I'm trying to build a regression based M/L model using tensorflow.
I am trying to estimate an object's ETA based on the following:
distance from target
distance from target (X component)
distance from target (Y component)
speed
The object travels on specific journeys. This could be represented as from A->B or from A->C or from D->F (POINT 1 -> POINT 2). There are 500 specific journeys (between a set of points).
These journeys aren't completely straight lines, and every journey is different (ie. the shape of the route taken).
I have two ways of getting around this problem:
I can have 500 different models with 4 features and one label(the training ETA data).
I can have 1 model with 5 features and one label.
My dilemma is that if I use option 1, that's added complexity, but will be more accurate as every model will be specific to each journey.
If I use option 2, the model will be pretty simple, but I don't know if it would work properly. The new feature that I would add are originCode+ destinationCode. Unfortunately these are not quantifiable in order to make any numerical sense or pattern - they're just text that define the journey (journey A->B, and the feature would be 'AB').
Is there some way that I can use one model, and categorize the features so that one feature is just a 'grouping' feature (in order separate the training data with respect to the journey.
In ML, I believe that option 2 is generally the better option. We prefer general models rather than tailoring many models to specific tasks, as that gets dangerously close to hardcoding, which is what we're trying to get away from by using ML!
I think that, depending on the training data you have available, and the model size, a one-hot vector could be used to describe the starting/end points for the model. Eg, say we have 5 points (ABCDE), and we are going from position B to position C, this could be represented by the vector:
0100000100
as in, the first five values correspond to the origin spot whereas the second five are the destination. It is also possible to combine these if you want to reduce your input feature space to:
01100
There are other things to consider, as Scott has said in the comments:
How much data do you have? Maybe the feature space will be too big this way, I can't be sure. If you have enough data, then the model will intuitively learn the general distances (not actually, but intrinsically in the data) between datapoints.
If you have enough data, you might even be able to accurately predict between two points you don't have data for!
If it does come down to not having enough data, then finding representative features of the journey will come into use, ie. length of journey, shape of the journey, elevation travelled etc. Also a metric for distance travelled from the origin could be useful.
Best of luck!
I would be inclined to lean toward individual models. This is because, for a given position along a given route and a constant speed, the ETA is a deterministic function of time. If one moves monotonically closer to the target along the route, it is also a deterministic function of distance to target. Thus, there is no information to transfer from one route to the next, i.e. "lumping" their parameters offers no a priori benefit. This is assuming, of course, that you have several "trips" worth of data along each route (i.e. (distance, speed) collected once per minute, or some such). If you have only, say, one datum per route then lumping the parameters is a must. However, in such a low-data scenario, I believe that including a dummy variable for "which route" would ultimately be fruitless, since that would introduce a number of parameters that rivals the size of your dataset.
As a side note, NEITHER of the models you describe could handle new routes. I would be inclined to build an individual model per route, data quantity permitting, and a single model neglecting the route identity entirely just for handling new routes, until sufficient data is available to build a model for that route.
Related
I am given a data that consists of N sequences of variable lengths of hidden variables and their corresponding observed variables (i.e., I have both the hidden variables and the observed variables for each sequence).
Is there a way to find the order K of the "best" HMM model for this data, without exhaustive search? (justified heuristics are also legitimate).
I think there may be a confusion about the word "order":
A first-order HMM is an HMM which transition matrix depends only on the previous state. A 2nd-order HMM is an HMM which transition matrix depends only on the 2 previous states, and so on. As the order increases, the theory gets "thicker" (i.e., the equations) and very few implementations of such complex models are implemented in mainstream libraries.
A search on your favorite browser with the keywords "second-order HMM" will bring you to meaningful readings about these models.
If by order you mean the number of states, and with the assumptions that you use single distributions assigned to each state (i.e., you do not use HMMs with mixtures of distributions) then, indeed the only hyperparameter you need to tune is the number of states.
You can estimate the optimal number of states using criteria such as the Bayesian Information Criterion, the Akaike Information Criterion, or the Minimum Message Length Criterion which are based on model's likelihood computations. Usually, the use of these criteria necessitates training multiple models in order to be able to compute some meaningful likelihood results to compare.
If you just want to get a blur idea of a good K value that may not be optimal, a k-means clustering combined with the percentage of variance explained can do the trick: if X clusters explain more than, let say, 90% of the variance of the observations in your training set then, going with an X-state HMM is a good start. The 3 first criteria are interesting because they include a penalty term that goes with the number of parameters of the model and can therefore prevent some overfitting.
These criteria can also be applied when one uses mixture-based HMMs, in which case there are more hyperparameters to tune (i.e., the number of states and the number of component of the mixture models).
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 being asked to take a look at a scenario where a company has many projects that they wish to complete, but with any company budget comes into play. There is a Y value of a predefined score, with multiple X inputs. There are also 3 main constraints of Capital Costs, Expense Cost and Time for Completion in Months.
The ask is could an algorithmic approach be used to optimize which projects should be done for the year given the 3 constraints. The approach also should give different results if the constraint values change. The suggested method is multiple regression. Though I have looked into different approaches in detail. I would like to ask the wider community, if anyone has dealt with a similar problem, and what approaches have you used.
Fisrt thing we should understood, a conclution of something is not base on one argument.
this is from communication theory, that every human make a frame of knowledge (understanding conclution), where the frame construct from many piece of knowledge / information).
the concequence is we cannot use single linear regression in math to create a ML / DL system.
at least we should use two different variabel to make a sub conclution. if we push to use single variable with use linear regression (y=mx+c). it's similar to push computer predict something with low accuration. what ever optimization method that you pick...it's still low accuracy..., why...because linear regresion if you use in real life, it similar with predict 'habbit' base on data, not calculating the real condition.
that's means...., we should use multiple linear regression (y=m1x1+m2x2+ ... + c) to calculate anything in order to make computer understood / have conclution / create model of regression. but, not so simple like it. because of computer try to make a conclution from data that have multiple character / varians ... you must classified the data and the conclution.
for an example, try to make computer understood phitagoras.
we know that phitagoras formula is c=((a^2)+(b^2))^(1/2), and we want our computer can make prediction the phitagoras side (c) from two input values (a and b). so to do that, we should make a model or a mutiple linear regresion formula of phitagoras.
step 1 of course we should make a multi character data of phitagoras.
this is an example
a b c
3 4 5
8 6 10
3 14 etc..., try put 10 until 20 data
try to make a conclution of regression formula with multiple regression to predic the c base on a and b values.
you will found that some data have high accuration (higher than 98%) for some value and some value is not to accurate (under 90%). example a=3 and b=14 or b=15, will give low accuration result (under 90%).
so you must make and optimization....but how to do it...
I know many method to optimize, but i found in manual way, if I exclude the data that giving low accuracy result and put them in different group then, recalculate again to the data group that excluded, i will get more significant result. do again...until you reach the accuracy target that you want.
each group data, that have a new regression, is a new class.
means i will have several multiple regression base on data that i input (the regression come from each group of data / class) and the accuracy is really high, 99% - 99.99%.
and with the several class, the regresion have a fuction as a 'label' of the class, this is what happens in the backgroud of the automation computation. but with many module, the user of the module, feel put 'string' object as label, but the truth is, the string object binding to a regresion that constructed as label.
with some conditional parameter you can get the good ML with minimum number of data train.
try it on excel / libreoffice before step more further...
try to follow the tutorial from this video
and implement it in simple data that easy to construct in excel, like pythagoras.
so the answer is yes...the multiple regression is the best approach for optimization.
I have a bayesian network, and I know the CPTs by learning the probabilities from existing data.
Suppose I receive a new data instance. Ideally I don't want to use all the data again to update the probabilities.
Is there a way to incrementally update the CPTs of the existing network each time new data comes in?
I think there should be, and I feel like I'm missing something :)
It's easiest to maintain the joint probability table, and rebuild the CPT from that as needed. Along with the JPT, keep a count of how many examples were used to produce it. When adding the nth example, multiply all probabilities by 1 - 1/n, and then add probability 1/n to the new example's associated probability.
If you're going to do this a bunch, you should maintain a count of examples for each row in the JPT instead of a probability. That'll cut down on numerical drift.
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.