I'm trying to predict sequences of 2D coordinates. But I don't want only the most probable future path but all the most probable paths to visualize it in a grid map.
For this I have traning data consisting of 40000 sequences. Each sequence consists of 10 2D coordinate pairs as input and 6 2D coordinate pairs as labels.
All the coordinates are in a fixed value range.
What would be my first step to predict all the probable paths? To get all probable paths I have to apply a softmax in the end, where each cell in the grid is one class right? But how to process the data to reflect this grid like structure? Any ideas?
A softmax activation won't do the trick I'm afraid; if you have an infinite number of combinations, or even a finite number of combinations that do not already appear in your data, there is no way to turn this into a multi-class classification problem (or if you do, you'll have loss of generality).
The only way forward I can think of is a recurrent model employing variational encoding. To begin with, you have a lot of annotated data, which is good news; a recurrent network fed with a sequence X (10,2,) will definitely be able to predict a sequence Y (6,2,). But since you want not just one but rather all probable sequences, this won't suffice. Your implicit assumption here is that there is some probability space hidden behind your sequences, which affects how they play out over time; so to model the sequences properly, you need to model that latent probability space. A Variational Auto-Encoder (VAE) does just that; it learns the latent space, so that during inference the output prediction depends on sampling over that latent space. Multiple predictions over the same input can then result in different outputs, meaning that you can finally sample your predictions to empirically approximate the distribution of potential outputs.
Unfortunately, VAEs can't really be explained within a single paragraph over stackoverflow, and even if they could I wouldn't be the most qualified person to attempt it. Try searching the web for LSTM-VAE and arm yourself with patience; you'll probably need to do some studying but it's definitely worth it. It might also be a good idea to look into Pyro or Edward, which are probabilistic network libraries for python, better suited to the task at hand than Keras.
Related
I have a 2 layered Neural Network that I'm training on about 10000 features (genomic data) with about 100 samples in my data set. Now I realized that anytime I run my model (i.e. compile & fit) I get varying validation/testing accuracys even if I leave the train/test/validation split untouched. Sometimes its around 70% sometimes around 90%.
Due to the stochastic nature of the NN I anticipate some variation but could these strong fluctuations be a sign of something else?
The reason why you're seeing such a big instability with your validation accuracy is because your neural network is huge in comparison to the data you train it on.
Even with just 12 neurons per layer, you still have 12 * 10000 + 12 = 120012 parameters in your first layer. Now think about what the neural network does under the hood. It takes your 10000 inputs, it multiplies each input by some weight and then sums all these inputs. Now you provide it only 64 training examples on which the training algorithm is supposed to decide what are the correct input weights. Just based on intuition, from a purely combinatorial perspective there is going to be large amount of weight assignments that do well on your 64 training samples. And you have no guarantee that the training algorithm will pick such weight assignment that will also do well on your out-of-sample data.
Given neural network is able to represent a wide variety of functions (it's been proven that under certain assumptions it can approximate any function, that's called general approximation). To select the function you want you provide the training algorithm with data to constrain the space of all possible functions the network can represent to a subspace of functions that fit your data. However, such function is in no way guaranteed to represent the true underlying relationship between the input and the output. And especially if the number of parameters is larger than the number of samples (in this case by a few orders of magnitude), you're nearly guaranteed to see your network simply memorize the samples in your training data, simply because it has the capacity to do so and you haven't constrained it enough.
In other words, what you're seeing is overfitting. In NNs, the general rule of thumb is that you want at least a couple of times more samples than you have parameters (look in to the Hoeffding Inequality for theoretical rationale of this) and in effect the more samples you have, the less you're afraid of overfitting.
So here is a couple of possible solutions:
Use an algorithm that's more suitable for the case where you have high input dimension and low sample count, such as Kernel SVM (Support Vector Machine). With such a low sample count, it's quite possible that a Kernel SVM algorithm will achieve better and more consistent validation accuracy. (You can easily test this, they are available in the scikit-learn package, really easy to use)
If you insist on using NN - use regularization. Given the fact you already have working code, this will be easy, just add kernel_regularizer to all your layers, I would try both L1 and L2 regularization (probably separately). L1 regularization tends to push weights to zero so it might help reduce the number of parameters in your problem. L2 just tries to make all the weights small. Use your validation set to decide the best value for each regularization. You can optimize both for the best mean accuracy and also the lowest variance in accuracy on your validation data (do something like 20 training runs for each parameter value of L1 and L2 regularization, usually just trying different orders of magnitude is sufficient, e.g. 1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1).
If most of your input features are not really predictive or if they are highly correlated, PCA (Principal Component Analysis) can be used to project your inputs into a much lower dimensional space (e.g. from 10000 to 20), where you'd have much smaller neural network (still I'd use L1 or L2 for regularization because even then you'd have more weights than training samples)
On a final note, the point of a testing set is to use it very sparsely (ideally only once). It should be the final reported metric after all your research and model tuning is done. You should not optimize any values on it. You should do all this on your validation set. To avoid overfitting on your validation set, look into k-fold cross validation.
I'm currently facing a Machine Learning problem and I've reached a point where I need some help to proceed.
I have various time series of positional (x, y, z) data tracked by sensors. I've developed some more features. For example, I rasterized the whole 3D space and calculated a cell_x, cell_y and cell_z for every time step. The time series itself have variable lengths.
My goal is to build a model which classifies every time step with the labels 0 or 1 (binary classification based on past and future values). Therefore I have a lot of training time series where the labels are already set.
One thing which could be very problematic is that there are very few 1's labels in the data (for example only 3 of 800 samples are labeled with 1).
It would be great if someone can help me in the right direction because there are too many possible problems:
Wrong hyperparameters
Incorrect model
Too few 1's labels, but I think that's not a big problem because I only need the model to suggests the right time steps. So I would only use the peaks of the output.
Bad or too less training data
Bad features
I appreciate any help and tips.
Your model seems very strange. Why only use 2 units in lstm layer? Also your problem is a binary classification. In this case you should choose only one neuron in your output layer (try to insert one additional dense layer between and lstm layer and try dropout layers between them).
Binary crossentropy does not make much sense with 2 output neurons, if you don't have a multi label problem. But if you're switching to one output neuron it's the right one. You also need sigmoid then as activation function.
As last advice: Try class weights.
http://scikit-learn.org/stable/modules/generated/sklearn.utils.class_weight.compute_class_weight.html
This can make a huge difference, if you're label are unbalanced.
You can create the model using tensorflow BasicLSTMCell, the shape of your data fits for BasicLSTMCell in TensorFlow you can find Documentation for BasicLSTMCell here and for creating the model this Documentation contain code that will help to build BasicLstmCell model . Hope this will help you, Cheers.
I have a multilayer perceptron with 5 hidden layers and 256 neurons each. When I start training, I get different prediction probabilities for each train sample until epoch 50, but then the number of duplicate predictions increases, on epoch 300 I already have 30% of duplicate predictions which does not make sense since the input data is different for all training samples. Any idea what causes this behavior?
Clarifications:
with "duplicate predictions", I mean items with the exactly same predicted probability to belong to class A (it's a binary classification problem)
I have 4000 training samples with 200 features each and all samples are different, it does not make sense that the number of duplicate predictions increases to 30% while training. So I wonder what can cause this behavior.
One point, you say you are doing a binary prediction, and when you say "duplicate predictions", even with your clarification it's hard to understand your meaning. I am guessing that you have two outputs for your binary classifier, one for class A and one for class B and you are getting roughly the same value for a given sample. If that's the case, then the first thing to do is to use 1 output. A binary classification problem is better modeled with 1 output that ranges between 0 and 1 (sigmoid the output neuron). This way there will be no ambiguity, the network will have to choose one or the other, or when it's confused you'll get ~0.5 and it will be clear.
Second, it is very common for a network to start learning well and then to perform more poorly after overtraining. Especially with small datasets such as what you have. In fact, even with the little knowledge I have of your dataset I would put a small bet on you getting better performance out of an algorithm like XGA Boost than a neural network (I assume you're using a neural net and not literally a perceptron).
But regarding the performance degrading over time. When this happens you want to look into something called "early stopping". At some point the network will start memorizing the input, and may be part of what's happening. Essentially you train until the performance on your held out test data starts to worsen.
To address this you can apply various forms of regularization (L2 regularization, dropout, batch normalization all come to mind). You can also reduce the size of your network. 5 layers of 256 neurons sounds too big for the problem. Try trimming this down and I bet your results will improve. There is a sweet spot for architecture size in neural networks. When your network is too large it can, and often will, over fit. When it's too small it won't be expressive enough for the data. Angrew Ng's coursera class has some helpful practical advice on dealing with this.
When one passes to tf.train.batch, it looks like the shape of the element has to be strictly defined, else it would complain that All shapes must be fully defined if there exist Tensors with shape Dimension(None). How, then, does one train on images of different sizes?
You could set dynamic_pad=True in the argument of tf.train.batch.
dynamic_pad: Boolean. Allow variable dimensions in input shapes. The given dimensions are padded upon dequeue so that tensors within a batch have the same shapes.
Usually, images are resized to a certain number of pixels.
Depending on your task you might be able to use other techniques in order to process images of varying sizes. For example, for face recognition and OCR, a fix sized window is used, that is then moved over the image. On other tasks, convolutional neural networks with pooling layers or recurrent neural networks can be helpful.
I see that this is quite old question, but in case someone will be searching how variable-size images can be still used in batches, I can tell what I did for Image-to-Image convolutional network (inference), which was trained for variable image size and batch 1. Why: when I tried to process images in batches using padding, the results become much worse, because signal was "spreading" inside of the network and started to influence its convolution pyramids.
So what I did is possible when you have source code and can load weights manually into convolutional layers. I modified the network in the following way: along with a batch of zero-padded images, I added additional placeholder which received a batch of binary masks with 1 where actual data was on the patch, and 0 where padding was applied. Then I multiplied signal by these masks after each convolutional layer inside the network, fighting "spreading". Multiplication isn't expensive operation, so it did not affect performance much.
The result was not deformed already, but still had some border artifacts, so I modified this approach further by adding small (2px) symmetric padding around input images (kernel size of all the layers of my CNN was 3), and kept it during propagation by using slightly bigger (+[2px,2px]) mask.
One can apply the same approach for training as well. Then some sort of "masked" loss is needed, where only the ROI on each patch is used to calculate loss. For example, for L1/L2 loss you can calculate the difference image between generated and label images and apply masks before summing up. More complicated losses might involve unstacking or iterating batch, and extracting ROI using tf.where or tf.boolean_mask.
Such training can be indeed beneficial in some cases, because you can combine small and big inputs for the network without small inputs being affected by the loss of big padded surroundings.
I'm using TensorFlow for a multi-target regression problem. Specifically, in a convolutional network with pixel-wise labeling with the input being an image and the label being a "heat-map" where each pixel has a float value. More specifically, the ground truth labeling for each pixel is lower bounded by zero, and, while technically having no upper bound, usually gets no larger than 1e-2.
Without batch normalization, the network is able to give a reasonable heat-map prediction. With batch normalization, the network takes much long to get to reasonable loss value, and the best it does is making every pixel the average value. This is using the tf.contrib.layers conv2d and batch_norm methods, with the batch_norm being passed to the conv2d's normalization_fn (or not in the case of no batch normalization). I had briefly tried batch normalization on another (single value) regression network, and had trouble then as well (though, I hadn't tested that as extensively). Is there a problem using batch normalization on regression problems in general? Is there a common solution?
If not, what could be some causes batch normalization failing on such an application? I've attempted a variety of initializations, learning rates, etc. I would expect the final layer (which of course does not use batch normalization) could use weights to scale the output of the penultimate layer to the appropriate regression values. Failing that, I removed batch norm from that layer, but with no improvement. I've attempted a small classification problem using batch normalization and saw no problem there, so it seems reasonable that it could be due somehow to the nature of the regression problem, but I don't know how that could cause such a drastic difference. Is batch normalization known to have trouble on regression problems?
I believe your issue is in the labels. Batch norm will scale all input values between 0 and 1. If the labels are not scaled to a similar range the task will be more difficult. This is because it requires the NN to learn values of a different scale.
By removing the batch norm from the penultimate layer, the task may be improved slightly, but you are still requiring an NN layer to learn to downscale values of its input while subsequently normalizing back to the range 0 - 1 (opposite to your objective).
To solve this problem, apply a 0 - 1 scaler to the labels such that your upper bound is no longer 1e-2. During inference, transform the predictions back with the same function to get the actual prediction.