I fitted a Lasso regression with a 10-fold cross-validation framework for time-to-event data (Cox family) [using 3,270 observations and 60 independent variables]. While I am quite okay with the Lasso's output, I think it would be good to also use the "Group lasso" because of its ability to select/drop categorical features as a whole (because Lasso sometimes selects only specific levels within a given feature). Question is, what informs the definition/specification of the "group" argument in the "cv.gglasso" function in R?
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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 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 use the python implementation of XGBoost. One of the objectives is rank:pairwise and it minimizes the pairwise loss (Documentation). However, it does not say anything about the scope of the output. I see numbers between -10 and 10, but can it be in principle -inf to inf?
good question. you may have a look in kaggle competition:
Actually, in Learning to Rank field, we are trying to predict the relative score for each document to a specific query. That is, this is not a regression problem or classification problem. Hence, if a document, attached to a query, gets a negative predict score, it means and only means that it's relatively less relative to the query, when comparing to other document(s), with positive scores.
It gives predicted score for ranking.
However, the scores are valid for ranking only in their own groups.
So we must set the groups for input data.
For esay ranking, refer to my project xgboostExtension
If I understand your questions correctly, you mean the output of the predict function on a model fitted using rank:pairwise.
Predict gives the predicted variable (y_hat).
This is the same for reg:linear / binary:logistic etc. The only difference is that reg:linear builds trees to Min(RMSE(y, y_hat)), while rank:pairwise build trees to Max(Map(Rank(y), Rank(y_hat))). However, output is always y_hat.
Depending on the values of your dependent variables, output can be anything. But I typically expect output to be much smaller in variance vs the dependent variable. This is usually the case as it is not necessary to fit extreme data values, the tree just needs to produce predictors that are large/small enough to be ranked first/last in the group.
I would like to perform feature analysis in WEKA. I have a data set of 8 features and 65 instances.
I would like to perform feature selection and optimization functionalities that are available for machine learning methods like SVM.
For example in Weka I would like to know how I can display which of the features contribute best to the classification result.
I think that WEKA provides a nice graphical user interface and allows a very detailed analysis of the influence of single features. But I dont know how to use it. Any help?
You have two options:
You can perform attribute selection using filters. For instance you can use the AttributeSelection tab (or filter) with the search method Ranker and the attribute evaluation metric InfoGainAttributeEval. This way you get a ranked list of the most predictive features according to its Information Gain score. I have done this many times with good results. Sometimes it helps even to increase the accuracy of SVMs, which are known not to need (too much) of feature selection. You can try with other search methods in order to find subgroups of coupled predictors, and with other metrics.
You can just look at the coefficients in the SVM output. For instance, in linear SVMs, the classifier is a polynomial like a1.f1 + a2.f2 + ... + an.fn + fn+1 > 0, being ai the attribute values for an instance, and fi the "weights" obtained in the SVM training algorithm. In consequence, those weights with values close to 0 represent attributes that do not count too much, thus being bad predictors; extreme weights (either positive or negative) represent good predictors.
Additionally, you can check the visualization options available for a particular classifier (e.g. J48 is a decision tree, the attribute used in the root test is for the best predictor). You can check the AttributeSelection tab visualization options as well.
I am having some problems understanding how the Baum-Welch algorithm exactly works. I read that it adjusts the parameters of the HMM (the transition and the emission probabilities) in order to maximize the probability that my observation sequence may be seen by the given model.
However, what does happen if I have multiple observation sequences? I want to train my HMM against a huge lot of observations (and I think this is what is usually done).
ghmm for example can take both a single observation sequence and a full set of observations for the baumWelch method.
Does it work the same in both situations? Or does the algorithm have to know all observations at the same time?
In Rabiner's paper, the parameters of GMMs (weights, means and covariances) are re-estimated in the Baum-Welch algorithm using these equations:
These are just for the single observation sequence case. In the multiple case, the numerators and denominators are just summed over all observation sequences, and then divided to get the parameters. (this can be done since they simply represent occupation counts, see pg. 273 of the paper)
So it's not required to know all observation sequences during an invocation of the algorithm. As an example, the HERest tool in HTK has a mechanism that allows splitting up the training data amongst multiple machines. Each machine computes the numerators and denominators and dumps them to a file. In the end, a single machine reads these files, sums up the numerators and denominators and divides them to get the result. See pg. 129 of the HTK book v3.4