GPy | Gaussian processes framework in python

This should be reasonably straightforward, though requires building a custom kernel. Basically, you need a kernel that can know for each input what the linear operator for the corresponding output is (whether this is a function observation/identity operator, integral observation, derivative observation, etc). You can achieve this by including an extra column in your input matrix X, similar to how it's done for the gpflow.kernels.Coregion kernel (see this notebook). You would need to then need to define a new kernel with K and K_diag methods that for each linear operator type find the corresponding rows in the input matrix, and pass it to the appropriate covariance function (using tf.dynamic_partition and tf.dynamic_stitch, this is used in a very similar way in GPflow's SwitchedLikelihood class).

The full implementation would probably take half a day or so, which is beyond what I can do here, but I hope this is a useful starting pointer, and you're very welcome to join the GPflow slack (invite link in the GPflow README) and discuss it in more detail there!

The module pickle is your friend here!

My walkaround to this problema is detailed in the update 2, but it's basically what I explained here: I’ve seen in this link (Error: C:\Program Files (x86)\Microsoft Visual Studio\2017\BuildTools\MSBuild\15.0\Bin\MSBuild.exe failed with exit code: 1) that some people tried a downgrade in the node version, I was using originally the version 12 and some say that with version 10 should work. After that I can perform the four steps provided in the answer:

You already have an omp parallel for pragma on the innermost loop. To give that effect, you probably need to enable OpenMP support in your compiler by setting a compiler flag (for example, with the GCC compiler suite, that would be the -fopenmp flag). You may also need to #include the omp.h header.

But with that said, I doubt you're going to gain much from this parallelization, because one run of the loop you are parallelizing just doesn't do much work. There is runtime overhead associated with parallelization that offsets the gains from running multiple loop iterations at the same time, so I don't think you're going to net very much.

There is no real answer to this question, but I'd like to distill some of the more important optimizations discussed in the comments. Let's focus on just the inner loops.

Primarily, you need to avoid excessive multiplications and function calls. And there are some tricks that aren't guaranteed to be optimized by compilers. For example, we know intuitively that pow(x, 2) just squares a value, but if your compiler doesn't optimize this, then it's much less efficient than simply x * x.

Further, it was identified that the O(N²) loop actually can be reduced to O(N²/2) because distances are symmetric. This is a big deal, if you're calling expensive things like pow and sqrt. You can just scale the final result of E1 by 2 to compensate for halving the number of calculations.

And on the subject of sqrt, it was also identified that you don't need to do that before your distance test. Do it after, because the test sqrt(d) < 5 is the same as d < 25.

Let's go even further, beyond the comments. Notice that the < 5 test actually relies on a multiplication involving kes. If you precomputed a distance-squared value that also incorporates the kes scaling, then you have even fewer multiplications.

You can also remove the kk value from the E1 calculation. That doesn't need to happen in a loop... probably. By that, I mean you're likely to have floating point error in all these calculations. So every time you change something, your final result might be slightly different. I'm gonna do it anyway.

So... After that introduction, let's go!

GPflow uses a single tf.Variable for each parameter - such as a kernel's lengthscales - and TensorFlow only allows you to change the trainable status of a Variable as a whole. Having a separate parameter per dimension would not be easy to implement for arbitrary dimensions, but you can easily subclass the kernel you want and override lengthscales with a property as follows:

I actually found a solution for this issue. Since the bugged version of pip gets installed as soon as your create the virtualenv, I forcibly uninstalled it and then installed the version that worked when I built my app. Here is the code that I used:

you have defined the kernel with X of dimention (-1, 4) and Y of dimension (-1, 1) but you are giving it X_pred of dimension (1, 1) (the first element of x_pred reshaped to (1, 1))

give the x_pred to the model for prediction (an input with dimension of (-1, 4))

I have ESP32 so my config sample will be ESP32 based. Download https://github.com/lixas/ESP32-Stubs-VSCode

OR

Use following to generate for your board: https://github.com/Josverl/micropython-stubber and download those files from board

My settings.json file: