I tried to use gams to find flow of material across network of nodes. I defined
set edge(i,n,nn);
positive variable flux(i,n,nn);
y.up(i,n,nn)$( not edge(i,n,nn)) = 0;
My intention is to define 3D matrix of variable for flux of matrial i from node n to nn, then use the set edge which specifies which of complete graph can have mass of flow.
This apparently working but when i tried to save y into gdx file, i have lots of lots of zeros. I only need subset of y where edge(i,n,nn) is true.
How can i subset the y when saving gdx file.
Thanks!
You could store things in a reduced parameter:
Parameter yLevel(i,n,nn);
yLevel(i,n,nn)$edge(i,n,nn) = y.l(i,n,nn);
execute_unload 'result.gdx' yLevel;
Just a note: Do you really need the complete y(i,n,nn)? This could be huge dependent on the size of the indexing sets. Or could you alternatively modify your model to just use y(i,n,nn)$edge(i,n,nn)?
Related
I have been trying to implement this paper . Basically what I want to do is sum the per client loss and compare the same with previous epoch. Then for each constituent layer of the model compare the KL divergence between the weights of the server and the client model to get the layer specific parameter updates and then doing a softmax and to decide whether an adaptive update or a normal FedAvg approach is needed.
The algorithm is as follows-
FedMed
I tried to make use of the code here to build a custom federated avg process. I got the basic understanding that there are some tf.computations and some tff.computations which are involved. I get that I need to make changes in the orchestration logic in the run_one_round function and basically manipulate the client outputs to do adaptive averaging instead of the vanilla federated averaging. The client_update tf.computation function basically returns all the values that I need i.e the weights_delta (can be used for client based model weights), model_output(which can be used to calculate the loss).
But I am not sure where exactly I should make the changes.
#tff.federated_computation(federated_server_state_type,
federated_dataset_type)
def run_one_round(server_state, federated_dataset):
server_message = tff.federated_map(server_message_fn, server_state)
server_message_at_client = tff.federated_broadcast(server_message)
client_outputs = tff.federated_map(
client_update_fn, (federated_dataset, server_message_at_client))
weight_denom = client_outputs.client_weight
# todo
# instead of using tff.federated_mean I wish to do a adaptive aggregation based on the client_outputs.weights_delta and server_state model
round_model_delta = tff.federated_mean(
client_outputs.weights_delta, weight=weight_denom)
#client_outputs.weights_delta has all the client model weights.
#client_outputs.client_weight has the number of examples per client.
#client_outputs.model_output has the output of the model per client example.
I want to make use of the server model weights using server_state object.
I want to calculate the KL divergence between the weights of server model and each client's model per layer. Then use a relative weight to aggregate the client weights instead of vanilla federated averaging.
Instead of using tff.federated_mean I wish to use a different strategy basically an adaptive one based on the algorithm above.
So I needed some suggestions on how to go about implementing this.
Basically what I want to do is :
1)Sum all the values of client losses.
2)Calculate the KL divergence per layerbasis of all the clients with server and then determine whether to use adaptive optimization or FedAvg.
Also is there a way to manipulate this value as a python value which will be helpful for debugging purposes( I tried to use tf.print but that was not helpful either). Thanks!
Simplest option: compute weights for mean on clients
If I read the algorithm above correctly, we need only compute some weights for a mean on-the-fly. tff.federated_mean accepts an optional CLIENTS-placed weight argument, so probably the simplest option here is to compute the desired weights on the clients and pass them in to the mean.
This would look something like (assuming the appropriate definitions of the variables used below, which we will comment on):
#tff.federated_computation(...)
def round_function(...):
...
# We assume there is a tff.Computation training_fn that performs training,
# and we're calling it here on the correct arguments
trained_clients = tff.federated_map(training_fn, clients_placed_arguments)
# Next we assume there is a variable in-scope server_model,
# representing the 'current global model'.
global_model_at_clients = tff.federated_broadcast(server_model)
# Here we assume a function compute_kl_divergence, which takes
# two structures of tensors and computes the KL divergence
# (as a scalar) between them. The two arguments here are clients-placed,
# so the result will be as well.
kl_div_at_clients = tff.federated_map(compute_kl_divergence,
(global_model_at_clients, trained_clients))
# Perhaps we wish to not use raw KL divergence as the weight, but rather
# some function thereof; if so, we map a postprocessing function to
# the computed divergences. The result will still be clients-placed.
mean_weight = tff.federated_map(postprocess_divergence, kl_div_at_clients)
# Now we simply use the computed weights in the mean.
return tff.federated_mean(trained_clients, weight=mean_weight)
More flexible tool: tff.federated_reduce
TFF generally encourages algorithm developers to implement whatever they can 'in the aggregation', and as such exposes some highly customizable primitives like tff.federated_reduce, which allow you to run arbitrary TensorFlow "in the stream" between clients and server. If the above reading of the desired algorithm is incorrect and something more involved is needed, or you wish to flexibly experiment with totally different notions of aggregation (something TFF encourages and is designed to support), this may be the option for you.
In TFF's heuristic typing language, tff.federated_reduce has signature:
<{T}#CLIENTS, U, (<U, T> -> U)> -> U#SERVER
Meaning, federated_reduce take a value of type T placed at the clients, a 'zero' in a reduction algebra of type U, and a function accepting a U and a T and producing a U, and applies this function 'in the stream' on the way between clients and server, producing a U placed at the server. The function (<U, T> -> U) will be applied to the partially accumulated value U, and the 'next' element in the stream T (note however that TFF does not guarantee ordering of these values), returning another partially accumulated value U. The 'zero' should represent whatever 'partially accumulated' means over the empty set in your application; this will be the starting point of the reduction.
Application to this problem
The components
Your reduction function needs access to two pieces of data: the global model state and the result of training on a given client. This maps quite nicely to the type T. In this application, we will have something like:
T = <server_model=server_model_type, trained_model=trained_model_type>
These two types are likely to be the same, but may not necessarily be so.
Your reduction function will accept the partial aggregate, your server model and your client-trained model, returning a new partial aggregate. Here we will start assuming the same reading of the algorithm as above, that of a weighted mean with particular weights. Generally, the easiest way to compute a mean is to keep two accumulators, one for numerator and one for denominator. This will affect the choice of zero and reduction function below.
Your zero should contain a structure of tensors with value 0 mapping to the weights of your model--this will be the numerator. This would be generated for you if you had an aggregation like tff.federated_sum (as TFF knows what the zero should be), but for this case you'll have to get your hands on such a tensor yourself. This shouldn't be too hard with tf.nest.map_structure and tf.zeros_like.
For the denominator, we will assume we just need a scalar. TFF and TF are much more flexible than this--you could keep a per-layer or per-parameter denominator if desired--but for simplicity we will assume that we just want to divide by a single float in the end.
Therefore our type U will be something like:
U = <numerator=server_model_type, denominator=tf.float32>
Finally we come to our reduction function. It will be more or less a different composition of the same pieces above; we will make slightly tighter assumptions about them here (in particular, that all the local functions are tff.tf_computations--a technical assumption, arguably a bug on TFF). Our reduction function will be along the lines (assuming appropriate type aliases):
#tff.tf_computation(U, T)
def reduction(partial_accumulate, next_element):
kl_div = compute_kl_divergence(
next_element.server_model, next_element.trained_model)
weight = postprocess_divergence(kl_div)
new_numerator = partial_accumulate.numerator + weight * next_element.trained_model
new_denominator = partial_accumulate.denominator + weight
return collections.OrderedDict(
numerator=new_numerator, denominator=new_denominator)
Putting them together
The basic outline of a round will be similar to the above; but we have put more computation 'in the stream', and consequently there wil be less on the clients. We assume here the same variable definitions.
#tff.federated_computation(...)
def round_function(...):
...
trained_clients = tff.federated_map(training_fn, clients_placed_arguments)
global_model_at_clients = tff.federated_broadcast(server_model)
# This zip I believe is not necessary, but it helps my mental model.
reduction_arg = tff.federated_zip(
collections.OrderedDict(server_model=global_model_at_clients,
trained_model=trained_clients))
# We assume a zero as specified above
return tff.federated_reduce(reduction_arg,
zero,
reduction)
When initialize SOM with random distribution the network may converge correctly but not, when initialize with the input. Why ?
Poor weight initialization can lead to entanglement in the neurons, and becomes a problem when it comes to topological mapping. The problem is when two neurons that should be far apart have ended up representing the same cluster of input data.
Using your first input as the initialization could be leading to this problem. However, a relatively easy check is to use Sammon Mapping to reduce the dimensions of the clustering nodes into a 2 dimensional representation of the distance between each other. This can be visualized as the nodes with lines connecting adjacent pairs. An unstable learning process can then be discerned from a Sammon map that folds over on itself.
Sammon Map
Sammon Map with folds
This doesn't mean initializing the weights with input data is a bad idea, however I would recommend using random input data as the initialization with the use of something like numpy.random.seed(), as using input data could speed up the learning process.
Is it possible to do batching in tensorflow without expanding the placeholder size by an extra dimension of None? Specifically I'd just like to feed multiple samples via the placeholders through feed_dict. The code base I'm working on would require a large amount of change to the code to account for adding an extra dimension for the batch size.
eg:
sess.run(feed_dict={var1:val1values, var2: val2values, ...})
Where val1values would represent a batch of size X instead of just one training sample.
The shape information including the number of dimensions is available to Python code to do arbitrary things with, and does affect the ops added to the graph (like which matmul kernel is used), so there's no general safe way to automatically add a batch dimension. Something like labeled_tensor may make code slightly less confusing to refactor.
As I read there is to kind of XYZ format:
x y z <--- in one line
and
x y z nx ny nz <--- in one line.
the function CGAL::make_surface_mesh() is extreamly slow if I use just x y z (without normals).
What is the proper way to retrieve normals from PCD-format (PCL-lib) ?
Or how to generate it manually (by my own code)?
There are several methods to estimate normals. One possibility is to insert all the points in a KdTree, then get a certain number of nearest neighbors from each point. Once you get the nearest neighbors, you can either fit a higher-order surface (quadric) to the points and compute its normal, or you can do a principal component analysis of the points and take the eigenvector associated with the smallest eigenvalue. Both methods as well as several refinements are implemented in the Point Cloud Processing package of CGAL:
http://doc.cgal.org/latest/Point_set_processing_3/index.html#Point_set_processing_3NormalEstimation
Depending on your input pointset, different methods / tunings will perform differently (it may require experimentation / parameter tuning).
Note: you may also try the different reconstruction algorithms available there:
http://doc.cgal.org/latest/Surface_reconstruction_points_3/
!I have values in the form of (x,y,z). By creating a list_plot3d plot i can clearly see that they are not quite evenly spaced. They usually form little "blobs" of 3 to 5 points on the xy plane. So for the interpolation and the final "contour" plot to be better, or should i say smoother(?), do i have to create a rectangular grid (like the squares on a chess board) so that the blobs of data are somehow "smoothed"? I understand that this might be trivial to some people but i am trying this for the first time and i am struggling a bit. I have been looking at the scipy packages like scipy.interplate.interp2d but the graphs produced at the end are really bad. Maybe a brief tutorial on 2d interpolation in sagemath for an amateur like me? Some advice? Thank you.
EDIT:
https://docs.google.com/file/d/0Bxv8ab9PeMQVUFhBYWlldU9ib0E/edit?pli=1
This is mostly the kind of graphs it produces along with this message:
Warning: No more knots can be added because the number of B-spline
coefficients
already exceeds the number of data points m. Probably causes:
either
s or m too small. (fp>s)
kx,ky=3,3 nx,ny=17,20 m=200 fp=4696.972223 s=0.000000
To get this graph i just run this command:
f_interpolation = scipy.interpolate.interp2d(*zip(*matrix(C)),kind='cubic')
plot_interpolation = contour_plot(lambda x,y:
f_interpolation(x,y)[0], (22.419,22.439),(37.06,37.08) ,cmap='jet', contours=numpy.arange(0,1400,100), colorbar=True)
plot_all = plot_interpolation
plot_all.show(axes_labels=["m", "m"])
Where matrix(c) can be a huge matrix like 10000 X 3 or even a lot more like 1000000 x 3. The problem of bad graphs persists even with fewer data like the picture i attached now where matrix(C) was only 200 x 3. That's why i begin to think that it could be that apart from a possible glitch with the program my approach to the use of this command might be totally wrong, hence the reason for me to ask for advice about using a grid and not just "throwing" my data into a command.
I've had a similar problem using the scipy.interpolate.interp2d function. My understanding is that the issue arises because the interp1d/interp2d and related functions use an older wrapping of FITPACK for the underlying calculations. I was able to get a problem similar to yours to work using the spline functions, which rely on a newer wrapping of FITPACK. The spline functions can be identified because they seem to all have capital letters in their names here http://docs.scipy.org/doc/scipy/reference/interpolate.html. Within the scipy installation, these newer functions appear to be located in scipy/interpolate/fitpack2.py, while the functions using the older wrappings are in fitpack.py.
For your purposes, RectBivariateSpline is what I believe you want. Here is some sample code for implementing RectBivariateSpline:
import numpy as np
from scipy import interpolate
# Generate unevenly spaced x/y data for axes
npoints = 25
maxaxis = 100
x = (np.random.rand(npoints)*maxaxis) - maxaxis/2.
y = (np.random.rand(npoints)*maxaxis) - maxaxis/2.
xsort = np.sort(x)
ysort = np.sort(y)
# Generate the z-data, which first requires converting
# x/y data into grids
xg, yg = np.meshgrid(xsort,ysort)
z = xg**2 - yg**2
# Generate the interpolated, evenly spaced data
# Note that the min/max of x/y isn't necessarily 0 and 100 since
# randomly chosen points were used. If we want to avoid extrapolation,
# the explicit min/max must be found
interppoints = 100
xinterp = np.linspace(xsort[0],xsort[-1],interppoints)
yinterp = np.linspace(ysort[0],ysort[-1],interppoints)
# Generate the kernel that will be used for interpolation
# Note that the default version uses three coefficients for
# interpolation (i.e. parabolic, a*x**2 + b*x +c). Higher order
# interpolation can be used by setting kx and ky to larger
# integers, i.e. interpolate.RectBivariateSpline(xsort,ysort,z,kx=5,ky=5)
kernel = interpolate.RectBivariateSpline(xsort,ysort,z)
# Now calculate the linear, interpolated data
zinterp = kernel(xinterp, yinterp)