I'm trying to figure out if there is a good way to merge two HMMs into one, when the underlying states are the same, but the observations aren't temporally linked.
I have two independent observation streams describing the same hidden state space. The underlying order of each observation stream remains the same, but they are not emitted at the same time.
For instance, say I have audio recordings of two separate speakers reading aloud the same passage of text, where the hidden state space becomes the letters in the text, while the stream of phonemes from each audio comprise the observation space. Each speaker records the audio separately, and use a different cadence when reading.
I can clearly make a prediction of the text using each speaker independently, and try and reconcile the results after the fact... but I sense that combining the observation streams into a single HMM may produce a better result.
Does anyone know a good way to reconcile this?
Merging the states would require aligning these streams first... ie some kind of log-likelihood optimization.
But its possible to use statistics from multiple streams to predict the "observations" - modern data compressors basically do just that.
Eg. see http://www.mattmahoney.net/dc/dce.html#Section_432
I am not sure if there are methods to merge two HMM's after they have each been fitted to different observation sequences.
But there exists an algotihm to train one Markov Model on multiple independent observation sequences.
It is coverered for example in the paper
"A tutorial to Hidden Markov models and selected applications in speech recognition"
by Rabiner
Unfortunately, I haven't yet found an implementiation of this algorithm.
Here is my corresponding question on stackexchange: https://stats.stackexchange.com/questions/53256/two-sequences-one-hmm
Related
I am starting with my study of RL and was wondering how would one approach the observation features, which are not able to represent the state(hidden)?
Is there some systematic approach or some guidelines on how one would prefer the feature vector to look like? Discrete, dimension, Markov properties, embedding quality...?
I would like to process machine operation data streams and actually have a lot of direct measurements and many high-dim feature-vector (also stream).
Thank you very much for you input.
I would like to increase the density of my AIS or GPS data in order to carry out more precise analyses afterwards. During my research I came across different approaches like interpolation, filtering or imputation. With the first two approaches, there is no doubt that these can be used to approximate the points between two collected data points.
In the case of imputation (e.g. MICE), however, I have not yet found an approach in the literature for determining position data.
That's why I wanted to ask if anyone knew a paper dealing with this subject and whether it makes sense at all to determine further position data approximately by imputation.
The problem you are describing there is trajectory reconstruction for AIS/GPS data. There's a number of papers for general trajectory reconstruction (see this for example), but AIS data are quite specific.
The irregularity of AIS data is a well know problem with no standard approach to deal with, as far as I know.
However, there is a handful of publications which try to deal with this issue. The problem of reconstruction is connected to the trajectory prediction problem, since both of these two shares some of the methods (the latter is more popular in the scientific community, I think).
Traditionally, AIS trajectory reconstruction is done using some physical models, which take into account the curvature of the earth and other factors, such as data noise (see examples here, here, and here).
More recent approach tries to use LSTM neural networks.
I don't know much about GPS data, but I think the methods are very similar to the ones mentioned above (especially taking into account the fact that you probably want to deal with maritime data).
I'm kinda new to Neural Networks and just started to learn coding them by trying some examples.
Two weeks ago I was searching for an interesting challenge and I found one. But I'm about to give up because it seems to be too hard for me... But I was curious to know if anyone of you is able to solve this?
The Problem: Assume there are ".htm"-files that contain tables about the same topic. But the table structure isn't the same for every file. For example: We have a lot ".htm"-files containing information about teachers substitutions per day per school. Because the structure of those ".htm"-files isn't the same for every file it would be hard to program a parser that could extract the data from those tables. So my thought was that this is a task for a Neural Network.
First Question: Is it a task a Neural Network can/should handle or am I mistaken by that?
Because for me a Neural Network seemed to fit for this kind of a challenge I tried to thing of an Input. I came up with two options:
First Input Option: Take the HTML Code (only from the body-tag) as string and convert it as Tensor
Second Input Option: Convert the HTML Tables into Images (via Canvas maybe) and feed this input to the DNN through Conv2D-Layers.
Second Question: Are those Options any good? Do you have any better solution to this?
After that I wanted to figure out how I would make a DNN output this heavily dynamic data for me? My thought was to convert my desired JSON-Output into Tensors and feed them to the DNN while training and for every prediction i would expect the DNN to return a Tensor that is convertible into a JSON-Output...
Third Question: Is it even possible to get such a detailed Output from a DNN? And if Yes: Do you think the Output would be suitable for this task?
Last Question: Assuming all my assumptions are correct - Wouldn't training this DNN take for ever? Let's say you have a RTX 2080 ti for it. What would you guess?
I guess that's it. I hope i can learn a lot from you guys!
(I'm sorry about my bad English - it's not my native language)
Addition:
Here is a more in-depth Example. Lets say we have a ".htm"-file that looks like this:
The task would be to get all the relevant informations from this table. For example:
All Students from Class "9c" don't have lessons in their 6th hour due to cancellation.
1) This is not particularly suitable problem for a Neural Network, as you domain is a structured data with clear dependcies inside. Tree based ML algorithms tend to show much better results on such problems.
2) Both you choices of input are very unstructured. To learn from such data would be nearly impossible. The are clear ways to give more knowledge to the model. For example, you have the same data in different format, the difference is only the structure. It means that a model needs to learn a mapping from one structure to another, it doesn't need to know any data. Hence, words can be Tokenized with unique identifiers to remove unnecessary information. Htm data can be parsed to a tree, as well as json. Then, there are different ways to represent graph structures, which can be used in a ML model.
3) It seems that the only adequate option for output is a sequence of identifiers pointing to unique entities from text. The whole problem then is similar to Seq2Seq best solved by RNNs with an decoder-encoder architecture.
I believe that, if there is enough data and htm files don't have huge amount of noise, the task can be completed. Training time hugely depends on selected model and its complexity, as well as diversity of initial data.
I am working on a project where I take a chess board position (FEN string converted to binary) & it's evaluation score and feed it to a neural network. My aim is to make the neural network differentiate between good and bad positions.
How I encode the position : There are 12 unique pieces in chess i.e pawn, rook, knight, bishop, queen and king for white as well as black. I encode each piece using 4 bits with 0000 denoting an empty square. So the 64 squares are encoded into 256 bits and I use 6 more bits to denote game state like whose turn it is to move, king-castle status, etc.
Problem : Since the input space for chess positions is neither smooth nor uni-modal (one small change in the board position can result in a huge change in the evaluation score), the neural network doesn't learn well. Now, the next logical thing to somehow extract useful features (like material difference, center control, etc) and feed it to the network.
I do not want to hand pick the features as I want the network to learn everything by itself. Therefore I am thinking of extracting features automatically using autoencoders. Is there any better way to accomplish this?
Summary : What is the best way to automatically extract features from a chess board position so that it can be fed into a neural network?
UPDATE : To generate training data, I have modified Stockfish to dump it's evaluation process into a log file. So every new move(position) it considers is written to a file as an FEN string along with it's eval score
Neural networks can give an approximation of any function. The only consideration to do is the dimensionality of the search space, which give constraints to the amount of data you have to get a good approximation.
For a supervised network (you use autoencoders, then I think you use some variant of backpropagation), it's difficult for me to immagine how you think to do the trainig using single positions because you need similar positions in your training set. Maybe your approach is different, but I'm convinced that second strategy (using features) is more promising. I think using positions require a huge amount of data training to get good results.
For features take a look here, and to the classical work of Shannon.
I taked also useful informations from the source code of Crafty.
But you have to extract these informations from the FEN string.
Autoencoders are a way to give a reduction of data (good because increase performances). It seems to be better the use of Pincipal Component Analysys, as reported here.
I hope this can help you.
I have a sequence of gps values each containing: timestamp, latitude, longitude, n_sats, gps_speed, gps_direction, ... (some subset of NMEA data). I'm not sure of what quality the direction and speed values are. Further, I cannot expect the sequence to be evenly spaced w.r.t. the timestamp. I want to get a smooth trajectory at an even time step.
I've read the Kalman Filter is the tool of choice for such tasks. Is this indeed the case?
I've found some implementations of the Kalman Filter for Python:
http://www.scipy.org/Cookbook/KalmanFiltering
http://ascratchpad.blogspot.de/2010/03/kalman-filter-in-python.html
These however appear to assume regularly spaced data, i.e. iterations.
What would it take to integrate support of irregularly spaced observations?
One thing I could imagine is to repeat/adapt the prediction step to a time-based model. Can you recommend such a model for this application? Would it need to take into account the NMEA speed values?
Having looked all over for an understandable resource on Kalman filters, I'd highly recommend this one: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
To your particular question regarding irregularly spaced observations: Look at Chapter 8 in the reference above, and under the heading "Nonstationary Processes". To summarize, you'll need to use a different state transition function and process noise covariance for each iteration. Those are the only things you'll need to change at each iteration, since they're the only components dependent on delta t.
You could also try kinematic interpolation to see if the results fit to what you expect.
Here's a Python implementation of one of these algorithms: https://gist.github.com/talespaiva/128980e3608f9bc5083b