I am trying to use PyBrain for time series prediction by implementing this solution. The others produce large offsets. The problem is that although I have tried changing the learning rate, momentum, max training epochs, continue epochs, neuron amount (1-500), and activation function, the result is always flat. What might the solution be?
Blue: original. Green: network's prediction.
INPUTS = 60
HIDDEN = 60
OUTPUTS = 1
def build_network():
net = buildNetwork(INPUTS, HIDDEN, OUTPUTS,
hiddenclass=LSTMLayer,
outclass=LinearLayer,
recurrent=True,
bias=True, outputbias=False)
net.sortModules()
return net
def prepare_datasets(data, training_data_ratio):
training_data, validation_data = split_list(data, training_data_ratio)
training_set = SequentialDataSet(INPUTS, OUTPUTS)
for i in range(len(training_data) - INPUTS - 1):
training_set.newSequence()
tr_inputs = training_data[i:i + INPUTS]
tr_output = training_data[i + INPUTS]
training_set.addSample(tr_inputs, tr_output)
validation_set = []
for i in range(len(validation_data) - INPUTS - 1):
validation_set.append(validation_data[i:i + INPUTS])
return training_set, validation_set
def train_network(net, data, max_iterations):
net.randomize()
learning_rate = 0.1
trainer = BackpropTrainer(net, data, verbose=True,
momentum=0.8,
learningrate=learning_rate)
errors = trainer.trainUntilConvergence(maxEpochs=max_iterations, continueEpochs=10)
return errors
def try_network(net, data):
outputs = []
for item in data:
output = net.activate(item)[0]
outputs.append(output)
return outputs
Normalize data:
data = data / max(data)
Related
I'm currently trying to put together some code that backtests a simple trading strategy involving sequencing through time series price data, incrementally fitting an ARIMA model, making future price predictions, and then either adding a share if the price is predicted to increase, or selling all accumulated shares if the price is predicted to go down. Currently, it's returning nan values for the projected returns from trades and appears to only be selling somehow.
I've attached my code below. There's just a few simple functions for calculating a sharpe ratio and then the main function for running backtests.
import yfinance as yf
from datetime import datetime, timedelta
import matplotlib.pyplot as plt
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.arima.model import ARIMA
import numpy as np
import seaborn as sns
from tqdm import tqdm
import pandas as pd
from statsmodels.tools.sm_exceptions import ValueWarning, HessianInversionWarning, ConvergenceWarning
import warnings
#in practice do not supress these warnings, they carry important information about the status of your model
warnings.filterwarnings('ignore', category=ValueWarning)
warnings.filterwarnings('ignore', category=HessianInversionWarning)
warnings.filterwarnings('ignore', category=ConvergenceWarning)
tickerSymbol = 'SPY'
data = yf.Ticker(tickerSymbol)
prices = data.history(start='2017-01-01', end='2019-01-01').Close
returns = prices.pct_change().dropna()
def std_dev(data):
# Get number of observations
n = len(data)
# Calculate mean
mean = sum(data) / n
# Calculate deviations from the mean
deviations = sum([(x - mean)**2 for x in data])
# Calculate Variance & Standard Deviation
variance = deviations / (n - 1)
s = variance**(1/2)
return s
# Sharpe Ratio From Scratch
def sharpe_ratio(data, risk_free_rate=0):
# Calculate Average Daily Return
mean_daily_return = sum(data) / len(data)
print(f"mean daily return = {mean_daily_return}")
# Calculate Standard Deviation
s = std_dev(data)
# Calculate Daily Sharpe Ratio
daily_sharpe_ratio = (mean_daily_return - risk_free_rate) / s
# Annualize Daily Sharpe Ratio
sharpe_ratio = 252**(1/2) * daily_sharpe_ratio
return sharpe_ratio
def run_simulation(returns, prices, amt, order, thresh, verbose=True, plot=True):
if type(order) == float:
thresh = None
sum_list = []
events_list = []
sharpe_list = []
init_amt = amt
#go through dates
for date, r in tqdm (returns.iloc[14:].items(), total=len(returns.iloc[14:])):
#if you're currently holding the stock, sell it
#get data til just before current date
curr_data = returns[:date]
if type(order) == tuple:
try:
#fit model
model = ARIMA(curr_data, order=order).fit(maxiter=200)
#get forecast
pred = model.forecast()[0][0]
except:
pred = thresh - 1
#if you predict a high enough return and not holding, buy stock
if ((type(order) == float and np.random.random() < order)
or (type(order) == tuple and pred > thresh)):
buy_price = prices.loc[date]
events_list.append(('b', date))
int_buy_price = int(buy_price)
sum_list.append(int_buy_price)
if verbose:
print('Bought at $%s'%buy_price)
print('Predicted Return: %s'%round(pred,4))
print('Actual Return: %s'%(round(ret, 4)))
print('=======================================')
continue
#if you predict below the threshold return, sell the stock
if ((type(order) == float and np.random.random() < order)
or (type(order) == tuple and thresh > pred)
or (order == 'last' and curr_data[-1] > 0)):
sell_price = prices.loc[date]
total_return = len(sum_list) * sell_price
ret = (total_return-sum(sum_list))/sum(sum_list)
amt *= (1+ret)
events_list.append(('s', date, ret))
sharpe_list.append(ret)
sum_list.clear()
if verbose:
print('Sold at $%s'%sell_price)
print('Predicted Return: %s'%round(pred,4))
print('Actual Return: %s'%(round(ret, 4)))
print('=======================================')
if verbose:
sharpe = sharpe_ratio(sharpe_list, risk_free_rate=0)
print('Total Amount: $%s'%round(amt,2))
print(f"Sharpe Ratio: {sharpe}")
#graph
if plot:
plt.figure(figsize=(10,4))
plt.plot(prices[14:])
y_lims = (int(prices.min()*.95), int(prices.max()*1.05))
shaded_y_lims = int(prices.min()*.5), int(prices.max()*1.5)
for idx, event in enumerate(events_list):
plt.axvline(event[1], color='k', linestyle='--', alpha=0.4)
if event[0] == 's':
color = 'green' if event[2] > 0 else 'red'
plt.fill_betweenx(range(*shaded_y_lims),
event[1], events_list[idx-1][1], color=color, alpha=0.1)
tot_return = round(100*(amt / init_amt - 1), 2)
sharpe = sharpe_ratio(sharpe_list, risk_free_rate=0)
tot_return = str(tot_return) + '%'
plt.title("%s Price Data\nThresh=%s\nTotal Amt: $%s\nTotal Return: %s"%(tickerSymbol, thresh, round(amt,2), tot_return), fontsize=20)
plt.ylim(*y_lims)
plt.show()
print(sharpe)
return amt
# A model with a dth difference to fit and ARMA(p,q) model is called an ARIMA process
# of order (p,d,q). You can select p,d, and q with a wide range of methods,
# including AIC, BIC, and empirical autocorrelations (Petris, 2009).
for thresh in [0.001]:
run_simulation(returns, prices, 100000, (7,1,7), thresh, verbose=True)
I've discovered that it's failing to fit the ARIMA model for some reason. Not converging to a solution, I guess. I'm not sure why though because it was fitting it just fine when I was running a different strategy using the same data and order.
My problem has a single state and an infinite amount of actions on a certain interval (0,1). After quite some time of googling I found a few paper about an algorithm called zooming algorithm which can solve problems with a continous action space. However my implementation is bad at exploiting. Therefore I'm thinking about adding an epsilon-greedy kind of behavior.
Is it reasonable to combine different methods?
Do you know other approaches to my problem?
Code samples:
import portion as P
def choose_action(self, i_ph):
# Activation rule
not_covered = P.closed(lower=0, upper=1)
for arm in self.active_arms:
confidence_radius = calc_confidence_radius(i_ph, arm)
confidence_interval = P.closed(arm.norm_value - confidence_radius, arm.norm_value + confidence_radius)
not_covered = not_covered - confidence_interval
if not_covered != P.empty():
rans = []
height = 0
heights = []
for i in not_covered:
rans.append(np.random.uniform(i.lower, i.upper))
height += i.upper - i.lower
heights.append(i.upper - i.lower)
ran_n = np.random.uniform(0, height)
j = 0
ran = 0
for i in range(len(heights)):
if j < ran_n < j + heights[i]:
ran = rans[i]
j += heights[i]
self.active_arms.append(Arm(len(self.active_arms), ran * (self.sigma_square - lower) + lower, ran))
# Selection rule
max_index = float('-inf')
max_index_arm = None
for arm in self.active_arms:
confidence_radius = calc_confidence_radius(i_ph, arm)
# indexfunction from zooming algorithm
index = arm.avg_learning_reward + 2 * confidence_radius
if index > max_index:
max_index = index
max_index_arm = arm
action = max_index_arm.value
self.current_arm = max_index_arm
return action
def learn(self, action, reward):
arm = self.current_arm
arm.avg_reward = (arm.pulled * arm.avg_reward + reward) / (arm.pulled + 1)
if reward > self.max_profit:
self.max_profit = reward
elif reward < self.min_profit:
self.min_profit = reward
# normalize reward to [0, 1]
high = 100
low = -75
if reward >= high:
reward = 1
self.high_count += 1
elif reward <= low:
reward = 0
self.low_count += 1
else:
reward = (reward - low)/(high - low)
arm.avg_learning_reward = (arm.pulled * arm.avg_learning_reward + reward) / (arm.pulled + 1)
arm.pulled += 1
# zooming algorithm confidence radius
def calc_confidence_radius(i_ph, arm: Arm):
return math.sqrt((8 * i_ph)/(1 + arm.pulled))
You may find this useful, full algorithm description is here. They grid out the probes uniformly, informing this choice (e.g. normal centering on a reputed high energy arm) is also possible (but this might invalidate a few bounds I am not sure).
I am running a logistic generalized linear mixed model and would like to plot my effects together with confidence intervals.
I use the lme4 package to fit my model:
glmer (cbind(positive, negative) ~ F1 * F2 * F3 + V1 + F1 * I(V1^2) + V2 + F1 * I(V2^2) + V3 + I(V3^2) + V4 + I(V4^2) + F4 + (1|OLRE) + (1|ind), family = binomial, data = try, na.action = na.omit, control=glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)))
OLRE means that I use an observational level random effect in order to overcome overdispersion.
If you wonder because of convergence warnings, I went through the lme4 troubleshooting protocol, and it should be fine.
In order to get effect plots with confidence intervals, I tried to use ggpredict:
sjPlot, e.g.:
plot_model(mod, type = "pred", terms = c("F1", "F2", "F3"), ci.lvl = 0.95)
I also tried to go through this protocol:
https://rpubs.com/hughes/84484
intdata <- expand.grid(
positive = c(0,1),
negative = c(0,1),
F1 = as.factor(c(0,1)),
F2 = as.factor(c(1,2,3)),
F3= as.factor(c(1,2,3,4)),
V1= as.numeric(median(try$V1)),
F4= as.factor(c(30, 31)),
ind= as.factor(c(68)),
OLRE = as.factor(c(2450)),
V2= as.numeric(median(try$V2)),
V3= as.numeric(median(try$V3)),
V4= as.numeric(median(try$V4))
)
#conditional variances
cV <- ranef(mod, condVar = TRUE)
ranvar <- attr(cV[[1]], "postVar")
sqrt(diag(ranvar[,,1]))
mm <- model.matrix(terms( mod), data=intdata,
contrasts.arg = lapply(intdata[,c(3:5, 7:9)], contrasts, contrasts=FALSE))
predFun<-function(.) mm%*%fixef(.)
bb<-bootMer(mod,FUN=predFun,nsim=3)
with some problems and warnings regarding contrasts and
Error in mm %*% fixef(.) : non-conformable arguments
Therefore, I am wondering if anyone might help me but so far I am not able to Nothing worked so far, so I would really appreciate some help.
Here the link to the data https://drive.google.com/file/d/1qZaJBbM1ggxwPnZ9bsTCXL7_BnXlvfkW/view?usp=sharing
I feel I must be missing something obvious, in struggling to get a positive control for logistic regression going in tensorflow probability.
I've modified the example for logistic regression here, and created a positive control features and labels data. I struggle to achieve accuracy over 60%, however this is an easy problem for a 'vanilla' Keras model (accuracy 100%). What am I missing? I tried different layers, activations, etc.. With this method of setting up the model, is posterior updating actually being performed? Do I need to specify an interceptor object? Many thanks..
### Added positive control
nSamples = 80
features1 = np.float32(np.hstack((np.reshape(np.ones(40), (40, 1)),
np.reshape(np.random.randn(nSamples), (40, 2)))))
features2 = np.float32(np.hstack((np.reshape(np.zeros(40), (40, 1)),
np.reshape(np.random.randn(nSamples), (40, 2)))))
features = np.vstack((features1, features2))
labels = np.concatenate((np.zeros(40), np.ones(40)))
featuresInt, labelsInt = build_input_pipeline(features, labels, 10)
###
#w_true, b_true, features, labels = toy_logistic_data(FLAGS.num_examples, 2)
#featuresInt, labelsInt = build_input_pipeline(features, labels, FLAGS.batch_size)
with tf.name_scope("logistic_regression", values=[featuresInt]):
layer = tfp.layers.DenseFlipout(
units=1,
activation=None,
kernel_posterior_fn=tfp.layers.default_mean_field_normal_fn(),
bias_posterior_fn=tfp.layers.default_mean_field_normal_fn())
logits = layer(featuresInt)
labels_distribution = tfd.Bernoulli(logits=logits)
neg_log_likelihood = -tf.reduce_mean(labels_distribution.log_prob(labelsInt))
kl = sum(layer.losses)
elbo_loss = neg_log_likelihood + kl
predictions = tf.cast(logits > 0, dtype=tf.int32)
accuracy, accuracy_update_op = tf.metrics.accuracy(
labels=labelsInt, predictions=predictions)
with tf.name_scope("train"):
optimizer = tf.train.AdamOptimizer(learning_rate=FLAGS.learning_rate)
train_op = optimizer.minimize(elbo_loss)
init_op = tf.group(tf.global_variables_initializer(),
tf.local_variables_initializer())
with tf.Session() as sess:
sess.run(init_op)
# Fit the model to data.
for step in range(FLAGS.max_steps):
_ = sess.run([train_op, accuracy_update_op])
if step % 100 == 0:
loss_value, accuracy_value = sess.run([elbo_loss, accuracy])
print("Step: {:>3d} Loss: {:.3f} Accuracy: {:.3f}".format(
step, loss_value, accuracy_value))
### Check with basic Keras
kerasModel = tf.keras.models.Sequential([
tf.keras.layers.Dense(1)])
optimizer = tf.train.AdamOptimizer(5e-2)
kerasModel.compile(optimizer = optimizer, loss = 'binary_crossentropy',
metrics = ['accuracy'])
kerasModel.fit(features, labels, epochs = 50) #100% accuracy
Compared to the github example, you forgot to divide by the number of examples when defining the KL divergence:
kl = sum(layer.losses) / FLAGS.num_examples
When I change this to your code, I quickly get to an accuracy of 99.9% on your toy data.
Additionaly, the output layer of your Keras model actually expects a sigmoid activation for this problem (binary classification):
kerasModel = tf.keras.models.Sequential([
tf.keras.layers.Dense(1, activation='sigmoid')])
It's a toy problem, but you will notice that the model gets to 100% accuracy faster with a sigmoid activation.
This is my source code and I want to reduce the possible errors. When running this code there is a lot of difference between trained output to target. I have tried different ways but didn't work so please help me reducing it.
a=[31 9333 2000;31 9500 1500;31 9700 2300;31 9700 2320;31 9120 2230;31 9830 2420;31 9300 2900;31 9400 2500]'
g=[35000;23000;3443;2343;1244;9483;4638;4739]'
h=[31 9333 2000]'
inputs =(a);
targets =[g];
% Create a Fitting Network
hiddenLayerSize = 1;
net = fitnet(hiddenLayerSize);
% Choose Input and Output Pre/Post-Processing Functions
% For a list of all processing functions type: help nnprocess
net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
net.outputs{2}.processFcns = {'removeconstantrows','mapminmax'};
% Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivide
net.divideFcn = 'dividerand'; % Divide data randomly
net.divideMode = 'sample'; % Divide up every sample
net.divideParam.trainRatio = 70/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 15/100;
% For help on training function 'trainlm' type: help trainlm
% For a list of all training functions type: help nntrain
net.trainFcn = 'trainlm'; % Levenberg-Marquardt
% Choose a Performance Function
% For a list of all performance functions type: help nnperformance
net.performFcn = 'mse'; % Mean squared error
% Choose Plot Functions
% For a list of all plot functions type: help nnplot
net.plotFcns = {'plotperform','plottrainstate','ploterrhist', ...
'plotregression','plotconfusion' 'plotfit','plotroc'};
% Train the Network
[net,tr] = train(net,inputs,targets);
plottrainstate(tr)
% Test the Network
outputs = net(inputs)
errors = gsubtract(targets,outputs)
fprintf('errors = %4.3f\t',errors);
performance = perform(net,targets,outputs);
% Recalculate Training, Validation and Test Performance
trainTargets = targets .* tr.trainMask{1};
valTargets = targets .* tr.valMask{1};
testTargets = targets .* tr.testMask{1};
trainPerformance = perform(net,trainTargets,outputs);
valPerformance = perform(net,valTargets,outputs);
testPerformance = perform(net,testTargets,outputs);
% View the Network
view(net);
sc=sim(net,h)
I think you need to be more specific.
What is the performance like on your training set and on your test set?
Have you tried doing any regularization?