I am currently trying to implement the Prentice, Williams and Peterson extension of the Cox model in R on survival data but I want a parametric model and can not get it done. Is there maybe a package I am unaware of or has anyone else created a parametric PWP model before? I would greatly appreciate any help with this.
Thanks
J
I don't see why you would use a parametric model.
This means specifying parametric forms for baseline hazards (and in PWP you have one for every event).
Regardless, you can use maximum likelihood for this, but you will probably have to program it yourself.
If you denote the hazard for the j-th event by lambda[0] (j), then the contribution of an individual i would be:
Just choose your parametric form for the lambdas, take the log, and plug into optim().
Related
I'm working on a simple project in which I'm trying to describe the relationship between two positively correlated variables and determine if that relationship is changing over time, and if so, to what degree. I feel like this is something people probably do pretty often, but maybe I'm just not using the correct terminology because google isn't helping me very much.
I've plotted the variables on a scatter plot and know how to determine the correlation coefficient and plot a linear regression. I thought this may be a good first step because the linear regression tells me what I can expect y to be for a given x value. This means I can quantify how "far away" each data point is from the regression line (I think this is called the squared error?). Now I'd like to see what the error looks like for each data point over time. For example, if I have 100 data points and the most recent 20 are much farther away from where the regression line/function says it should be, maybe I could say that the relationship between the variables is showing signs of changing? Does that make any sense at all or am I way off base?
I have a suspicion that there is a much simpler way to do this and/or that I'm going about it in the wrong way. I'd appreciate any guidance you can offer!
I can suggest two strands of literature that study changing relationships over time. Typing these names into google should provide you with a large number of references so I'll stick to more concise descriptions.
(1) Structural break modelling. As the name suggest, this assumes that there has been a sudden change in parameters (e.g. a correlation coefficient). This is applicable if there has been a policy change, change in measurement device, etc. The estimation approach is indeed very close to the procedure you suggest. Namely, you would estimate the squared error (or some other measure of fit) on the full sample and the two sub-samples (before and after break). If the gains in fit are large when dividing the sample, then you would favour the model with the break and use different coefficients before and after the structural change.
(2) Time-varying coefficient models. This approach is more subtle as coefficients will now evolve more slowly over time. These changes can originate from the time evolution of some observed variables or they can be modeled through some unobserved latent process. In the latter case the estimation typically involves the use of state-space models (and thus the Kalman filter or some more advanced filtering techniques).
I hope this helps!
I'm trying to understand how the feature importance is calculated for regression trees (and their ensemble counterparts). I'm looking at the source code for the function compute_feature_importances in /sklearn/tree/_tree.pyx and cannot quite follow the logic - and there is no reference.
Sorry this may be a very basic question, but I couldn't find a good literature reference for this, and I was hoping someone could either point me in the right direction, or quickly explain the code so I can keep digging.
Thanks
The reference is in the docs rather than the code:
`feature_importances_` : array of shape = [n_features]
The feature importances. The higher, the more important the
feature. The importance of a feature is computed as the (normalized)
total reduction of the criterion brought by that feature. It is also
known as the Gini importance [4]_.
.. [4] L. Breiman, and A. Cutler, "Random Forests",
http://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm
Summing up my understanding of the topic 'Dummy Coding' is usually understood as coding a nominal attribute with K possible values as K-1 binary dummies. The usage of K values would cause redundancy and would have a negative impact e.g. on logistic regression, as far as I learned it. That far, everything's clear to me.
Yet, two issues are unclear to me:
1) Bearing in mind the issue stated above, I am confused that the 'Logistic' classifier in WEKA actually uses K dummies (see picture). Why would that be the case?
2) An issue arises as soon as I consider attribute selection. Where the left-out attribute value is implicitly included as the case where all dummies are zero if all dummies are actually used for the model, it isn't included clearly anymore, if one dummy is missing (as not selected in attribute selection). The issue is much easy to understand with the sketch I uploaded. How can that issue be treated?
Secondly
Images
WEKA Output: The Logistic algorithm was run on the UCI dataset German Credit, where the possible values of the first attribute are A11,A12,A13,A14. All of them are included in the logistic regression model. http://abload.de/img/bildschirmfoto2013-089out9.png
Decision Tree Example: Sketch showing the issue when it comes to running decision trees on datasets with dummy-coded instances after attribute selection. http://abload.de/img/sketchziu5s.jpg
The output is generally more easy to read, interpret and use when you use k dummies instead of k-1 dummies. I figure that is why everybody seems to actually use k dummies.
But yes, as the k values sum up to 1, there exists a correlation that may cause problems. But correlations in data sets are common, you will never completely get rid of them!
I believe feature selection and dummy coding just doesn't fit. It equals dropping some values from the attribute. Why do you insist on doing feature selection?
You really should be using weighting, or consider more advanced algorithms that can handle such data. In fact the dummy variables can cause just as much trouble, because they are binary, and oh so many algorithms (e.g. k-means) don't make much sense on binary variables.
As for the decision tree: don't perform, feature selection on your output attribute...
Plus, as a decision tree already selects features, it does not make sense to do all this anyway... leave it to the decision tree to decide upon which attribute to use for splitting. This way, it can learn dependencies, too.
I created a multi-class SVM model using libSVM for categorizing images. I optimized for the C and G parameters using grid search and used the RBF kernel.
The classes are 1) animal 2) floral 3) landscape 4) portrait.
My training set is 100 images from each category, and for each image, I extracted a 920-length vector using Lear's Gist Descriptor C code: http://lear.inrialpes.fr/software.
Upon testing my model on 50 images/category, I achieved ~50% accuracy, which is twice as good as random (25% since there are four classes).
I'm relatively new to computer vision, but familiar with machine learning techniques. Any suggestions on how to improve accuracy effectively?
Thanks so much and I look forward to your responses!
This is very very very open research challenge. And there isn't necessarily a single answer that is theoretically guaranteed to be better.
Given your categories, it's not a bad start though, but keep in mind that Gist was originally designed as a global descriptor for scene classification (albeit has empirically proven useful for other image categories). On the representation side, I recommend trying color-based features like patch-based histograms as well as popular low-level gradient features like SIFT. If you're just beginning to learn about computer vision, then I would say SVM is plenty for what you're doing depending on the variability in your image set, e.g. illumination, view-angle, focus, etc.
Does anyone can give an example of a SVM? Especially how to get the w and b from a training set?
I tried to search in the internet but it only gives me a large amount of abstract mathematics.
As I am not good at it, so could anyone give me an illustration of a SVM with an example in very details?
Thank you so much.
This diagram on wikipedia provides a good example of what the goal is, but in truth a support vector machine is a lot of complicated math. You find the values for w and b by optimizing a quadratic programming system, and when hidden behind vector mathematics, it's not entirely clear what's going on unless you're well-tuned to the math.