1, dJdW2, dJdW3, dJdW4, dJdW5 = self.costFunctionPrime(X, y)
return np.concatenate((dJdW1.ravel(), dJdW2.ravel(), dJdW3.ravel(), dJdW4.ravel(), dJdW5.ravel()))

def computeNumericalGradient(N, X, y):
paramsInitial = N.getParams()
numgrad = np.zeros(paramsInitial.shape)
perturb = np.zeros(paramsInitial.shape)
e = 1e-4

for p in range(len(paramsInitial)):
#Set perturbation vector
perturb[p] = e
N.setParams(paramsInitial + perturb)
loss2 = N.costFunction(X, y)

N.setParams(paramsInitial - perturb)
loss1 = N.costFunction(X, y)

#Compute Numerical Gradient
numgrad[p] = (loss2 - loss1) / (2*e)

#Return the value we changed to zero:
perturb[p] = 0

#Return Params to original value:
N.setParams(paramsInitial)

return numgrad

NN = Neural_Network()
numgrad = computeNumericalGradient(NN, X, y)
grad = NN.computeGradients(X,y)

print numgrad
print grad

Note that this code should be used in proper format, in order to work. If you need the exact format let me know.

You can do manually.

Just want to show visually the hidden layers that machine learning tries to ascertain in a regular 5 dimensional game. Or pick 5.

As oppose to an easier 3 dimensional matrix;

The above python code is as follows, written in mathematical terms;

You appear to be a mathematically gifted person, but now how does all of this genius relate to the Lottery ???  How do you choose which lottery numbers to play, based on all of your calculations ??

Hi,

The main reason of this post, is to hopefully find help (from someone) in finishing the algorithm to find patterns in previous lottery draws in order to predict future numbers.

This algorithm is still not complete. But to answer your question, the outlook of the algorithm is to find hidden variables in order to compute predictions with zero error, such using Artificial Intelligence.

In choosing the numbers, I have found that prior numbers drawn prior to the day of game play, provide higher chances of giving a true prediction of today's winning numbers.

Reality is, the idea is for machine learning or a computer to predict next winning numbers on a given game.

Have you seen this: Lottery prediction using GA+BF ANN+FL(GeneticAlogrithm+ArtificalNeuralNetwork+FuzzyLogicControl) based on SciPy/NumPy/matplotlib

This is a great topic.. I do believe it may be possible to make accurate predictions on such a game like the pick 3 win 4 (ideally) and take 5 any Mega and powrball is a different beast but it may be possible to conquer.. From my experiences I have come to the conclusion that the lottery results stem from the first day it was ever played on any game.. Now this is something almost out of the universe the correlations from then and now but is possible to create an advantage without even going to day 1.. Its is something to keep in mind as we all play these games and stop looking for answers that mostly mean nothing.. the game is based og calculated risks and some people seem not to believe in an educated guess (hypothesis) yes u may get lucky here and there but an educated guess(s) every draw is by far more powerful to succeeding in the game.. The lottery ball catcher shown on tv and our qp generator are 2 different entitys so it kills me when people say more people win on qp's than any other way into he game.. that is pure luck that the two come together.. Brother honestly to cracking the code of a game like win 4 may be easier than math we can talk more about this ...tell me your take

I suggest you work on stocks or sports betting as NN don't work on random.  I have built many and tried

just about every prediction method.  Sure you can build something that will give you the best numbers to

play based on the history of the game, just don't expect the best numbers to show in the next game or

the one after that or even the game after that.   Using a NN to come to a solution looks attractive until the

drawing.  At best it might get a couple numbers, just enough to keep you chasing you tail so to say.  Check

the math forum as there is a ongoing NN topic with download.

RL

"just don't expect the best numbers to show in the next game"

Isn't that what trying to predict winners is all about?