I am trying to run a GP regression over 2D space + 1D time with ~8000 observations and a composite kernel with 4 Matern 3/2 covariance functions -- more than a single core can handle.
It would be great to be able to distribute the GPR computation over multiple nodes rather than having to resort to variational GP. This github issue explains how to execute multithreading in GPflow 1.0, but I am not looking for a way to parallelize many predict_f calls.
Rather, I want to do GPR on a large dataset, which means inverting a covariance matrix larger than a single core can handle. Is there a way to parallelize this computation for a cluster or the Cloud?
In terms of computation, the GPflow can do whatever TensorFlow does. In other words, if TensorFlow supported cloud evaluations, the GPflow would support it as well. But, it doesn't mean that you cannot implement your version of TensorFlow computation, maybe more efficient and be able to run it on the cloud. You can start looking into TensorFlow custom ops: https://www.tensorflow.org/guide/create_op.
The linalg operations, like Cholesky, are hardly parallelisable and benefit of time-saving from it would be questionable. Although memory-wise the advantage of cluster computing is obvious.
If you're interested in MVM-based inference we have a bit of a start here:
https://github.com/tensorflow/probability/blob/7c70d4a3389680670e989b93561440caaa0fb8cd/tensorflow_probability/python/experimental/linalg/linear_operator_psd_kernel.py#L252
I've been playing with stochastic lanczos quadrature for logdet, and preconditioned CG for the solve, but so far have not committed those into TFP.
Related
I want to use MLPRegressor from sklearn with all 12 cores available to me, however I do not see any option to select the amount of cores (such as with RandomForestClassifier which has the option with n_jobs).
Is there another way to make sure it uses all 12 cores? I vaguely heard about joblib, but how would I use it correctly?
MLPRegressor does not contain any multithreading per se, though the matrix operations will be vectorized and parallelized via numpy.
You may be able to get better performance by varying your batch size, but if performance is critical you should use a deep learning library like Tensorflow.
I'm using PyTorch to implement an intense sequence of matrix operations, using methods such as torch.mm or torch.dot. I was wondering if PyTorch uses multithreading or other optimization mechanisms to speed up the process. I am not utilizing a GPU. I appreciate if you could inform me of how fast these methods are and whether I need to take any actions to help the process.
PyTorch uses an efficient BLAS implementation and multithreading (openMP, if I'm not wrong) to parallelize such operations with multiple cores. Some performance loss comes from the Python itself - since this is an interpreted language, no significant compiler-like optimization can be done. You can use the jit module to speed up the "wrapper" code around the matrix multiplies, but for anything more than very small matrices this cost is probably negligible.
One big improvement you may be able to get manually, but which PyTorch doesn't apply automatically, is to properly order the matrix multiplies. As you probably know, depending on matrix shapes, a multiplication ABCD may have different performance computed as A(B(CD)) than if computed as (AB)(CD), etc.
I'm not an expert in distributed system and CUDA. But there is one really interesting feature that PyTorch support which is nn.DataParallel and nn.DistributedDataParallel. How are they actually implemented? How do they separate common embeddings and synchronize data?
Here is a basic example of DataParallel.
import torch.nn as nn
from torch.autograd.variable import Variable
import numpy as np
class Model(nn.Module):
def __init__(self):
super().__init__(
embedding=nn.Embedding(1000, 10),
rnn=nn.Linear(10, 10),
)
def forward(self, x):
x = self.embedding(x)
x = self.rnn(x)
return x
model = nn.DataParallel(Model())
model.forward(Variable.from_numpy(np.array([1,2,3,4,5,6], dtype=np.int64)).cuda()).cpu()
PyTorch can split the input and send them to many GPUs and merge the results back.
How does it manage embeddings and synchronization for a parallel model or a distributed model?
I wandered around PyTorch's code but it's very hard to know how the fundamentals work.
That's a great question.
PyTorch DataParallel paradigm is actually quite simple and the implementation is open-sourced here . Note that his paradigm is not recommended today as it bottlenecks at the master GPU and not efficient in data transfer.
This container parallelizes the application of the given :attr:module by
splitting the input across the specified devices by chunking in the batch
dimension (other objects will be copied once per device). In the forward
pass, the module is replicated on each device, and each replica handles a
portion of the input. During the backwards pass, gradients from each replica
are summed into the original module.
As of DistributedDataParallel, thats more tricky. This is currently the more advanced approach and it is quite efficient (see here).
This container parallelizes the application of the given module by
splitting the input across the specified devices by chunking in the batch
dimension. The module is replicated on each machine and each device, and
each such replica handles a portion of the input. During the backwards
pass, gradients from each node are averaged.
There are several approaches towards how to average the gradients from each node. I would recommend this paper to get a real sense how things work. Generally speaking, there is a trade-off between transferring the data from one GPU to another, regarding bandwidth and speed, and we want that part to be really efficient. So one possible approach is to connect each pairs of GPUs with a really fast protocol in a circle, and to pass only part of gradients from one to another, s.t. in total, we transfer less data, more efficiently, and all the nodes get all the gradients (or their average at least). There will still be a master GPU in that situation, or at least a process, but now there is no bottleneck on any GPU, they all share the same amount of data (up to...).
Now this can be further optimized if we don't wait for all the batches to finish compute and start do a time-sharing thing where each node sends his portion when he's ready. Don't take me on the details, but it turns out that if we don't wait for everything to end, and do the averaging as soon as we can, it might also speed up the gradient averaging.
Please refer to literature for more information about that area as it is still developing (as of today).
PS 1: Usually these distributed training work better on machines that are set for that task, e.g. AWS deep learning instances that implement those protocols in HW.
PS 2: Disclaimer: I really don't know what protocol PyTorch devs chose to implement and what is chosen according to what. I work with distributed training and prefer to follow PyTorch best practices without trying to outsmart them. I recommend for you to do the same unless you are really into researching this area.
References:
[1] Distributed Training of Deep Learning Models: A Taxonomic Perspective
Approach to ml parallelism with Pytorch
DataParallel & DistributedDataParallel
Model parallel https://pytorch.org/tutorials/intermediate/model_parallel_tutorial.html
See Will switching GPU device affect the gradient in PyTorch back propagation?
I have used kmeans and PCA to attempt to visualise high dimensional k-means clusters in two dimensions but have lost the meaning of the clusters in 2D.
Is there anyway to project the features onto to 2D plot to return some interpretability?
Any non-linear dimensionality reduction method might work better (also called "manifold learning", e.g. see sklearn's suite). The t-sne method is generally quite popular for this.
However, these do not take your cluster labels into account. If you wanted to do that (although generally you do not), you could add a penalty to the manifold learning technique that forces same-cluster points to be close together, for example.
I want to implement the Asynchronous Advantage Actor Critic (A3C) model for reinforcement learning in my local machine (1 CPU, 1 cuda compatible GPU). In this algorithm, several "learner" networks interact with copies of an environment and update a central model periodically.
I've seen implementations that create n "worker" networks and one "global" network inside the same graph and use threading to run these. In these approaches, the global net is updated by applying gradients to the trainable parameters with a "global" scope.
However, I recently read a bit about distributed tensorflow and now I'm a bit confused. Would it be easier/faster/better to implement this using the distributed tensorflow API? In the documentation and talks they always make expicit mention of using it in multi-device environments. I don't know if it's an overkill to use it in a local async algorithm.
I would also like to ask, is there a way to batch the gradients calculated by every worker to be applied together after n steps?
After implementing both, in the end I found using threading simpler than the distributed tensorflow API, however it also runs slower. The more CPU cores you use, the faster distributed tensorflow becomes compared to threads.
However this only holds for asynchronous training. If the available CPU cores are limited and you want to make use of a GPU, you might want to use synchronous training with multiple workers instead, like OpenAI does in their A2C implementation. There only the environments are parallelized (through multiprocessing) and tensorflow uses the GPU without any graph parallelization. OpenAI reported that their results were better with synchronous training than with A3C.
edit:
Here are some more details:
The problem with distributed tensorflow for A3C is that you need to call multiple tensorflow forward passes (to get the actions during the n steps) before you call the learning step. However since you learn asynchronously your network will change during the n steps by the other workers. So your policy will change during the n steps and the learning step will happen with wrong weights. Distributed tensorflow will not prevent that. Therefore you need a global and a local network in distributed tensorflow as well, making the implementation not easier than an implementation with threading (and for threading you don't have to learn how to make distributed tensorflow work). Runtime wise, on 8 CPU cores or less there will be no large difference.