I'm trying to uncover the transition parameters of data of a hidden Markov Model using MATLAB. Using the built in hmmtrain function, I can estimate the parameters quite well (I already know what they are supposed to be as it's simulated data for now), but they are always off by a little. So what I want to do is construct a confidence interval for these parameters.
Now, I've searched the web for this quite a bit and it seems as if this is not easy to do. The 'easiest' solution appears to be bootstrapping, but I personally don't know how to go about and implement something like that in MATLAB, for a model as complex as a HMM. Does anyone have any references I could look at that could help me write a script for this, or does anyone know of a package out there that already has this built in?
Edit:
The main issue I have is that I wouldn't know how a bootstrap method would tackle the problem of HMM. Isn't the whole idea of HMM that you get a specific sequence from which you learn about the parameters? Wouldn't cutting it up for the purpose of bootstrapping automatically create some errors?
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we want to publish an Open-Source for integrating Reinforcement Learning to Smartgrid optimization.
We use OpenModelica as GUI, PyFMI for the import to Python and Gym.
Nearly everything is running, but a possibility to connect or disconnect additional loads during the simulation is missing. Everything we can do for now is a variation of the parameters of existing loads, which gives some flexibility, but way less then the possibility to switch loads on and off.
Using the implemented switches in OpenModelica is not really an option. They just place a resistor at this spot, giving it either a very low or very high resistance. First, its not really decoupled, and second, high resistances make the ODE-system stiff, which makes it really hard (and costly) to solve it. In tests our LSODA solver (in stiff cases basically a BDF) ran often in numerical errors, regardless of how the jacobian was calculated (analytically by directional derivatives or with finite differences).
Has anyone an idea how we can implement a real "switching effect"?
Best regards,
Henrik
Ideal connection and disconnection of components during simulation
requires structure variability, which is not fully supported
by Modelica (yet). See also this answer https://stackoverflow.com/a/30487641/8725275
One solution for this problem is to translate all possible
model structures in advance and switch the simulation model if certain conditions are met. As there is some overhead involved, this approach only makes sense, when the model is not switched very often.
There is a python framework, which was built to support this process: DySMo. The tool was written by Alexandra Mehlhase, who made a lot of interesting publications regarding structure variability, e.g. An example of beneficial use of
variable-structure modeling to enhance an existing rocket model.
The paper Simulating a Variable-structure Model of an Electric Vehicle for Battery Life Estimation Using Modelica/Dymola and Python of Moritz Stueber is also worth a look. It contains a nice introduction about variable structure systems and available solutions.
Hello guys I'd like to know the answer to the question that is the titled named by.
For example if I have physical system described in differential equation(s), how should I know when I should use step, pulse or ramp generator?
What exactly does it do?
Thank you for your answers.
They are mostly the remnants of the classical control times. The main reason why they are so famous is because of their simple Laplace transform terms. 1,1/s and 1/s^2. Then you can multiply these with the plant and you would get the Laplace transform of the output.
Back in the day, what you only had was partial fraction expansion and Laplace transform tables to get an idea what the response would look like. And today, you can basically simulate whatever input you like. So they are not really neeeded which is the answer to your question.
But since people used these signals so often they have spotted certain properties. For example, step response is good for assessing the transients and the steady state tracking error value, ramp response is good for assessing (reference) following error (which introduces double integrators) and so on. Hence, some consider these signals as the characteristic functions though it is far from the truth. Especially, you should keep in mind that, just because the these responses are OK, the system is not necessarily stable.
However, keep in mind that these are extremely primitive ways of assessing the system. Currently, they are taught because they are good for giving homeworks and making people acquainted with Simulink etc.
They are used to determine system characteristics. If you are studying a system of differential equations you would want to know different characteristics from the response of the system from these kinds of inputs since these inputs are the very fundamental ones. For example a system whose output blows up for a pulse input is unstable, and you would not want to have such a system in real life(except in rare situations). It's too difficult for me to explain it all in an answer, you should start with this wiki page.
I am currently running a multiple linear regression using MATLAB's LinearModel.fit function, and I am bit confused in regards to how to properly add interaction terms to the model by hand. As I am aware, LinearModel.fit does not standardize variables on its own, so I have been doing so manually.
So far, the way I have done it has been to
Standardize the observations for each variables
Multiply corresponding standardized values from specific variables to create the interaction terms and then add these new variables to the set of regression data
Run the regression
Is this the correct way to go about doing this? Should I standardize the interaction term variables also after calculating the 'raw' terms? Any help would be greatly appreciated!
Whether or not to standardize interaction terms probably depends on what you intend to do with the model. Standardization typically does not affect model performance as much as it allows for more straightforward model interpretation as your learned coefficients will be on similar scales. I suspect whether to do this or not is largely a matter of opinion. Here is a relevant stats.stackexchange post that may help.
My intuition would be the same as how you have described your process so far.
I'm working on a feed-forward backpropagation network in C++ but cannot seem to make it work properly. The network I'm basing mine on is using the cross-entropy error function. However, I'm not very familiar with it and even though I'm trying to look it up I'm still not sure. Sometimes it seems easy, sometimes difficult. The network will solve a multinomial classification problem and as far as I understand, the cross-entropy error function is suitable for these cases.
Someone that knows how it works?
Ah yes, good 'ole backpropagation. The joy of it is that it doesn't really matter (implementation wise) what error function you use, so long as it differentiable. Once you know how to calculate the cross entropy for each output unit (see the wiki article), you simply take the partial derivative of that function to find the weights for the hidden layer, and once again for the input layer.
However, if your question isn't about implementation, but rather about training difficulties, then you have your work cut out for you. Different error functions are good at different things (best to just reason it out based on the error function's definition) and this problem is compounded by other parameters like learning rates.
Hope that helps, let me know if you need any other info; your question was a lil vague...
I'm quite new with this topic so any help would be great. What I need is to optimize a neural network in MATLAB by using GA. My network has [2x98] input and [1x98] target, I've tried consulting MATLAB help but I'm still kind of clueless about what to do :( so, any help would be appreciated. Thanks in advance.
Edit: I guess I didn't say what is there to be optimized as Dan said in the 1st answer. I guess most important thing is number of hidden neurons. And maybe number of hidden layers and training parameters like number of epochs or so. Sorry for not providing enough info, I'm still learning about this.
If this is a homework assignment, do whatever you were taught in class.
Otherwise, ditch the MLP entirely. Support vector regression ( http://www.csie.ntu.edu.tw/~cjlin/libsvm/ ) is much more reliably trainable across a broad swath of problems, and pretty much never runs into the stuck-in-a-local-minima problem often hit with back-propagation trained MLP which forces you to solve a network topography optimization problem just to find a network which will actually train.
well, you need to be more specific about what you are trying to optimize. Is it the size of the hidden layer? Do you have a hidden layer? Is it parameter optimization (learning rate, kernel parameters)?
I assume you have a set of parameters (# of hidden layers, # of neurons per layer...) that needs to be tuned, instead of brute-force searching all combinations to pick a good one, GA can help you "jump" from this combination to another one. So, you can "explore" the search space for potential candidates.
GA can help in selecting "helpful" features. Some features might appear redundant and you want to prune them. However, say, data has too many features to search for the best set of features by some approaches such as forward selection. Again, GA can "jump" from this set candidate to another one.
You will need to find away to encode the data (input parameters, features...) fed to GA. For finding a set of input paras or a good set of features, I think binary encoding should work. In addition, choosing operators for GA to reproduce offsprings is also important. Yet GA needs to be tuned, too (early stopping which can also be applied to ANN).
Here are just some ideas. You might want to search for more info about GA, feature selection, ANN pruning...
Since you're using MATLAB already I suggest you look into the Genetic Algorithms solver (known as GATool, part of the Global Optimization Toolbox) and the Neural Network Toolbox. Between those two you should be able to save quite a bit of figuring out.
You'll basically have to do 2 main tasks:
Come up with a representation (or encoding) for your candidate solutions
Code your fitness function (which basically tests candidate solutions) and pass it as a parameter to the GA solver.
If you need help in terms of coming up with a fitness function, or encoding of candidate solutions then you'll have to be more specific.
Hope it helps.
Matlab has a simple but great explanation for this problem here. It explains both the ANN and GA part.
For more info on using ANN in command line see this.
There is also plenty of litterature on the subject if you google it. It is however not related to MATLAB, but simply the results and the method.
Look up Matthew Settles on Google Scholar. He did some work in this area at the University of Idaho in the last 5-6 years. He should have citations relevant to your work.