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I'm dealing with the following senario:
My input has the shape of: [batch_size, input_sequence_length, input_features]
where:
input_sequence_length = 10
input_features = 3
My output has the shape of: [batch_size, output_sequence_length]
where:
output_sequence_length = 5
i.e: for each time slot of 10 units (each slot with 3 features) I need to predict the next 5 slots values.
I built the following model:
import torch
import torch.nn as nn
import torchinfo
class MyModel(nn.Module):
def __init__(self):
super(MyModel, self).__init__()
self.GRU = nn.GRU(input_size=3, hidden_size=32, num_layers=2, batch_first=True)
self.fc = nn.Linear(32, 5)
def forward(self, input_series):
output, h = self.GRU(input_series)
output = output[:, -1, :] # get last state
output = self.fc(output)
output = output.view(-1, 5, 1) # reorginize output
return output
torchinfo.summary(MyModel(), (512, 10, 3))
==========================================================================================
Layer (type:depth-idx) Output Shape Param #
==========================================================================================
MyModel [512, 5, 1] --
├─GRU: 1-1 [512, 10, 32] 9,888
├─Linear: 1-2 [512, 5] 165
==========================================================================================
I'm getting good results (very small MSE loss, and the predictions looks good),
but I'm not sure if the model output (5 sequence values) are really ordered by the model ?
i.e the second output based on the first output and the third output based on the second output ...
I know that the GRU output based on the learned sequence history.
But I'm also used linear layer, so is the output (after the linear layer) still sorted by time ?
UPDATE
This answer isn't quite right, see this follow-up question. The best way is to write the math and show that the 5 scalar outputs aren't functions of each other.
Old Answer
I'm not sure if the model output (5 sequence values) are really ordered by the model ? i.e the second output based on the first output and the third output based on the second output
No, they aren't. You can check that the gradients of, say, the last output w.r.t to the previous outputs are zeroes, which basically means that the last output isn't a function of the previous outputs.
model = MyModel()
x = torch.rand([2, 10, 3])
y = model(x)
y.retain_grad() # allows accessing y.grad although y is a non-leaf Tensor
y[:, -1].sum().backward() # computes gradients of last output
assert torch.allclose(y.grad[:, :-1], torch.tensor(0.)) # gradients w.r.t previous outputs are zeroes
A popular model to capture dependencies among output labels is conditional random fields. But since you're already happy with the predictions of the current model, perhaps modelling the output dependencies isn't that important.
I was performing semantic segmentation using PyTorch. There are a total of 103 different classes in the dataset and the targets are RGB images with only the Red channel containing the labels. I was using nn.CrossEntropyLoss as my loss function. For sanity, I wanted to check if using nn.CrossEntropyLoss is correct for this problem and whether it has the expected behaviour
I pick a random mask from my dataset and create a categorical version of it using this custom transform
class ToCategorical:
def __init__(self, n_classes: int) -> None:
self.n_classes = n_classes
def __call__(self, sample: torch.Tensor):
mask = sample.permute(1, 2, 0)
categories = torch.unique(mask).tolist()[1:] # get all categories other than 0
# build a tensor with `n_classes` channels
one_hot_image = torch.zeros(self.n_classes, *mask.shape[:-1])
for category in categories:
# get spacial locs where the categ is present
rows, cols, _ = torch.where(mask == category)
# in same spacial loc but in `categ` channel fill 1
one_hot_image[category, rows, cols] = 1
return one_hot_image
And then I send this image as the output (prediction) and use the ground truth mask as the target to the loss function.
import torch.nn as nn
mask = T.PILToTensor()(Image.open("path_to_image").convert("RGB"))
categorical_mask = ToCategorical(103)(mask).unsqueeze(0)
mask = mask[0].unsqueeze(0) # get only the red channel, add fake batch_dim
loss_fn = nn.CrossEntropyLoss()
target = mask
output = categorical_mask
print(output.shape, target.shape)
print(loss_fn(output, target.to(torch.long)))
I expected the loss to be zero but to my surprise, the output is as follows
torch.Size([1, 103, 600, 800]) torch.Size([1, 600, 800])
tensor(4.2836)
I verified with other samples in the dataset and I obtained similar values for other masks as well. Am I doing something wrong? I expect the loss to be = 0 when the output is the same as the target.
PS. I also know that nn.CrossEntropyLoss is the same as using log_softmax followed by nn.NLLLoss() but even I obtained the same value by using nllloss as well
For Reference
Dataset used: UECFoodPixComplete
I would like to adress this:
I expect the loss to be = 0 when the output is the same as the target.
If the prediction matches the target, i.e. the prediction corresponds to a one-hot-encoding of the labels contained in the dense target tensor, but the loss itself is not supposed to equal to zero. Actually, it can never be equal to zero because the nn.CrossEntropyLoss function is always positive by definition.
Let us take a minimal example with number of #C classes and a target y_pred and a prediction y_pred consisting of prefect predictions:
As a quick reminder:
The softmax is applied on the logits (q_i) as p_i = log(exp(q_i)/sum_j(exp(q_j)):
>>> p = F.softmax(y_pred, 1)
Similarly if you are using the log-softmax, defined as logp_i = log(p_i):
>>> logp = F.log_softmax(y_pred, 1)
Then comes the negative likelihood function computed between x the input and y the target: -y*x. In association with the softmax, it comes down to -y*p, or -y*logp respectively. In any case, whether you apply the log or not, only the predictions corresponding to the true classes will remain since the others ones are zeroed-out.
That being said, applying the NLLLoss on y_pred would indeed result with a 0 as you expected in your question. However, here we apply it on the probability distribution or log-probability: p, or logp respectively!
In our specific case, p_i = 1 for the true class and p_i = 0 for all other classes (there are #C - 1 of those). This means the softmax of the logit associated with the true class will equal to exp(1)/sum_i(p_i). And since sum_i(p_i) = (#C-1)*exp(0) + exp(1). We therefore have:
softmax(p) = e / (#C - 1 + e)
Similarly for log-softmax:
log-softmax(p) = log(e / (#C-1 + e)) = 1 - log(#C - 1 + e)
If we proceed by applying the negative likelihood function we simply get cross-entropy(y_pred, y_true) = (nllloss o log-softmax)(y_pred, y_true). This results in:
loss = - (1 - log(#C - 1 + e)) = log(#C - 1 + e) - 1
This effectively corresponds to the minimum of the nn.CrossEntropyLoss function.
Regarding your specific case where #C = 103, you may have an issue in your code... since the average loss should equal to log(102 + e) - 1 i.e. around 3.65.
>>> y_true = torch.randint(0,103,(1,1,2,5))
>>> y_pred = torch.zeros(1,103,2,5).scatter(1, y_true, value=1)
You can see for yourself with one of the provided methods:
the builtin function nn.functional.cross_entropy:
>>> F.cross_entropy(y_pred, y_true[:,0])
tensor(3.6513)
manually computing the quantity:
>>> logp = F.log_softmax(y_pred, 1)
>>> -logp.gather(1, y_true).mean()
tensor(3.6513)
analytical result:
>>> log(102 + e) - 1
3.6513
I would like to estimate the parameters of a mixture model of normal distributions in OpenTURNS (that is, the distribution of a weighted sum of Gaussian random variables). OpenTURNS can create such a mixture, but it cannot estimate its parameters. Moreover, I need to create the mixture as an OpenTURNS distribution in order to propagate uncertainty through a function.
For example, I know how to create a mixture of two normal distributions:
import openturns as ot
mu1 = 1.0
sigma1 = 0.5
mu2 = 3.0
sigma2 = 2.0
weights = [0.3, 0.7]
n1 = ot.Normal(mu1, sigma1)
n2 = ot.Normal(mu2, sigma2)
m = ot.Mixture([n1, n2], weights)
In this example, I would like to estimate mu1, sigma1, mu2, sigma2 on a given sample. In order to create a working example, it is easy to generate a sample by simulation.
s = m.getSample(100)
You can rely on scikit-learn's GaussianMixture to estimate the parameters and then use them to define a Mixture model in OpenTURNS.
The script hereafter contains a Python class MixtureFactory that estimates the parameters of a scikitlearn GaussianMixture and outputs an OpenTURNS Mixture distribution:
from sklearn.mixture import GaussianMixture
from sklearn.utils.validation import check_is_fitted
import openturns as ot
import numpy as np
class MixtureFactory(GaussianMixture):
"""
Representation of a Gaussian mixture model probability distribution.
This class allows to estimate the parameters of a Gaussian mixture
distribution using scikit algorithms & provides openturns Mixture object.
Read more in scikit learn user guide & openturns theory.
Parameters:
-----------
n_components : int, defaults to 1.
The number of mixture components.
covariance_type : {'full' (default), 'tied', 'diag', 'spherical'}
String describing the type of covariance parameters to use.
Must be one of:
'full'
each component has its own general covariance matrix
'tied'
all components share the same general covariance matrix
'diag'
each component has its own diagonal covariance matrix
'spherical'
each component has its own single variance
tol : float, defaults to 1e-3.
The convergence threshold. EM iterations will stop when the
lower bound average gain is below this threshold.
reg_covar : float, defaults to 1e-6.
Non-negative regularization added to the diagonal of covariance.
Allows to assure that the covariance matrices are all positive.
max_iter : int, defaults to 100.
The number of EM iterations to perform.
n_init : int, defaults to 1.
The number of initializations to perform. The best results are kept.
init_params : {'kmeans', 'random'}, defaults to 'kmeans'.
The method used to initialize the weights, the means and the
precisions.
Must be one of::
'kmeans' : responsibilities are initialized using kmeans.
'random' : responsibilities are initialized randomly.
weights_init : array-like, shape (n_components, ), optional
The user-provided initial weights, defaults to None.
If it None, weights are initialized using the `init_params` method.
means_init : array-like, shape (n_components, n_features), optional
The user-provided initial means, defaults to None,
If it None, means are initialized using the `init_params` method.
precisions_init : array-like, optional.
The user-provided initial precisions (inverse of the covariance
matrices), defaults to None.
If it None, precisions are initialized using the 'init_params' method.
The shape depends on 'covariance_type'::
(n_components,) if 'spherical',
(n_features, n_features) if 'tied',
(n_components, n_features) if 'diag',
(n_components, n_features, n_features) if 'full'
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
warm_start : bool, default to False.
If 'warm_start' is True, the solution of the last fitting is used as
initialization for the next call of fit(). This can speed up
convergence when fit is called several times on similar problems.
In that case, 'n_init' is ignored and only a single initialization
occurs upon the first call.
See :term:`the Glossary <warm_start>`.
verbose : int, default to 0.
Enable verbose output. If 1 then it prints the current
initialization and each iteration step. If greater than 1 then
it prints also the log probability and the time needed
for each step.
verbose_interval : int, default to 10.
Number of iteration done before the next print.
"""
def __init__(self, n_components=2, covariance_type='full', tol=1e-6,
reg_covar=1e-6, max_iter=1000, n_init=1, init_params='kmeans',
weights_init=None, means_init=None, precisions_init=None,
random_state=41, warm_start=False,
verbose=0, verbose_interval=10):
super().__init__(n_components, covariance_type, tol, reg_covar,
max_iter, n_init, init_params, weights_init, means_init,
precisions_init, random_state, warm_start, verbose, verbose_interval)
def fit(self, X):
"""
Fit the mixture model parameters.
EM algorithm is applied here to estimate the model parameters and build a
Mixture distribution (see openturns mixture).
The method fits the model ``n_init`` times and sets the parameters with
which the model has the largest likelihood or lower bound. Within each
trial, the method iterates between E-step and M-step for ``max_iter``
times until the change of likelihood or lower bound is less than
``tol``, otherwise, a ``ConvergenceWarning`` is raised.
If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single
initialization is performed upon the first call. Upon consecutive
calls, training starts where it left off.
Parameters
----------
X : array-like, shape (n_samples, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
"""
data = np.array(X)
# Evaluate the model parameters.
super().fit(data)
# openturns mixture
# n_components ==> weight of size n_components
weights = self.weights_
n_components = len(weights)
# Create ot distribution
collection = n_components * [0]
# Covariance matrices
cov = self.covariances_
mu = self.means_
# means : n_components x n_features
n_components, n_features = mu.shape
# Following the type of covariance, we define the collection of gaussians
# Spherical : C_k = Identity * sigma_k
if self.covariance_type is 'spherical':
c = ot.CorrelationMatrix(n_features)
for l in range(n_components):
sigma = np.sqrt(cov[l])
collection[l] = ot.Normal(list(mu[l]), [ sigma ] * n_features , c)
elif self.covariance_type is 'diag' :
for l in range(n_components):
c = ot.CovarianceMatrix(n_features)
for i in range(n_features):
c[i,i] = cov[l, i]
collection[l] = ot.Normal(list(mu[l]), c)
elif self.covariance_type == 'tied':
# Same covariance for all clusters
c = ot.CovarianceMatrix(n_features)
for i in range(n_features):
for j in range(0, i+1):
c[i,j] = cov[i,j]
# Define the collection with the same covariance
for l in range(n_components):
collection[l] = ot.Normal(list(mu[l]), c)
else:
n_features = cov.shape[1]
for l in range(n_components):
c = ot.CovarianceMatrix(n_features)
for i in range(n_features):
for j in range(0, i+1):
c[i,j] = cov[l][i,j]
collection[l] = ot.Normal(list(mu[l]), c)
self._mixture = ot.Mixture(collection, weights)
return self
def get_mixture(self):
"""
Returns the Mixture object
"""
check_is_fitted(self)
return self._mixture
if __name__ == "__main__":
mu1 = 1.0
sigma1 = 0.5
mu2 = 3.0
sigma2 = 2.0
weights = [0.3, 0.7]
n1 = ot.Normal(mu1, sigma1)
n2 = ot.Normal(mu2, sigma2)
m = ot.Mixture([n1, n2], weights)
x = m.getSample(1000)
est_dist = MixtureFactory(random_state=1)
est_dist.fit(x)
print(est_dist.get_mixture())
I have actually tried this method and it works perfectly. On top of that the fit of the model through the SciKit GMM and the ulterior adjustment thanks to OpenTurns are very fast. I recommend future users to test several numbers of components and covariance matrix structures, as it will not take a lot of time and can substantially improve the goodness of fit to the data.
Thanks for the answer.
Here is a pure OpenTURNS solution. It is probably slower than the scikit-learn-based method, but it is more generic: you could use it to estimate the parameters of any mixture model, not necessarily a mixture of normal distributions.
The idea is to retrieve the log-likelihood function from the Mixture object and minimize it.
In the following, let us assume that s is the sample we want to fit the mixture on.
First, we need to build the mixture we want to estimate the parameters of. We can specify any valid set of parameters, it does not matter. In your example, you want a mixture of 2 normal distributions.
mixture = ot.Mixture([ot.Normal()]*2, [0.5]*2)
There is a small hurdle. All weights sum to 1, thus one of them is determined by the others: the solver must not be allowed to freely set it. The order of the parameters of an OpenTURNS Mixture is as follows:
weight of the first distribution;
parameters of the first distribution;
weight of the second distribution;
parameters of the second distribution:
...
You can view all parameters with mixture.getParameter() and their names with mixture.getParameterDescription(). The following is a helper function that:
takes as input the list containing of all mixture parameters except the weight of its first distribution;
outputs a Point containing all parameters including the weight of the first distribution.
def full(params):
"""
Point of all mixture parameters from a list that omits the first weight.
"""
params = ot.Point(params)
aux_mixture = ot.Mixture(mixture)
dist_number = aux_mixture.getDistributionCollection().getSize()
index = aux_mixture.getDistributionCollection()[0].getParameter().getSize()
list_weights = []
for num in range(1, dist_number):
list_weights.append(params[index])
index += 1 + aux_mixture.getDistributionCollection()[num].getParameter().getSize()
complementary_weight = ot.Point([abs(1.0 - sum(list_weights))])
complementary_weight.add(params)
return complementary_weight
The next function computes the opposite of the log-likelihood of a given list of parameters (except the first weight).
For the sake of numerical stability, it divides this value by the number of observations.
We will minimize this function in order to find the Maximum Likelihood Estimate.
def minus_log_pdf(params):
"""
- log-likelihood of a list of parameters excepting the first weight
divided by the number of observations
"""
aux_mixture = ot.Mixture(mixture)
full_params = full(params)
try:
aux_mixture.setParameter(full_params)
except TypeError:
# case where the proposed parameters are invalid:
# return a huge value
return [ot.SpecFunc.LogMaxScalar]
res = - aux_mixture.computeLogPDF(s).computeMean()
return res
To use OpenTURNS optimization facilities, we need to turn this function into a PythonFunction object.
OT_minus_log_pdf = ot.PythonFunction(mixture.getParameter().getSize()-1, 1, minus_log_pdf)
Cobyla is usually good at likelihood optimization.
problem = ot.OptimizationProblem(OT_minus_log_pdf)
algo = ot.Cobyla(problem)
In order to decrease chances of Cobyla being stuck on a local minimum, we are going to use MultiStart. We pick a starting set of parameters and randomly change the weights. The following helper function makes it easy:
def random_weights(params, nb):
"""
List of nb Points representing mixture parameters with randomly varying weights.
"""
aux_mixture = ot.Mixture(mixture)
full_params = full(params)
aux_mixture.setParameter(full_params)
list_params = []
for num in range(nb):
dirichlet = ot.Dirichlet([1.0] * aux_mixture.getDistributionCollection().getSize()).getRealization()
dirichlet.add(1.0 - sum(dirichlet))
aux_mixture.setWeights(dirichlet)
list_params.append(aux_mixture.getParameter()[1:])
return list_params
We pick 10 starting points and increase the number of maximum evaluations of the log-likelihood from 100 (by default) to 10000.
init = mixture.getParameter()[1:]
starting_points = random_weights(init, 10)
algo_multistart = ot.MultiStart(algo, starting_points)
algo_multistart.setMaximumEvaluationNumber(10000)
Let's run the solver and retrieve the result.
algo_multistart.run()
result = algo_multistart.getResult()
All that remains is to set the mixture's parameters to the optimal value.
We must not forget to add the first weight back!
optimal_parameters = result.getOptimalPoint()
mixture.setParameter(full(optimal_parameters))
Below is an alternative.
The first step creates a new GaussianMixture class, derived from PythonDistribution. The key point is to implement the computeLogPDF method and the set/getParameters methods. Notice that this parametrization of a mixture only has one single weight w.
class GaussianMixture(ot.PythonDistribution):
def __init__(self, mu1 = -5.0, sigma1 = 1.0, \
mu2 = 5.0, sigma2 = 1.0, \
w = 0.5):
super(GaussianMixture, self).__init__(1)
if w < 0.0 or w > 1.0:
raise ValueError('The weight is not in [0, 1]. w=%s.' % (w))
self.mu1 = mu2
self.sigma1 = sigma1
self.mu2 = mu2
self.sigma2 = sigma2
self.w = w
collDist = [ot.Normal(mu1, sigma1), ot.Normal(mu2, sigma2)]
weight = [w, 1.0 - w]
self.distribution = ot.Mixture(collDist, weight)
def computeCDF(self, x):
p = self.distribution.computeCDF(x)
return p
def computePDF(self, x):
p = self.distribution.computePDF(x)
return p
def computeQuantile(self, prob, tail = False):
quantile = self.distribution.computeQuantile(prob, tail)
return quantile
def getSample(self, size):
X = self.distribution.getSample(size)
return X
def getParameter(self):
parameter = ot.Point([self.mu1, self.sigma1, \
self.mu2, self.sigma2, \
self.w])
return parameter
def setParameter(self, parameter):
[mu1, sigma1, mu2, sigma2, w] = parameter
self.__init__(mu1, sigma1, mu2, sigma2, w)
return parameter
def computeLogPDF(self, sample):
logpdf = self.distribution.computeLogPDF(sample)
return logpdf
In order to create the distribution, we use the Distribution class:
gm = ot.Distribution(GaussianMixture())
Estimating the parameters of this distribution is straightforward with MaximumLikelihoodFactory. However, we must set the bounds, because sigma cannot be negative and that w is in (0, 1).
factory = ot.MaximumLikelihoodFactory(gm)
lowerBound = [0.0, 1.e-6, 0.0, 1.e-6, 0.01]
upperBound = [0.0, 0.0, 0.0, 0.0, 0.99]
finiteLowerBound = [False, True, False, True, True]
finiteUpperBound = [False, False, False, False, True]
bounds = ot.Interval(lowerBound, upperBound, finiteLowerBound, finiteUpperBound)
factory.setOptimizationBounds(bounds)
Then we configure the optimization solver.
solver = factory.getOptimizationAlgorithm()
startingPoint = [-4.0, 1.0, 7.0, 1.5, 0.3]
solver.setStartingPoint(startingPoint)
factory.setOptimizationAlgorithm(solver)
Estimating the parameters is based on the build method.
distribution = factory.build(sample)
There are two limitations with this implementation.
First, it is not as fast as it should be, because of a limitation of the PythonDistribution (see https://github.com/openturns/openturns/issues/1391).
Estimating the parameters may be difficult, because the problem may have local optimas that cannot be retrieved with the default algorithm in MaximumLikelihoodFactory. This kind of task is generally done with the EM algorithm.
i was implementing DQN in mountain car problem of openai gym. this problem is special as the positive reward is very sparse. so i thought of implementing prioritized experience replay as proposed in this paper by google deep mind.
there are certain things that are confusing me:
how do we store the replay memory. i get that pi is the priority of transition and there are two ways but what is this P(i)?
if we follow the rules given won't P(i) change every time a sample is added.
what does it mean when it says "we sample according to this probability distribution". what is the distribution.
finally how do we sample from it. i get that if we store it in a priority queue we can sample directly but we are actually storing it in a sum tree.
thanks in advance
According to the paper, there are two ways for calculating Pi and base on your choice, your implementation differs. I assume you selected Proportional Prioriziation then you should use "sum-tree" data structure for storing a pair of transition and P(i). P(i) is just the normalized version of Pi and it shows how important that transition is or in other words how effective that transition is for improving your network. When P(i) is high, it means it's so surprising for the network so it can really help the network to tune itself.
You should add each new transition with infinity priority to make sure it will be played at least once and there is no need to update all the experience replay memory for each new coming transition. During the experience replay process, you select a mini-batch and update the probability of those experiences in the mini-batch.
Each experience has a probability so all of the experiences together make a distribution and we select our next mini-batch according to this distribution.
You can sample via this policy from your sum-tree:
def retrieve(n, s):
if n is leaf_node: return n
if n.left.val >= s: return retrieve(n.left, s)
else: return retrieve(n.right, s - n.left.val)
I have taken the code from here.
You can reuse the code in OpenAI Baseline or using SumTree
import numpy as np
import random
from baselines.common.segment_tree import SumSegmentTree, MinSegmentTree
class ReplayBuffer(object):
def __init__(self, size):
"""Create Replay buffer.
Parameters
----------
size: int
Max number of transitions to store in the buffer. When the buffer
overflows the old memories are dropped.
"""
self._storage = []
self._maxsize = size
self._next_idx = 0
def __len__(self):
return len(self._storage)
def add(self, obs_t, action, reward, obs_tp1, done):
data = (obs_t, action, reward, obs_tp1, done)
if self._next_idx >= len(self._storage):
self._storage.append(data)
else:
self._storage[self._next_idx] = data
self._next_idx = (self._next_idx + 1) % self._maxsize
def _encode_sample(self, idxes):
obses_t, actions, rewards, obses_tp1, dones = [], [], [], [], []
for i in idxes:
data = self._storage[i]
obs_t, action, reward, obs_tp1, done = data
obses_t.append(np.array(obs_t, copy=False))
actions.append(np.array(action, copy=False))
rewards.append(reward)
obses_tp1.append(np.array(obs_tp1, copy=False))
dones.append(done)
return np.array(obses_t), np.array(actions), np.array(rewards), np.array(obses_tp1), np.array(dones)
def sample(self, batch_size):
"""Sample a batch of experiences.
Parameters
----------
batch_size: int
How many transitions to sample.
Returns
-------
obs_batch: np.array
batch of observations
act_batch: np.array
batch of actions executed given obs_batch
rew_batch: np.array
rewards received as results of executing act_batch
next_obs_batch: np.array
next set of observations seen after executing act_batch
done_mask: np.array
done_mask[i] = 1 if executing act_batch[i] resulted in
the end of an episode and 0 otherwise.
"""
idxes = [random.randint(0, len(self._storage) - 1) for _ in range(batch_size)]
return self._encode_sample(idxes)
class PrioritizedReplayBuffer(ReplayBuffer):
def __init__(self, size, alpha):
"""Create Prioritized Replay buffer.
Parameters
----------
size: int
Max number of transitions to store in the buffer. When the buffer
overflows the old memories are dropped.
alpha: float
how much prioritization is used
(0 - no prioritization, 1 - full prioritization)
See Also
--------
ReplayBuffer.__init__
"""
super(PrioritizedReplayBuffer, self).__init__(size)
assert alpha >= 0
self._alpha = alpha
it_capacity = 1
while it_capacity < size:
it_capacity *= 2
self._it_sum = SumSegmentTree(it_capacity)
self._it_min = MinSegmentTree(it_capacity)
self._max_priority = 1.0
def add(self, *args, **kwargs):
"""See ReplayBuffer.store_effect"""
idx = self._next_idx
super().add(*args, **kwargs)
self._it_sum[idx] = self._max_priority ** self._alpha
self._it_min[idx] = self._max_priority ** self._alpha
def _sample_proportional(self, batch_size):
res = []
p_total = self._it_sum.sum(0, len(self._storage) - 1)
every_range_len = p_total / batch_size
for i in range(batch_size):
mass = random.random() * every_range_len + i * every_range_len
idx = self._it_sum.find_prefixsum_idx(mass)
res.append(idx)
return res
def sample(self, batch_size, beta):
"""Sample a batch of experiences.
compared to ReplayBuffer.sample
it also returns importance weights and idxes
of sampled experiences.
Parameters
----------
batch_size: int
How many transitions to sample.
beta: float
To what degree to use importance weights
(0 - no corrections, 1 - full correction)
Returns
-------
obs_batch: np.array
batch of observations
act_batch: np.array
batch of actions executed given obs_batch
rew_batch: np.array
rewards received as results of executing act_batch
next_obs_batch: np.array
next set of observations seen after executing act_batch
done_mask: np.array
done_mask[i] = 1 if executing act_batch[i] resulted in
the end of an episode and 0 otherwise.
weights: np.array
Array of shape (batch_size,) and dtype np.float32
denoting importance weight of each sampled transition
idxes: np.array
Array of shape (batch_size,) and dtype np.int32
idexes in buffer of sampled experiences
"""
assert beta > 0
idxes = self._sample_proportional(batch_size)
weights = []
p_min = self._it_min.min() / self._it_sum.sum()
max_weight = (p_min * len(self._storage)) ** (-beta)
for idx in idxes:
p_sample = self._it_sum[idx] / self._it_sum.sum()
weight = (p_sample * len(self._storage)) ** (-beta)
weights.append(weight / max_weight)
weights = np.array(weights)
encoded_sample = self._encode_sample(idxes)
return tuple(list(encoded_sample) + [weights, idxes])
def update_priorities(self, idxes, priorities):
"""Update priorities of sampled transitions.
sets priority of transition at index idxes[i] in buffer
to priorities[i].
Parameters
----------
idxes: [int]
List of idxes of sampled transitions
priorities: [float]
List of updated priorities corresponding to
transitions at the sampled idxes denoted by
variable `idxes`.
"""
assert len(idxes) == len(priorities)
for idx, priority in zip(idxes, priorities):
assert priority > 0
assert 0 <= idx < len(self._storage)
self._it_sum[idx] = priority ** self._alpha
self._it_min[idx] = priority ** self._alpha
self._max_priority = max(self._max_priority, priority)
In PyTorch, we can define architectures in multiple ways. Here, I'd like to create a simple LSTM network using the Sequential module.
In Lua's torch I would usually go with:
model = nn.Sequential()
model:add(nn.SplitTable(1,2))
model:add(nn.Sequencer(nn.LSTM(inputSize, hiddenSize)))
model:add(nn.SelectTable(-1)) -- last step of output sequence
model:add(nn.Linear(hiddenSize, classes_n))
However, in PyTorch, I don't find the equivalent of SelectTable to get the last output.
nn.Sequential(
nn.LSTM(inputSize, hiddenSize, 1, batch_first=True),
# what to put here to retrieve last output of LSTM ?,
nn.Linear(hiddenSize, classe_n))
Define a class to extract the last cell output:
# LSTM() returns tuple of (tensor, (recurrent state))
class extract_tensor(nn.Module):
def forward(self,x):
# Output shape (batch, features, hidden)
tensor, _ = x
# Reshape shape (batch, hidden)
return tensor[:, -1, :]
nn.Sequential(
nn.LSTM(inputSize, hiddenSize, 1, batch_first=True),
extract_tensor(),
nn.Linear(hiddenSize, classe_n)
)
According to the LSTM cell documentation the outputs parameter has a shape of (seq_len, batch, hidden_size * num_directions) so you can easily take the last element of the sequence in this way:
rnn = nn.LSTM(10, 20, 2)
input = Variable(torch.randn(5, 3, 10))
h0 = Variable(torch.randn(2, 3, 20))
c0 = Variable(torch.randn(2, 3, 20))
output, hn = rnn(input, (h0, c0))
print(output[-1]) # last element
Tensor manipulation and Neural networks design in PyTorch is incredibly easier than in Torch so you rarely have to use containers. In fact, as stated in the tutorial PyTorch for former Torch users PyTorch is built around Autograd so you don't need anymore to worry about containers. However, if you want to use your old Lua Torch code you can have a look to the Legacy package.
As far as I'm concerned there's nothing like a SplitTable or a SelectTable in PyTorch. That said, you are allowed to concatenate an arbitrary number of modules or blocks within a single architecture, and you can use this property to retrieve the output of a certain layer. Let's make it more clear with a simple example.
Suppose I want to build a simple two-layer MLP and retrieve the output of each layer. I can build a custom class inheriting from nn.Module:
class MyMLP(nn.Module):
def __init__(self, in_channels, out_channels_1, out_channels_2):
# first of all, calling base class constructor
super().__init__()
# now I can build my modular network
self.block1 = nn.Linear(in_channels, out_channels_1)
self.block2 = nn.Linear(out_channels_1, out_channels_2)
# you MUST implement a forward(input) method whenever inheriting from nn.Module
def forward(x):
# first_out will now be your output of the first block
first_out = self.block1(x)
x = self.block2(first_out)
# by returning both x and first_out, you can now access the first layer's output
return x, first_out
In your main file you can now declare the custom architecture and use it:
from myFile import MyMLP
import numpy as np
in_ch = out_ch_1 = out_ch_2 = 64
# some fake input instance
x = np.random.rand(in_ch)
my_mlp = MyMLP(in_ch, out_ch_1, out_ch_2)
# get your outputs
final_out, first_layer_out = my_mlp(x)
Moreover, you could concatenate two MyMLP in a more complex model definition and retrieve the output of each one in a similar way.
I hope this is enough to clarify, but in case you have more questions, please feel free to ask, since I may have omitted something.