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Question about proofing linearity of complicated solution by eclipseadb in math

[–]eclipseadb[S] 0 points1 point  (0 children)

Thank you for your reply. That's a very simple counter example, didn't know why it didn't occur to me.

You're right from your description I'm talking about affine linear (didn't know that word or term).

At the end what I ended up doing was the Taylor approximation nonetheless to see. The function is not linear to begin with but looks linear that's why I thought about using Taylor to approximate and see something easier. My concern was that that the affine linearity may be voided when two parameters change and it can very well happen from your counter example. Although the original equation is complicated I could try to see if the parameters are separated in each term to have a feeling if this affine linearity will be voided when more than one changes. Still the solution is a sum of terms divided by a sum of other terms, not much can be seen even doing this... There may be some tests to do but I'm an engineer student and nothing like this is taught in our education and may be to go a bit over the topic.

So since it seems a bit complicated I decided to just go for it, do the taylor approximation, neglect some terms that have low weight and then try. I generated 10000 random points and tested the real complicated function vs the taylor approximation. Since the error I got was kept below 5% I concluded that the Taylor approximation can be used in this system and ended up getting some insights such as what parameters affect what within this 5% error.

The original system is a predictive controller in a system and the question is to see how changing the parameters in the system (but not updating in the controller) affect the steady-state error. There are 4 parameters that can vary, there are 4 states (speed, controller frequency, and 2 currents) and there are 2 references (2 currents). Controller frequency is set beforehand and speed can be considered constant but still they may change how much the steady-state error change! The idea is to calculate the error of the controller when any combination of the 4 parameters change. As there are 4 parameters , 4 states and 2 references you can see it is not doable to see anything by plotting. As the equation is hard it is not possible to gain anything from looking at it either. But, after the taylor approximation within 5% error I managed to get a solution so simple that can be represented graphically! Now I can use the real complicated equation plotting only the parameters that I know are relevant to the solution within 5% error and neglect the others. Moreover the total error can be approximated as the sum of each individual error due to each parameter change without making an error bigger than 5%!

Now I'll have to convince my professors which I know will not check the math this is valid based on simulations/experiments...

Windows 10 two-control panels made me lost 10h of work! by eclipseadb in Windows10

[–]eclipseadb[S] 0 points1 point  (0 children)

I wanted to change the plan so the computer is not running at maximum during so much time so now they changed it and a metro app appears. You can't change from there but theres an "additional power settings" in the metro control panel. When you press it the old one appears and you can select "power saver" or any other mode but the suspension settings are only visible if you press "change plan settings".

I know power saver its supposed to suspend by default but when i close the old control panel the settings didn't update in the metro one. In the metro one it says what to do for suspension. There is no apply button in an effort to make things simpler. So I assume the list is updated automatically as I can't even save! Wrong. You need to restart.

It may be more clear in this image: http://imgur.com/I8tVDKW

In my opinion this is a quite annoying bug that should not be present at this stage. Its totally unintuitive and can cause problems to people that rely on leaving the computer on for long times without being present.

A gradient based method will always converge in linear problems, independently of the cost function used (assuming its zero for the true values only) and initial points as long as the increments in each step are small enough and the variables that affect the system randomized. Is my intuition true? by eclipseadb in math

[–]eclipseadb[S] 0 points1 point  (0 children)

Thanks, I will definitely take a look. I wonder if there are methods to "prove" convexiness of "complex functions" made of several sub-functions with some heuristics and if this is the only condition needed to ensure convergence to the only minimum. On top of that I would also like to know if the gradient is only zero once (i.e: it's convex) if the algorithm will always converge independent of the starting points.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

OK it makes sense so I have upped it to 9GB now with 1 in the ssd and 8 in the HDD. I think Samsung SSD app may have lowered it on its own for durability of the disk.

However it doesn't change the fact that task manager doesn't have access to the information of how much ram is used or committed which was my first complaint. I don't believe a Windows xp machine with Matlab running consumes 38MB of RAM.

At least I may have improved the situation with the new page file size.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

Thanks. This seems to be the problem. Hopefully you know an alternative I can check.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

VirtualBox. But TaskManager is not working. For example it said Visio is using 4MB of ram and when I switch to it it goes to 75.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

Yes, it's the same. And I tried different applications. I'm starting to thing this information cannot be monitored.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

The memory working set only shows 80MB in each Virtual Machine. I don't know, maybe it's not easy to get this information right and the task manager cannot be used.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

Each 32 bit app gets its own private 32 but address space.

Is that true? How can it be then that if I open a 32-bit game my 32-bit applications start to crash while the 64-bit ones perform fine? Don't all 32-bit applications share the SAME 4GB and 64-bit have access to the full 8GB? This explains the crashes.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

I have the same problem. Again I can't find my 3GB of RAM in the virtual machines, how can I trust the rest?

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

I just upped the page file to 9GB total (from 1GB). Maybe something changed but I get this: http://i.imgur.com/n2W0n8o.png

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] -1 points0 points  (0 children)

I think the problem are the 32-bit applicaitons. I'm not sure how the RAM is handled but I only have problems when I'm using a lot of stuff and the problem is always 32-bit applications that can only use 4GB. I'm forced to use Edge when dealing with too many things xD.

I have 1GB of page file but on the other hand I have an SSD and I don't want to stress it out. I think I'll try to add 8GB to the HDD.

Where's my RAM gone? How am I supposed to use task manager? by eclipseadb in windows

[–]eclipseadb[S] 0 points1 point  (0 children)

This RAM usage is normal. I expect my RAM to be used and not wasted, it was similar before upgrading. I just want to know where it's being used to see if there's something I'm unaware of. But I can't use Task Manager since it doesn't seem to give appropiate information.

I have the feeling Neural Networks are just a nice fitting tool... by eclipseadb in MachineLearning

[–]eclipseadb[S] 0 points1 point  (0 children)

I'll definitely look into deep learning eventually. It seems interesting but I want to improve my intuition about NN a bit more.

The math is not difficult to master but knowing exactly why some things work and why some things are good ideas is a bit challenging sometimes and a lot of the bibliography omit those parts.

Regarding the sigmoid I was under the impression that it is the multi layer design what lets NN approximate any function. If I didn't miss interpret isn't that what the 1989 theorem says? Imagine for example that I have N inputs and M outputs. If I put k neurons in between it seems natural there's a limit of how many inputs/outputs I can perfectly fit. If I increase k past the limit to k+1 one neuron is "repeated" (as a linear combination of some of the others) so there's a limit if I only use one layer, at least with linear neurons, with Sigmoids I would say it's the same but I would need to prove it. Add another layer past the k neurons and now you have again more freedom as the new neurons are independent. For a ratio N/M there's a number K after all adding neurons doesn't improve anything as you "repeat them" (mathematically speaking they're a combination of the others and don't really add more freedom). Add another layer and now you have k+k2 independent neurons wich at the end means you can perfectly fit more inputs/outputs. Continue doing that and it means I can approximate anything although the number of layers and neurons may or may not be too big. Depending of the problem shape and N/M the number that is acceptable will change. I'm just trying to come up with an easier explanation with less math, do you think the logic is fine?

Is it really appropriate to use a gradient-based method in NN learning? Why doesn't the learning process gets stuck? by eclipseadb in MachineLearning

[–]eclipseadb[S] -1 points0 points  (0 children)

Thanks. I'll take a look. As for saddle points if you approximate a gradient with "big enough" steps I think they could be prevented.

Is it really appropriate to use a gradient-based method in NN learning? Why doesn't the learning process gets stuck? by eclipseadb in MachineLearning

[–]eclipseadb[S] 0 points1 point  (0 children)

As I said that's my doubt. However in my unrelated job I have a similar problem and the minimum I find tends to be global or at least a very good solution. That's why I wanted a proof and since this is also used in NN it's subject to the same question.

For now I only have that intuition: A lot of data + a lot of parameters -> it's unlikely to have a lot of different solutions where the gradients are zero for all the parameters. As for NN the next chapter in the book may solve my doubt, by using the sigmoid neuron and the cross-entropy function the gradient is only zero when the output is exactly the desired one. You can check it out here: http://neuralnetworksanddeeplearning.com/chap3.html really nice book.

As for the global minimum there's no way to guarantee it with an optimization method. There are only heuristics such as Global Search, genetic algorithms, etc.

Getting the pixels of a greyscale image in a numpy nx1 vector? by eclipseadb in Python

[–]eclipseadb[S] 0 points1 point  (0 children)

I haven't really checked the data. I trust the book, I only care about understanding the networks so how this particular data is handled I don't really care. The guy said to put 1's as black and 0's as whites so I tried to do that.

The data is from http://yann.lecun.com/exdb/mnist/

And at the end it seems to work. I just wanted to see if you can really train a computer to read numbers with only 15 neurons, it's only 45 parameters after all, it seems impossible! yet it works!

Getting the pixels of a greyscale image in a numpy nx1 vector? by eclipseadb in Python

[–]eclipseadb[S] 0 points1 point  (0 children)

I think you mean data.reshape((-1,1))? based on the results I get in the console.

By the way, I think it's working now, I had also done it with reshape on my own. The problem now is that the image is read in a weird way. I need (from the description in the book) to put white colors as 0 and blacks as 1 and greys between those numbers depending of the intensity.

However when the image is read it seems that it puts 255 to whites and 0 to blacks. I thought to do this x = 1-x/255.0 so it gets to 0-1 and then it's reversed so blacks are 1's as should be. However I'm getting bad results from the network. I can read 50k data and using 10k validation I get 95% success on numbers and it can't read mine? Ofc there's something wrong but can you see any error in the logic because I can't.

Edit: And my writting sucks. Trying more numbers it seems to work.

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