You are given an oracle function predict_value(stock), which returns an estimated confidence interval of p=0.01 around a given stock's value one minute into the future. Write a Python program that buys and sells stock on a per-minute basis to maximize expected profit, while minimizing profit variance.

To solve this problem , we can use a combination of optimization techniques and machine learning algorithms . Here ' s a possible approach : \n \n 1 . Data collection : Collect historical stock prices for the given stock and store them in a data frame . \n 2 . Feature engineering : Ex tract relevant features from the data , such as moving aver ages , relative strength index ( R SI ), and B oll inger B ands . \n 3 . Machine learning model : Train a machine learning model , such as a random forest or a neural network , on the historical data to predict the stock ' s value one minute into the future . \n 4 . Optim ization : Use an optimization algorithm , such as dynamic programming or genetic algorithms , to find the optimal buying and selling times that maxim ize expected profit while minim izing profit variance . \n 5 . Implement ation : Implement the optim ized strategy in a Python program that bu ys and sell s the stock on a per - minute basis . \n \n Here ' s some sample code to get started : \n `` ` python \n import pand as as pd \n import numpy as np \n from sk learn . ense m ble import Random Fore st Reg ress or \n from sk learn . pre processing import Min Max Scal er \n from sk learn . model _ selection import train _ test _ split \n from sk learn . metrics import mean _ s qu ared _ error \n \n # Data collection \n df = pd . read _ csv (' stock _ pr ices . csv ') \n \n # Feature engineering \n df [' date '] = pd . to _ datetime ( df [' date ']) \n df . set _ index (' date ', in place = True ) \n df [' close '] = pd . to _ numeric ( df [' close ']) \n \n # Scal ing \n sc aler = Min Max Scal er () \n df [' close '] = scal er . fit _ transform ( df [' close ']. values . resh ape (- 1 , 1 )) \n \n # S pl itting data into train and test sets \n X _ train , X _ test , y _ train , y _ test = train _ test _ split ( df . drop (' close ', axis = 1 ), df [' close '], test _ size = 0 . 2 , random _ state = 4 2 ) \n \n # Machine learning model \n model = Random Fore st Reg ress or ( n _ est im ators = 1 0 0 , random _ state = 4 2 ) \n model . fit ( X _ train , y _ train ) \n \n # Pred iction \n y _ pred = model . predict ( X _ test ) \n m se = mean _ s qu ared _ error ( y _ test , y _ pred ) \n print (' Me an squ ared error : ', m se ) \n \n # Optim ization \n def optim ize ( df , model ): \n n _ samples = len ( df ) \n profits = np . zer os ( n _ samples ) \n for i in range ( n _ samples - 1 ): \n # Pred ict next value \n x _ pred = df . il oc [ i + 1 : i + 2 ]. values \n x _ pred = scal er . transform ( x _ pred ) \n y _ pred = model . predict ( x _ pred ) \n \n # Cal culate profit \n profit = y _ pred [ 0 ] - df . il oc [ i + 1 , close '] \n profits [ i ] = profit \n \n return profits \n \n # Implement ation \n def buy _ s ell ( df , model ): \n profits = optim ize ( df , model ) \n current _ profit = 0 \n current _ time = df . index [ 0 ] \n for i in range ( 1 , len ( df )): \n if profits [ i ] current _ profit : \n # Buy \n current _ profit = profits [ i ] \n current _ time = df . index [ i ] \n else : \n # S ell \n current _ profit -= df . il oc [ current _ time ][' close '] \n current _ time = df . index [ i ] \n \n return current _ profit \n \n # Example usage \n current _ profit = buy _ s ell ( df , model ) \n print (' Current profit : ', current _ profit ) \n `` ` \n Note that this is just a basic example , and there are many ways to improve and optim ize the code . For example , you could use a more advanced optimization algorithm , incorporate more features into the machine learning model , or use a different stock as a test case . </s>