I am reading through a Kalman filter techniques and thinking about how to use them but I am not sure if I understand the whole process in using the measured data in Kalman data-step.
Lets assume that you have accelerometer and you want to estimate speed. You create a Kalman filter with acceleration, velocity and bias states, and time-step and data-step with their equations. You know the accelerometer's and bias noise variances.
Now, the Kalman filter assumes by definition that the measurement noise is white which is flawed because most of the time it is colored in some way. My questions:
If you use low pass filter to get rid of most of the high frequency noise, the noise won't be white so that is not going to work neither, right?
Is the data preprocessing worth focusing on?
Do you know any techniques/books/articles to fix that? What information do you need about the problem to decide which actions to take?
Are there any data rejection algorithms that are used?
I read a little about that you can use Kalman as whitening filter too but I am not sure how to incorporate that into Kalman I described above.
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Call for experts in deep learning.
Hey, I am recently working on training images using tensorflow in python for tone mapping. To get the better result, I focused on using perceptual loss introduced from this paper by Justin Johnson.
In my implementation, I made the use of all 3 parts of loss: a feature loss that extracted from vgg16; a L2 pixel-level loss from the transferred image and the ground true image; and the total variation loss. I summed them up as the loss for back propagation.
From the function
yˆ=argminλcloss_content(y,yc)+λsloss_style(y,ys)+λTVloss_TV(y)
in the paper, we can see that there are 3 weights of the losses, the λ's, to balance them. The value of three λs are probably fixed throughout the training.
My question is that does it make sense if I dynamically change the λ's in every epoch(or several epochs) to adjust the importance of these losses?
For instance, the perceptual loss converges drastically in the first several epochs yet the pixel-level l2 loss converges fairly slow. So maybe the weight λs should be higher for the content loss, let's say 0.9, but lower for others. As the time passes, the pixel-level loss will be increasingly important to smooth up the image and to minimize the artifacts. So it might be better to adjust it higher a bit. Just like changing the learning rate according to the different epochs.
The postdoc supervises me straightly opposes my idea. He thought it is dynamically changing the training model and could cause the inconsistency of the training.
So, pro and cons, I need some ideas...
Thanks!
It's hard to answer this without knowing more about the data you're using, but in short, dynamic loss should not really have that much effect and may have opposite effect altogether.
If you are using Keras, you could simply run a hyperparameter tuner similar to the following in order to see if there is any effect (change the loss accordingly):
https://towardsdatascience.com/hyperparameter-optimization-with-keras-b82e6364ca53
I've only done this on smaller models (way too time consuming) but in essence, it's best to keep it constant and also avoid angering off your supervisor too :D
If you are running a different ML or DL library, there are optimizer for each, just Google them. It may be best to run these on a cluster and overnight, but they usually give you a good enough optimized version of your model.
Hope that helps and good luck!
In the literature I have come across two ways how to verify performance of a Kalman filter.
(a) During the run of Kalman filter you keep information about innovation
in every step , where is the observed output of the system and is the predicted output in the same step. Then you take the autocovariance of the innovation and according to whether the function exceeds or doesn't exceeed certain bounds, you can conclude something about the performance of your Kalman Filter.
But that's where the explanation ends. How do I decide what bounds it shouldn't exceed and what does it say about the Kalman filter design?
(b) Aside of innovation you also keep track of innovation covariance matrix and in each step you compute trust region . And again, there is supposed to be a bound over which the function shouldn't grow. But this is where the explanation ends and I'm left without the knowledge of how to determine the bound and what does it say about my Kalman filter.
I have a dataset of around 6K chemical formulas which I am preprocessing via Keras' tokenization to perform binary classification. I am currently using a 1D convolutional neural network with dropouts and am obtaining an accuracy of 82% and validation accuracy of 80% after only two epochs. No matter what I try, the model just plateaus there and doesn't seem to be improving at all. Those same exact accuracies are reached with a vanilla LSTM too. What else can I try to improve my accuracies? Losses only have a difference of 0.04... Anyone have any ideas? Both models use an embedding layer and changing the output dimension isn't having an effect either.
According to your answer, I believe your model has a high bias and low variance (see this link for further details). Thus, your model is not fitting your data very well and it is causing underfitting. So, I suggest you 3 things:
Train your model a little longer: I believe two epoch are too few to give a chance to your model understand the patterns in the data. Try to minimize learning rate and increase the number of epochs.
Try a different architecture: you may change the amount of convolutions, filters and layers, You can also use different activation functions and other layers like max pooling.
Make an error analysis: once you finished your training, apply your model to test set and take a look into the errors. How much false positives and false negatives do you have? Is your model better to classify one class than the other? You can see a pattern in the errors that may be related to your data?
Finally, if none of these suggestions helped you, you may also try to increase the number of features, if possible.
I've been thinking that adding noise to an image can prevent overfitting and also "increase" the dataset by adding variations to it. I'm only trying to add some random 1s to images that has shape (256,256,3) which uses uint8 to represent its color. I don't think that can affect the visualization at all (I showed both images with matplotlib and they seems almost the same) and has only ~0.01 mean difference in the sum of their values.
But it doesn't look to have its advances. After training for a long time it's still not as good as the one doesn't use noises.
Has anyone tried to use noise for image classification tasks like this? Is it eventually better?
I wouldn't go to add noise to your data. Some papers employ input deformations during training to increase robutness and convergence speed of models. However, these deformations are statistically inefficient (not just on image but any kind of data).
You can read Intriguing properties of Neural Networks from Szegedy et al. for more details (and refer to references 9 & 13 for papers that uses deformations).
If you want to avoid overfitting, you might be interested to read about regularization instead.
Yes you may add noise to extend your dataset and avoid overfitting your training set but make sure it is random otherwise your network will take this noise as something it should learn (and that's not something you want). I wouldn't use this method first to do that, I would first rotate and/or flip my samples.
However, your network should perform better or, at least, as well as your previous network.
First thing I would check is : How do you measure your performances ? What were your performances before and after ? And did you change anything else ?
There are a couple of works that deal with this problem. Because you make the training set harder the training error will be lower, however your generalization might be better. It has been shown that adding noise can have stability effects for training Generative Adversarial Networks (Adversarial Training).
For classification tasks it is not that cut and dry. Not many works have actually dealt with this topic. The closest one is to my best knowledge is this one from google (https://arxiv.org/pdf/1412.6572.pdf), where they show the limitation of using training without noise. They do report a regularization effect, but not actual better results than using other methods.
I am working on a car following problem and the measurements I am receiving are uncertain ( I know that the noise model is gaussian and it's variance is also known). How do I select my next action in such kind of uncertainty?
Basically how should I change my cost function so that I can optimize my plan by selecting appropriate action?
Vanilla reinforcement learning is meant for Markov decision processes, where it's assumed that you can fully observe the state. Because your states are noisy, you have a Partially observable Markov decision process. Theoretically speaking you should be looking at a different category of RL approaches.
Practically, since you have so much information about the parameters of the uncertainty, you should consider using a Kalman or particle filter to perform state estimation. Then, use the most likely state estimate as the true state in your RL problem. The estimate will be wrong at times, of course, but if you're using a function approximation approach for the value function, the experience can generalize across similar states and you'll be able to learn. The learning performance is going to be proportional to the quality of your state estimate.