In neural networks, in general, which model should yield a better and accurate output between both for time series?
As you rightly mentioned, We can use linear regression with time series data as long as:
The inclusion of lagged terms as regressors does not create a collinearity problem.
Both the regressors and the explained variable are stationary.
Your errors are not correlated with each other.
The other linear regression assumptions apply.
No autocorrelation is the single most important assumption in linear regression. If autocorrelation is present the consequences are the following:
Bias: Your “best fit line” will likely be way off because it will be pulled away from the “true line” by the effect of the lagged errors.
Inconsistency: Given the above, your sample estimators are unlikely to converge to the population parameters.
Inefficiency: While it is theoretically possible, your residuals are unlikely to be homoskedastic if they are autocorrelated. Thus, your confidence intervals and your hypothesis tests will be unreliable.
While, The Long Short Term Memory neural network is a type of a Recurrent Neural Network (RNN). RNNs use previous time events to inform the later ones. For example, to classify what kind of event is happening in a movie, the model needs to use information about previous events. RNNs work well if the problem requires only recent information to perform the present task. If the problem requires long term dependencies, RNN would struggle to model it. The LSTM was designed to learn long term dependencies. It remembers the information for long periods.
To focus on the 1st sequence. The model takes the feature of the time bar at index 0 and it tries to predict the target of the time bar at index 1. Then it takes the feature of the time bar at index 1 and it tries to predict the target of the time bar at index 2, etc. The feature of 2nd sequence is shifted by 1 time bar from the feature of 1st sequence, the feature of 3rd sequence is shifted by 1 time bar from 2nd sequence, etc. With this procedure, we get many shorter sequences that are shifted by a single time bar.
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Maybe this is a silly question but I didn't find much about it when I google it.
I have a dataset and I use it for regression but a normal regression with FFNN didn't worked so I thought why not try an LSTM since my data is time dependent I think because it was token from a vehicle while driving so the data is monotonic and maybe I can use LSTM in this Case to do a regression to predict a continuous value (if this doesn't make sense please tell me).
Now the first step is to prepare my data for using LSTM, since I ll predict the future I think my target(Ground truth or labels) should be shifted to the up, am I right?
So if I have a pandas dataframe where each row hold the features and the target(at the end of the row), I assume that the features should stay where they are and the target would be shifted it one step up so that the features in the first row will correspond to the target of the second row (am I wrong).
This way the LSTM will be able to predict the future value from those features.
I didn't find much about this in the internet so please can you provide me how can I do this with some Code?
I also know what I can use pandas.DataFrame.shift to shift a dataset but the last value will hold a NaN I think! how to deal with this? it would be great if you show me some examples or code.
We might need a bit more information regarding the data you are using. Also, I would suggest starting with a more simple recurrent neural network before you start going for LSTMs. The way these networks work is by you feeding the first bit of information, then the next bit of information, then the next bit etc. Let's say that when you feed the first bit of information in, it occurs at time t, then the second bit of information is fed at time t+1 ... etc. up until time t+n.
You can have the neural network output a value at each time step (so a value is outputted at time t, t+1... t+n after each respective input has been fed in). This is a many-to-many network. Or you can have the neural network output a value after all inputs have been provided (i.e. the value is outputted at time t+n). This is called a many-to-one network. What you need is dependednt on your use-case.
For example, say you were recording vehicle behaviour every 100ms and after 10 seconds (i.e. the 100th time step), you wanted to predict the likelihood that the driver was under the influence of alcohol. In this case, you would use a many-to-one network where you put in subsequent vehicle behaviour recordings at subsequent time steps (the first recording at time t, then the next recording at time t+1 etc.) and then the final timestep has the probability value outputted.
If you want a value outputted after every time step, you use a many-to-many design. It's also possible to output a value every k timesteps.
I am modeling a perceptual process in tensorflow. In the setup I am interested in, the modeled agent is playing a resource game: it has to choose 1 out of n resouces, by relying only on the label that a classifier gives to the resource. Each resource is an ordered pair of two reals. The classifier only sees the first real, but payoffs depend on the second. There is a function taking first to second.
Anyway, ideally I'd like to train the classifier in the following way:
In each run, the classifier give labels to n resources.
The agent then gets the payoff of the resource corresponding to the highest label in some predetermined ranking (say, A > B > C > D), and randomly in case of draw.
The loss is taken to be the normalized absolute difference between the payoff thus obtained and the maximum payoff in the set of resources. I.e., (Payoff_max - Payoff) / Payoff_max
For this to work, one needs to run inference n times, once for each resource, before calculating the loss. Is there a way to do this in tensorflow? If I am tackling the problem in the wrong way feel free to say so, too.
I don't have much knowledge in ML aspects of this, but from programming point of view, I can see doing it in two ways. One is by copying your model n times. All the copies can share the same variables. The output of all of these copies would go into some function that determines the the highest label. As long as this function is differentiable, variables are shared, and n is not too large, it should work. You would need to feed all n inputs together. Note that, backprop will run through each copy and update your weights n times. This is generally not a problem, but if it is, I heart about some fancy tricks one can do by using partial_run.
Another way is to use tf.while_loop. It is pretty clever - it stores activations from each run of the loop and can do backprop through them. The only tricky part should be to accumulate the inference results before feeding them to your loss. Take a look at TensorArray for this. This question can be helpful: Using TensorArrays in the context of a while_loop to accumulate values
I am having problem finding a cause for diverging values in all tests of my multilayer neural network for recognizing hand written patterns.
Here is a photo of output:
Each column represents a specific letter. The result should be that first letter would dominate in first row, second letter in second row, ...
In every run of few tests, one letter dominates in all values. What could be a cause for this?
Answer can depend to some degree from kind of neural network model that you use (
Perceptron, backprop, recurrent neural network, LSTM ) but what is easy to notice is data that you feed into your NN. Three inputs that you mentioned are very close to each other. First column has very small difference between each other. They are quite identical: 0.31659 and 0.31660. Second column has the same challenge for NN:0.3993. And third column is also quite similar: 0.2657. For NN it's not easy to build some kind of manifold that separated between those values. You should consider somehow to increase contrast between those three columns because they look pretty similar to each other. NN considers those changes as insignificant and you need many iterations before you'll be able to build hyperplane which correctly classifies your letters.
I have a question about a reason why setting TensorFlow's variable with small stddev.
I guess many people do test MNIST test code from TensorFlow beginner's guide.
As following it, the first layer's weights are initiated by using truncated_normal with stddev 0.1.
And I guessed if setting it with more bigger value, then it would be the same result, which is exactly accurate.
But although increasing epoch count, it doesn't work.
Is there anybody know this reason?
original :
W_layer = tf.Variable(tf.truncated_normal([inp.get_shape()[1].value, size],stddev=0.1), name='w_'+name)
#result : (990, 0.93000001, 0.89719999)
modified :
W_layer = tf.Variable(tf.truncated_normal([inp.get_shape()[1].value, size],stddev=200), name='w_'+name)
#result : (99990, 0.1, 0.098000005)
The reason is because you want to keep all the layer's variances (or standard deviations) approximately the same, and sane. It has to do with the error backpropagation step of the learning process and the activation functions used.
In order to learn the network's weights, the backpropagation step requires knowledge of the network's gradient, a measure of how strong each weight influences the input to reach the final output; layer's weight variance directly influences the propagation of gradients.
Say, for example, that the activation function is sigmoidal (e.g. tf.nn.sigmoid or tf.nn.tanh); this implies that all input values are squashed into a fixed output value range. For the sigmoid, it is the range 0..1, where essentially all values z greater or smaller than +/- 4 are very close to one (for z > 4) or zero (for z < -4) and only values within that range tend to have some meaningful "change".
Now the difference between the values sigmoid(5) and sigmoid(1000) is barely noticeable. Because of that, all very large or very small values will optimize very slowly, since their influence on the result y = sigmoid(W*x+b) is extremely small. Now the pre-activation value z = W*x+b (where x is the input) depends on the actual input x and the current weights W. If either of them is large, e.g. by initializing the weights with a high variance (i.e. standard deviation), the result will necessarily be (relatively) large, leading to said problem. This is also the reason why truncated_normal is used rather than a correct normal distribution: The latter only guarantees that most of the values are very close to the mean, with some less than 5% chance that this is not the case, while truncated_normal simply clips away every value that is too big or too small, guaranteeing that all weights are in the same range, while still being normally distributed.
To make matters worse, in a typical neural network - especially in deep learning - each network layer is followed by one or many others. If in each layer the output value range is big, the gradients will get bigger and bigger as well; this is known as the exploding gradients problem (a variation of the vanishing gradients, where gradients are getting smaller).
The reason that this is a problem is because learning starts at the very last layer and each weight is adjusted depending on how much it contributed to the error. If the gradients are indeed getting very big towards the end, the very last layer is the first one to pay a high toll for this: Its weights get adjusted very strongly - likely overcorrecting the actual problem - and then only the "remaining" error gets propagated further back, or up, the network. Here, since the last layer was already "fixed a lot" regarding the measured error, only smaller adjustments will be made. This may lead to the problem that the first layers are corrected only by a tiny bit or not at all, effectively preventing all learning there. The same basically happens if the learning rate is too big.
Finding the best weight initialization is a topic by itself and there are somewhat more sophisticated methods such as Xavier initialization or Layer-sequential unit variance, however small normally distributed values are usually simply a good guess.
I'm developing machine learning algorithms which classify images based on training data.
During the image preprocessing stages, there are several parameters which I can modify that affect the data I feed my algorithms (for example, I can change the Hessian Threshold when extracting SURF features). So the flow thus far looks like:
[param1, param2, param3...] => [black box] => accuracy %
My problem is: with so many parameters at my disposal, how can I systematically pick values which give me optimized results/accuracy? A naive approach is to run i nested for-loops (assuming i parameters) and just iterate through all parameter combinations, but if it takes 5 minute to calculate an accuracy from my "black box" system this would take a long, long time.
This being said, are there any algorithms or techniques which can search for optimal parameters in a black box system? I was thinking of taking a course in Discrete Optimization but I'm not sure if that would be the best use of my time.
Thank you for your time and help!
Edit (to answer comments):
I have 5-8 parameters. Each parameter has its own range. One parameter can be 0-1000 (integer), while another can be 0 to 1 (real number). Nothing is stopping me from multithreading the black box evaluation.
Also, there are some parts of the black box that have some randomness to them. For example, one stage is using k-means clustering. Each black box evaluation, the cluster centers may change. I run k-means several times to (hopefully) avoid local optima. In addition, I evaluate the black box multiple times and find the median accuracy in order to further mitigate randomness and outliers.
As a partial solution, a grid search of moderate resolution and range can be recursively repeated in the areas where the n-parameters result in the optimal values.
Each n-dimensioned result from each step would be used as a starting point for the next iteration.
The key is that for each iteration the resolution in absolute terms is kept constant (i.e. keep the iteration period constant) but the range decreased so as to reduce the pitch/granular step size.
I'd call it a ‘contracting mesh’ :)
Keep in mind that while it avoids full brute-force complexity it only reaches exhaustive resolution in the final iteration (this is what defines the final iteration).
Also that the outlined process is only exhaustive on a subset of the points that may or may not include the global minimum - i.e. it could result in a local minima.
(You can always chase your tail though by offsetting the initial grid by some sub-initial-resolution amount and compare results...)
Have fun!
Here is the solution to your problem.
A method behind it is described in this paper.