Markov Regime Switching Regression Models - Time Varying Probabiliites - regression

I am looking into estimating a markov regime switching model with time varying probs. Please help me if you know a simpler way to estimate such model.

This paper might answer your needs.

Related

Different generation quality with one model

I am training a Beta-VAE using BDD-100k driving dataset. Here are my hyperparameters: Adam optimizer, 0.0001 learning rate, and my latent dimension is 16, loss function is reconstruction loss(MSE) and KLD loss multiplied to Beta factor. After a while of training, the model seems learned something, but with different samples the exact same model's performance is absolutely different. Can anyone give me some hint for how to understand what is going on there? Thanks! Here are examples of same model generating different results.
bad generation
good generation
I would really appreciate if you can leave me some advices!
Thank you!

Fine-tuning with a very low learning rate. Any sign that something is not good?

I have working with deep reinforcement learning and in the literature, usually the learning rates are lower than I found in other settings.
My model is the following one:
def create_model(self):
model = Sequential()
model.add(LSTM(HIDDEN_NODES, input_shape=(STATE_SIZE, STATE_SPACE), return_sequences=False))
model.add(Dense(HIDDEN_NODES, activation='relu', kernel_regularizer=regularizers.l2(0.000001)))
model.add(Dense(HIDDEN_NODES, activation='relu', kernel_regularizer=regularizers.l2(0.000001)))
model.add(Dense(ACTION_SPACE, activation='linear'))
# Compile the model
model.compile(loss=tf.keras.losses.Huber(delta=1.0), optimizer=Adam(lr=LEARNING_RATE, clipnorm=1))
return model
Where the initial learning rate (lr) is 3e-5. For the fine-tuning, I freeze the first two layers (this step is essential in my settings) and decrease the learning rate to 3e-9. During the fine-tuning, the model might suffer from a distributional shift once the source of samples is perturbed data. Is there another source of problems besides this for such a low learning rate to keep my model improving?
First, Show me your data sample.
Theoretical Answer:
We have learned how perturbation helps in solving various issues related to neural network training or trained model. Here, we have seen perturbation in three components (gradients, weights, inputs) associated with neural-network training and trained model; perturbation, in gradients is to tackle vanishing gradient problem, in weights for escaping saddle point, and in inputs to avoid malicious attacks. Overall, perturbations in different ways play the role of strengthening the model against various instabilities, for example, it can avoid staying at correctness wreckage point since such position will be tested with perturbation (input, weight, gradient) which will make the model approach towards correctness attraction point.
As of now, perturbation is mainly contingent to empirical-experimentation designed from intuition to solve encountering problems. One needs to experiment if perturbing a component of the training process makes sense intuitively, and further verify empirically if it helps mitigate the problem. Nevertheless, in future, we will see more on perturbation theory in deep learning or machine learning in general which might also be backed by a theoretical guarantee.

In deep learning, can I change the weight of loss dynamically?

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!

Convolutional filter design in neural networks by data clustering

My understanding is that filters in convolutional neural networks are going to extract features in raw data (or previous layers), so designing them by supervised learning through backpropagation makes complete sense. But I have seen some papers in which the filters are found by unsupervised clustering of input data samples. That looks strange to me how cluster centers can be regarded as good filters for feature extraction. Does anybody have a good explanation for that?
Certain popular clustering algorithms such as k-means are vector quantization methods.
They try to find a good least-squares quantization of the data, such that every data point can be represented by a similar vector with least-squares difference.
So from a least-squares approximation point of view, the cluster centers are good approximations (we can't afford to find the optimal centers, but we have a good chance at finding reasonably good centers). Whether or not least squares is appropriate depends a lot on the data, for example all attributes should be of the same kind. For a typical image processing task, where each pixel is represented the same way, this will be a good starting point for later supervised optimization. But I believe soft factorizations will usually be better that do not assume every patch is of exactly one kind.

Calculating ROC and AUC in Caffe?

I have trained imagenet in Caffe. Now i am trying to calculate ROC/AUC for my model and the trained model provided by caffe. I have two questions:
1) ROC/AUC is mainly used for binary classes, but i also found that in some cases people used it for multi-classes. Is it possible for 1000 classes. And what will be its impact? As in reviews people didn't give good answer for ROC/AUC in multi-class problems.
2) If possible, and comparing two models based on ROC/AUC will be a good idea, Can anybody tell how to do it for these 1000 classes in Caffe? And do i have to retrain the models from scratch, or can i calculate only with final trained models?
Regards
This discussion addresses multi-class ROC/AUC analysis nicely. Answering your questions:
You can do multiple one-vs-all classifications for each class, thus building multiple ROC curves.
Having computed 1000 AUC values, you can come up with the mean AUC over all classes and use this metric to compare goodness of your models. No, you don't need to retrain your models.
Also, pay an attention that ROC/AUC metrics are quite specific and used mostly in detection/biometry tasks like voice identification.