Particle swarm optimization in regression problem - dataframe

I am trying to optimize my Random forest regression model using a particle swarm optimizer to minimize the prediction error. But getting this error:UFuncTypeError: ufunc 'add' did not contain a loop with signature matching types (dtype('<U33'), dtype('<U33')) -> None
Can anyone please help me with this. I really appreciate any help you can provide.
My dataset contains 24 independent variables (X) and one dependent variable (y).
CODE:
import numpy as np
import pandas as pd
import re
import os
import random
import seaborn as sns
import matplotlib.pyplot as plt
from matplotlib import animation, rc
%matplotlib inline
from matplotlib.animation import FuncAnimation
from sklearn.model_selection import cross_val_predict, train_test_split
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score, mean_absolute_percentage_error
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.20, random_state=1)
from sklearn.ensemble import RandomForestRegressor
RFR = RandomForestRegressor()
RFR.fit(X_train, y_train)
######################### Particle swarm optimization ##################################
#### error rate
#### The objective is to find minimum error
def fitness_function(xtest, ytest):
# Prediction
ypred = RFR.predict(X_test)
error = mean_squared_error(y_test, ypred)
#r2 = r2_score(ytest, ypred)
return f'The error is: {error}'
from matplotlib import animation
import random
####### velocity #######################################
def update_velocity(particle, velocity, pbest, gbest, w_min=0.5, max=1.0, c=0.1):
# Initialise new velocity array
num_particle = len(particle)
new_velocity = np.array([0.2 for i in range(num_particle)])
# Randomly generate r1, r2 and inertia weight from normal distribution
r1 = random.uniform(0,max)
r2 = random.uniform(0,max)
w = random.uniform(w_min,max)
c1 = c
c2 = c
# Calculate new velocity
for i in range(num_particle):
new_velocity[i] = w*velocity[i] + c1*r1*(pbest[i]-particle[i])+c2*r2*(gbest[i]-particle[i])
return new_velocity
############## update position ##############
def update_position(particle, velocity):
# Move particles by adding velocity
new_particle = particle + velocity
return new_particle
######################################### PSO Main function ###################################
def pso_2d(population, dimension, position_min, position_max, generation, fitness_criterion):
# Initialization
# Population
particles = [[np.random.uniform(position_min[0:24], position_max[0 :24]) for j in range(population)] for i in range(dimension)] # generating random particle position
# Particle's best position
pbest_position = particles # personal best position
# Fitness
pbest_fitness = [fitness_function(p[0:24],p[1]) for p in particles] # personal best fitness
# Index of the best particle
# np.reshape(np.ravel(p[0]), (2, 31))
gbest_index = np.argmin(pbest_fitness)
# Global best particle position
gbest_position = pbest_position[gbest_index]
# Velocity (starting from 0 speed)
velocity = [[0.0 for j in range(dimension)] for i in range(population)]
# Loop for the number of generation
for t in range(generation):
# Stop if the average fitness value reached a predefined success criterion
if np.average(pbest_fitness) <= fitness_criterion:
break
else:
for n in range(population):
# Update the velocity of each particle
velocity[n] = update_velocity(particles[n], velocity[n], pbest_position[n], gbest_position)
# Move the particles to new position
particles[n] = update_position(particles[n], velocity[n])
# Calculate the fitness value
pbest_fitness = [fitness_function(p[0:24],p[1]) for p in particles]
# Find the index of the best particle
gbest_index = np.argmin(pbest_fitness)
# Update the position of the best particle
gbest_position = pbest_position[gbest_index]
# Print the results
print('Global Best Position: ', gbest_position)
print('Best Fitness Value: ', min(pbest_fitness))
print('Average Particle Best Fitness Value: ', np.average(pbest_fitness))
print('Number of Generation: ', t)
position_min = [-0.44306155, -0.52971118, -0.10311188, -0.60053201, -0.78198029,
-0.37737778, -0.14371436, -0.01623235, -0.88660182, -0.06182274,
-0.30084403, -0.98080838, -0.11787062, -0.84172055, -0.709991 ,
-0.9841236 , -0.32976052, -0.26586302, -0.87641669, -0.23728611,
-0.08874495, -0.03091284, -0.29987714, -0.96795309]
position_max = [0.44306155, 0.52971118, 0.10311188, 0.60053201, 0.78198029,
0.37737778, 0.14371436, 0.01623235, 0.88660182, 0.06182274,
0.30084403, 0.98080838, 0.11787062, 0.84172055, 0.709991 ,
0.9841236 , 0.32976052, 0.26586302, 0.87641669, 0.23728611,
0.08874495, 0.03091284, 0.29987714, 0.96795309]
pso_2d(100, 24, position_min, position_max, 400, 10e-4)
Output: UFuncTypeError: ufunc 'add' did not contain a loop with signature matching types (dtype('<U33'), dtype('<U33')) -> None

Related

Error when using tensorflow HMC to marginalise GPR hyperparameters

I would like to use tensorflow (version 2) to use gaussian process regression
to fit some data and I found the google colab example online here [1].
I have turned some of this notebook into a minimal example that is below.
Sometimes the code fails with the following error when using MCMC to marginalize the hyperparameters: and I was wondering if anyone has seen this before or knows how to get around this?
tensorflow.python.framework.errors_impl.InvalidArgumentError: Input matrix is not invertible.
[[{{node mcmc_sample_chain/trace_scan/while/body/_168/smart_for_loop/while/body/_842/dual_averaging_step_size_adaptation___init__/_one_step/transformed_kernel_one_step/mh_one_step/hmc_kernel_one_step/leapfrog_integrate/while/body/_1244/leapfrog_integrate_one_step/maybe_call_fn_and_grads/value_and_gradients/value_and_gradient/gradients/leapfrog_integrate_one_step/maybe_call_fn_and_grads/value_and_gradients/value_and_gradient/PartitionedCall_grad/PartitionedCall/gradients/JointDistributionNamed/log_prob/JointDistributionNamed_log_prob_GaussianProcess/log_prob/JointDistributionNamed_log_prob_GaussianProcess/get_marginal_distribution/Cholesky_grad/MatrixTriangularSolve}}]] [Op:__inference_do_sampling_113645]
Function call stack:
do_sampling
[1] https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Gaussian_Process_Regression_In_TFP.ipynb#scrollTo=jw-_1yC50xaM
Note that some of code below is a bit redundant but it should
in some sections but it should be able to reproduce the error.
Thanks!
import time
import numpy as np
import tensorflow.compat.v2 as tf
import tensorflow_probability as tfp
tfb = tfp.bijectors
tfd = tfp.distributions
tfk = tfp.math.psd_kernels
tf.enable_v2_behavior()
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
#%pylab inline
# Configure plot defaults
plt.rcParams['axes.facecolor'] = 'white'
plt.rcParams['grid.color'] = '#666666'
#%config InlineBackend.figure_format = 'png'
def sinusoid(x):
return np.sin(3 * np.pi * x[..., 0])
def generate_1d_data(num_training_points, observation_noise_variance):
"""Generate noisy sinusoidal observations at a random set of points.
Returns:
observation_index_points, observations
"""
index_points_ = np.random.uniform(-1., 1., (num_training_points, 1))
index_points_ = index_points_.astype(np.float64)
# y = f(x) + noise
observations_ = (sinusoid(index_points_) +
np.random.normal(loc=0,
scale=np.sqrt(observation_noise_variance),
size=(num_training_points)))
return index_points_, observations_
# Generate training data with a known noise level (we'll later try to recover
# this value from the data).
NUM_TRAINING_POINTS = 100
observation_index_points_, observations_ = generate_1d_data(
num_training_points=NUM_TRAINING_POINTS,
observation_noise_variance=.1)
def build_gp(amplitude, length_scale, observation_noise_variance):
"""Defines the conditional dist. of GP outputs, given kernel parameters."""
# Create the covariance kernel, which will be shared between the prior (which we
# use for maximum likelihood training) and the posterior (which we use for
# posterior predictive sampling)
kernel = tfk.ExponentiatedQuadratic(amplitude, length_scale)
# Create the GP prior distribution, which we will use to train the model
# parameters.
return tfd.GaussianProcess(
kernel=kernel,
index_points=observation_index_points_,
observation_noise_variance=observation_noise_variance)
gp_joint_model = tfd.JointDistributionNamed({
'amplitude': tfd.LogNormal(loc=0., scale=np.float64(1.)),
'length_scale': tfd.LogNormal(loc=0., scale=np.float64(1.)),
'observation_noise_variance': tfd.LogNormal(loc=0., scale=np.float64(1.)),
'observations': build_gp,
})
x = gp_joint_model.sample()
lp = gp_joint_model.log_prob(x)
print("sampled {}".format(x))
print("log_prob of sample: {}".format(lp))
# Create the trainable model parameters, which we'll subsequently optimize.
# Note that we constrain them to be strictly positive.
constrain_positive = tfb.Shift(np.finfo(np.float64).tiny)(tfb.Exp())
amplitude_var = tfp.util.TransformedVariable(
initial_value=1.,
bijector=constrain_positive,
name='amplitude',
dtype=np.float64)
length_scale_var = tfp.util.TransformedVariable(
initial_value=1.,
bijector=constrain_positive,
name='length_scale',
dtype=np.float64)
observation_noise_variance_var = tfp.util.TransformedVariable(
initial_value=1.,
bijector=constrain_positive,
name='observation_noise_variance_var',
dtype=np.float64)
trainable_variables = [v.trainable_variables[0] for v in
[amplitude_var,
length_scale_var,
observation_noise_variance_var]]
# Use `tf.function` to trace the loss for more efficient evaluation.
#tf.function(autograph=False, experimental_compile=False)
def target_log_prob(amplitude, length_scale, observation_noise_variance):
return gp_joint_model.log_prob({
'amplitude': amplitude,
'length_scale': length_scale,
'observation_noise_variance': observation_noise_variance,
'observations': observations_
})
# Now we optimize the model parameters.
num_iters = 1000
optimizer = tf.optimizers.Adam(learning_rate=.01)
# Store the likelihood values during training, so we can plot the progress
lls_ = np.zeros(num_iters, np.float64)
for i in range(num_iters):
with tf.GradientTape() as tape:
loss = -target_log_prob(amplitude_var, length_scale_var,
observation_noise_variance_var)
grads = tape.gradient(loss, trainable_variables)
optimizer.apply_gradients(zip(grads, trainable_variables))
lls_[i] = loss
print('Trained parameters:')
print('amplitude: {}'.format(amplitude_var._value().numpy()))
print('length_scale: {}'.format(length_scale_var._value().numpy()))
print('observation_noise_variance: {}'.format(observation_noise_variance_var._value().numpy()))
num_results = 100
num_burnin_steps = 50
sampler = tfp.mcmc.TransformedTransitionKernel(
tfp.mcmc.HamiltonianMonteCarlo(
target_log_prob_fn=target_log_prob,
step_size=tf.cast(0.1, tf.float64),
num_leapfrog_steps=8),
bijector=[constrain_positive, constrain_positive, constrain_positive])
adaptive_sampler = tfp.mcmc.DualAveragingStepSizeAdaptation(
inner_kernel=sampler,
num_adaptation_steps=int(0.8 * num_burnin_steps),
target_accept_prob=tf.cast(0.75, tf.float64))
initial_state = [tf.cast(x, tf.float64) for x in [1., 1., 1.]]
# Speed up sampling by tracing with `tf.function`.
#tf.function(autograph=False, experimental_compile=False)
def do_sampling():
return tfp.mcmc.sample_chain(
kernel=adaptive_sampler,
current_state=initial_state,
num_results=num_results,
num_burnin_steps=num_burnin_steps,
trace_fn=lambda current_state, kernel_results: kernel_results)
t0 = time.time()
samples, kernel_results = do_sampling()
t1 = time.time()
print("Inference ran in {:.2f}s.".format(t1-t0))
This can happen if you have multiple index points that are very close, so you might consider using np.linspace or just doing some post filtering of your random draw. I would also suggest a bit bigger epsilon, maybe 1e-6.

Using scipy.odr to fit curve

I'm trying to fit a set of data points via a fit function that depends on two variables, let's call these xdata and sdata. Problem is my curve is rather flat I want it to more or less "follow the points".
I've tried using scipy.odr to fit the curve it works rather well except that the curve is too flat:
import numpy as np
from math import pi
from math import sqrt
from math import log
from scipy import optimize
import scipy.optimize
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.odr import *
mudr=np.array([ 57.43708609, 46.26119205, 55.60688742, 33.21615894,
28.27072848, 22.54649007, 21.80662252, 11.21483444, 5.80211921])
#xdata points
dme=array([ 128662.54890776, 105265.32915726, 128652.56835434,
77968.67019573, 66273.56542068, 58464.58559543,
54570.66624991, 27286.90038703, 19480.92689266]) #xdata error
dmss22=np.array([ 4.90050000e+17, 4.90050000e+17, 4.90050000e+17,
4.90050000e+17, 4.90050000e+17, 4.90050000e+17,
4.90050000e+17, 4.90050000e+17, 4.90050000e+17]) #sdata points
dmse=np.array([ 1.09777592e+21, 1.11512117e+21, 1.13381702e+21,
1.15033267e+21, 1.14883089e+21, 1.27076265e+21,
1.22637165e+21, 1.19237598e+21, 1.64539205e+21]) # sdata error
F=np.array([ 115.01944248, 110.24354867, 112.77812389, 104.81830088,
104.35746903, 101.32016814, 100.54513274, 96.94226549,
93.00424779]) #ydata points
dF=np.array([ 72710.75386699, 72590.6256987 , 176539.40403673,
130555.27503081, 124299.52080164, 176426.64340597,
143013.52848306, 122117.93022746, 157547.78395513])#ydata error
def Ffitsso(p,X,B=2.58,Fc=92.2,mu=770,Za=0.9468): #fitfunction
temp1 = (2*B*X[0])/(4*pi*Fc)**2
temp2 = temp1*(afij[0]+afij[1]*np.log((2*B*X[0])/mu**2))
temp3 = temp1**2*(afij[2]+afij[3]*np.log((2*B*X[0])/mu**2)+\
afij[4]*(np.log((2*B*X[0])/mu**2))**2)
temp4 = temp1**3*(afij[5]+afij[6]*np.log((2*B*X[0])/mu**2)+\
afij[7]*(np.log((2*B*X[0])/mu**2))**2+\
afij[8]*(np.log((2*B*X[0])/mu**2))**3)
return Fc/Za*(1+p[0]*X[1])*(1+temp2+temp3+temp4)+p[1]
#fitting using scipy.odr
xtot=np.row_stack( (mudr, dmss22) )
etot=np.row_stack( (Ze, dmss22e) )
fitting = Model(Ffitsso)
mydata = RealData(xtot, F, sx=etot2, sy=dF)
myodr = ODR(mydata, fitting, beta0=[0, 100])
myoutput = myodr.run()
myoutput.pprint()
bet=myoutput.beta
plt.plot(mudr,F,"b^")
plt.plot(mudr,Ffitsso(bet,[mudr,dmss22]))
p[0]*X[0] in the fitfunction is supposed to be small compared to 1 but with the fit the value for p[0] is in order of e-18 whilst dmss22 values are in the order of e-17 which is not small enough.
Even worse is that it's negative meaning the function decreases which is not supposed to happen it's supposed to increase like the plotted data points.
Edit: I fixed, didn't know that it was so sensitive to initial beta values, put beta[0]=1.5*10(-15) and it works!**
Here is a graphical fitter with both curve_fit and ODR fitters using scipy's Differential Evolution (DE) genetic algorithm to supply initial parameter estimates for the non-linear solvers. The scipy implementation of DE uses the Latin Hypercube algorithm to ensure a thorough search of parameter space, and this requires parameter bounds within which to search - in this example, these bounds are taken from the data maximum and minimum values. Note that it is much easier to give bounds for the initial parameter estimates rather than individual specific values.
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import scipy.odr
from scipy.optimize import differential_evolution
import warnings
xData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.0, 6.6, 7.7, 0.0])
yData = numpy.array([1.1, 20.2, 30.3, 40.4, 50.0, 60.6, 70.7, 0.1])
def func(x, a, b, c, d, offset): # curve fitting function for curve_fit()
return a*numpy.exp(-(x-b)**2/(2*c**2)+d) + offset
def func_wrapper_for_ODR(parameters, x): # parameter order for ODR
return func(x, *parameters)
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = func(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
# min and max used for bounds
maxX = max(xData)
minX = min(xData)
maxY = max(yData)
minY = min(yData)
parameterBounds = []
parameterBounds.append([minY, maxY]) # search bounds for a
parameterBounds.append([minX, maxX]) # search bounds for b
parameterBounds.append([minX, maxX]) # search bounds for c
parameterBounds.append([minY, maxY]) # search bounds for d
parameterBounds.append([0.0, maxY]) # search bounds for Offset
# "seed" the numpy random number generator for repeatable results
result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
return result.x
geneticParameters = generate_Initial_Parameters()
##########################
# curve_fit section
##########################
fittedParameters_curvefit, pcov = curve_fit(func, xData, yData, geneticParameters)
print('Fitted parameters curve_fit:', fittedParameters_curvefit)
print()
modelPredictions_curvefit = func(xData, *fittedParameters_curvefit)
absError_curvefit = modelPredictions_curvefit - yData
SE_curvefit = numpy.square(absError_curvefit) # squared errors
MSE_curvefit = numpy.mean(SE_curvefit) # mean squared errors
RMSE_curvefit = numpy.sqrt(MSE_curvefit) # Root Mean Squared Error, RMSE
Rsquared_curvefit = 1.0 - (numpy.var(absError_curvefit) / numpy.var(yData))
print()
print('RMSE curve_fit:', RMSE_curvefit)
print('R-squared curve_fit:', Rsquared_curvefit)
print()
##########################
# ODR section
##########################
data = scipy.odr.odrpack.Data(xData,yData)
model = scipy.odr.odrpack.Model(func_wrapper_for_ODR)
odr = scipy.odr.odrpack.ODR(data, model, beta0=geneticParameters)
# Run the regression.
odr_out = odr.run()
print('Fitted parameters ODR:', odr_out.beta)
print()
modelPredictions_odr = func(xData, *odr_out.beta)
absError_odr = modelPredictions_odr - yData
SE_odr = numpy.square(absError_odr) # squared errors
MSE_odr = numpy.mean(SE_odr) # mean squared errors
RMSE_odr = numpy.sqrt(MSE_odr) # Root Mean Squared Error, RMSE
Rsquared_odr = 1.0 - (numpy.var(absError_odr) / numpy.var(yData))
print()
print('RMSE ODR:', RMSE_odr)
print('R-squared ODR:', Rsquared_odr)
print()
##########################################################
# graphics output section
def ModelsAndScatterPlot(graphWidth, graphHeight):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
# first the raw data as a scatter plot
axes.plot(xData, yData, 'D')
# create data for the fitted equation plots
xModel = numpy.linspace(min(xData), max(xData))
yModel_curvefit = func(xModel, *fittedParameters_curvefit)
yModel_odr = func(xModel, *odr_out.beta)
# now the models as line plots
axes.plot(xModel, yModel_curvefit)
axes.plot(xModel, yModel_odr)
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
plt.show()
plt.close('all') # clean up after using pyplot
graphWidth = 800
graphHeight = 600
ModelsAndScatterPlot(graphWidth, graphHeight)

Fit sigmoid curve in python

Thanks ahead! I am trying to fit a sigmoid curve over some data, below is my code
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
====== some code in between =======
plt.scatter(drag[0].w,drag[0].s, s = 10, label = 'drag%d'%0)
def sigmoid(x,x0,k):
y = 1.0/(1.0+np.exp(-x0*(x-k)))
return y
popt,pcov = curve_fit(sigmoid, drag[0].w, drag[0].s)
xx = np.linspace(10,1000,10)
yy = sigmoid(xx, *popt)
plt.plot(xx,yy,'r-', label='fit')
plt.legend(loc='upper left')
plt.xlabel('weight(kg)', fontsize=12)
plt.ylabel('wing span(m)', fontsize=12)
plt.show()
this is now showing the graph below which is not very rightfitting curve is the red one at bottom
What are the possible solutions?
Also I am open to other methods of fitting logistic curves on this set of data
Thanks again!
Here is an example graphical fitter using your equation with an amplitude scaling factor for my test data. This code uses scipy's Differential Evolution genetic algorithm to provide initial parameter estimates for curve_fit(), as the scipy default initial parameter estimates of all 1.0 are not always optimal. The scipy implementation of Differential Evolution uses the Latin Hypercube algorithm to ensure a thorough search of parameter space, and this requires bounds within which to search. In this example those bounds are taken from the example data I provide, when using your own data please check that the bounds seem reasonable. Note that ranges on the parameters are much easier to provide than specific values for the initial parameter estimates.
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
xData = numpy.array([19.1647, 18.0189, 16.9550, 15.7683, 14.7044, 13.6269, 12.6040, 11.4309, 10.2987, 9.23465, 8.18440, 7.89789, 7.62498, 7.36571, 7.01106, 6.71094, 6.46548, 6.27436, 6.16543, 6.05569, 5.91904, 5.78247, 5.53661, 4.85425, 4.29468, 3.74888, 3.16206, 2.58882, 1.93371, 1.52426, 1.14211, 0.719035, 0.377708, 0.0226971, -0.223181, -0.537231, -0.878491, -1.27484, -1.45266, -1.57583, -1.61717])
yData = numpy.array([0.644557, 0.641059, 0.637555, 0.634059, 0.634135, 0.631825, 0.631899, 0.627209, 0.622516, 0.617818, 0.616103, 0.613736, 0.610175, 0.606613, 0.605445, 0.603676, 0.604887, 0.600127, 0.604909, 0.588207, 0.581056, 0.576292, 0.566761, 0.555472, 0.545367, 0.538842, 0.529336, 0.518635, 0.506747, 0.499018, 0.491885, 0.484754, 0.475230, 0.464514, 0.454387, 0.444861, 0.437128, 0.415076, 0.401363, 0.390034, 0.378698])
def sigmoid(x, amplitude, x0, k):
return amplitude * 1.0/(1.0+numpy.exp(-x0*(x-k)))
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = sigmoid(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
# min and max used for bounds
maxX = max(xData)
minX = min(xData)
maxY = max(yData)
minY = min(yData)
parameterBounds = []
parameterBounds.append([minY, maxY]) # search bounds for amplitude
parameterBounds.append([minX, maxX]) # search bounds for x0
parameterBounds.append([minX, maxX]) # search bounds for k
# "seed" the numpy random number generator for repeatable results
result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
return result.x
# by default, differential_evolution completes by calling curve_fit() using parameter bounds
geneticParameters = generate_Initial_Parameters()
# now call curve_fit without passing bounds from the genetic algorithm,
# just in case the best fit parameters are aoutside those bounds
fittedParameters, pcov = curve_fit(sigmoid, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()
modelPredictions = sigmoid(xData, *fittedParameters)
absError = modelPredictions - yData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print()
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
# first the raw data as a scatter plot
axes.plot(xData, yData, 'D')
# create data for the fitted equation plot
xModel = numpy.linspace(min(xData), max(xData))
yModel = sigmoid(xModel, *fittedParameters)
# now the model as a line plot
axes.plot(xModel, yModel)
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
plt.show()
plt.close('all') # clean up after using pyplot
graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)

Use matplotlib to plot scikit learn linear regression results

How can you plot the linear regression results from scikit learn after the analysis to see the "testing" data (real values vs. predicted values) at the end of the program? The code below is close but I believe it is missing a scaling factor.
input:
import pandas as pd
import numpy as np
import datetime
pd.core.common.is_list_like = pd.api.types.is_list_like # temp fix
import fix_yahoo_finance as yf
from pandas_datareader import data, wb
from datetime import date
from sklearn.linear_model import LinearRegression
from sklearn import preprocessing, cross_validation, svm
import matplotlib.pyplot as plt
df = yf.download('MMM', start = date (2012, 1, 1), end = date (2018, 1, 1) , progress = False)
df_low = df[['Low']] # create a new df with only the low column
forecast_out = int(5) # predicting some days into future
df_low['low_prediction'] = df_low[['Low']].shift(-forecast_out) # create a new column based on the existing col but shifted some days
X_low = np.array(df_low.drop(['low_prediction'], 1))
X_low = preprocessing.scale(X_low) # scaling the input values
X_low_forecast = X_low[-forecast_out:] # set X_forecast equal to last 5 days
X_low = X_low[:-forecast_out] # remove last 5 days from X
y_low = np.array(df_low['low_prediction'])
y_low = y_low[:-forecast_out]
X_low_train, X_low_test, y_low_train, y_low_test = cross_validation.train_test_split(X_low, y_low, test_size = 0.2)
clf_low = LinearRegression() # classifier
clf_low.fit(X_low_train, y_low_train) # training
confidence_low = clf_low.score(X_low_test, y_low_test) # testing
print("confidence for lows: ", confidence_low)
forecast_prediction_low = clf_low.predict(X_low_forecast)
print(forecast_prediction_low)
plt.figure(figsize = (17,9))
plt.grid(True)
plt.plot(X_low_test, color = "red")
plt.plot(y_low_test, color = "green")
plt.show()
image:
You plot y_test and X_test, while you should plot y_test and clf_low.predict(X_test) instead, if you want to compare target and predicted.
BTW, clf_low in your code is not a classifier, it is a regressor. It's better to use the alias model instead of clf.

TensorFlow example save mandelbrot image

Learning how to use tensorflow, first tutorial code on mandelbrot set below
# Import libraries for simulation
import tensorflow as tf
import numpy as np
# Imports for visualization
import PIL.Image
from io import BytesIO
from IPython.display import Image, display
def DisplayFractal(a, fmt='jpeg'):
"""Display an array of iteration counts as a
colorful picture of a fractal."""
a_cyclic = (6.28*a/20.0).reshape(list(a.shape)+[1])
img = np.concatenate([10+20*np.cos(a_cyclic),
30+50*np.sin(a_cyclic),
155-80*np.cos(a_cyclic)], 2)
img[a==a.max()] = 0
a = img
a = np.uint8(np.clip(a, 0, 255))
f = BytesIO()
PIL.Image.fromarray(a).save(f, fmt)
display(Image(data=f.getvalue()))
sess = tf.InteractiveSession()
# Use NumPy to create a 2D array of complex numbers
Y, X = np.mgrid[-1.3:1.3:0.005, -2:1:0.005]
Z = X+1j*Y
xs = tf.constant(Z.astype(np.complex64))
zs = tf.Variable(xs)
ns = tf.Variable(tf.zeros_like(xs, tf.float32))
tf.global_variables_initializer().run()
# Compute the new values of z: z^2 + x
zs_ = zs*zs + xs
# Have we diverged with this new value?
not_diverged = tf.abs(zs_) < 4
# Operation to update the zs and the iteration count.
#
# Note: We keep computing zs after they diverge! This
# is very wasteful! There are better, if a little
# less simple, ways to do this.
#
step = tf.group(
zs.assign(zs_),
ns.assign_add(tf.cast(not_diverged, tf.float32))
)
for i in range(200): step.run()
DisplayFractal(ns.eval())
returns this on shell
<IPython.core.display.Image at 0x7fcdee1da810>
It doesn't display the image and I'd prefer if it saved the image.
How can I save the result as an image?
Scipy has an easy image save function! https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.misc.imsave.html
You should try this:
import scipy.misc
scipy.misc.imsave('mandelbrot.png',ns.eval())
I hope this works! Regardless, let me know!