I am a beginner in machine learning. So any help or suggestion would be of great help.
I have read that putting weights on features and Predicting is a very bad idea. But what if few features needs to be weighted.
In a classification problem let's say it's a common norm that age is most dependent, how do I give weights to this feature. I was thinking to normalize it but with a variance of 1.5 or 2 (other features with variance 1), I believe that this feature will have more weight. Is this fundamentally wrong ? If wrong any other method.
Does it effect differently for classification and regression problems ?
If we are talking specifically about random forests (as you tagged) then you can use the Weighted Subspace Random Forest algorithm (in R wsrf package). The algorithm determines a weight for each variable and then uses these during the model building.
The informativeness of a variable with respect to the class is
measured by an information gain ratio. The measure is used as the
probability of that variable being selected for inclusion in the
variable subspace when splitting a specific node during the tree
building process. Therefore, variables with higher values by the
measure are more likely to be chosen as candidates during variable
selection and a stronger tree can be built.
Generally if a feature has more Importance compared to other features and the model is Dense enough, with enough training sample, your model will automatically give it more Importance by optimizing weight matrices to account for that because we have partial derivatives in back propagation which calculate change by each connection, so it learns to give more importance to that feature on itself. If you don't normalize it, but scale it to a higher scale, you might have overstated it's important.
In practice a neural network works best if the inputs are centered and white. That means that their covariance is diagonal and the mean is the zero vector. This improves optimization of the neural net, since the hidden activation functions don't saturate that fast and thus do not give you near zero gradients early on in learning.
If you do scale just one feature up by a small value, it may or may not have desired effects, but the higher probability is of saturated gradients, so we avoid it.
Related
I am working on an article where I focus on a simple problem – linear regression over a large data set in the presence of standard normal or uniform noise. I chose Estimator API from TensorFlow as the modeling framework.
I am finding that, hyperparameter tuning is, in fact, of little importance for such a machine learning problem when the number of training steps can be made sufficiently large. By hyperparameter I mean batch size or number of epochs in the training data stream.
Is there any paper/article with formal proof of this?
I don't think there is a paper specifically focused on this question, because it's a more or less fundamental fact. The introductory chapter of this book discusses the probabilistic interpretation of machine learning in general and loss function optimization in particular.
In short, the idea is this: mini-batch optimization wrt (x1,..., xn) is equivalent to consecutive optimization steps wrt x1, ..., xn inputs, because the gradient is a linear operator. This means that mini-batch update equals to the sum of its individual updates. Important note here: I assume that NN doesn't apply batch-norm or any other layer that adds an explicit variation to the inference model (in this case the math is a bit more hairy).
So the batch size can be seen as a pure computational idea that speeds up the optimization through vectorization and parallel computing. Assuming that one can afford arbitrarily long training and the data are properly shuffled, the batch size can be set to any value. But it isn't automatically true for all hyperparameters, for example very high learning rate can easily force the optimization to diverge, so don't make a mistake thinking hyperparamer tuning isn't important in general.
I've got a set of F features e.g. Lab color space, entropy. By concatenating all features together, I obtain a feature vector of dimension d (between 12 and 50, depending on which features selected.
I usually get between 1000 and 5000 new samples, denoted x. A Gaussian Mixture Model is then trained with the vectors, but I don't know which class the features are from. What I know though, is that there are only 2 classes. Based on the GMM prediction I get a probability of that feature vector belonging to class 1 or 2.
My question now is: How do I obtain the best subset of features, for instance only entropy and normalized rgb, that will give me the best classification accuracy? I guess this is achieved, if the class separability is increased, due to the feature subset selection.
Maybe I can utilize Fisher's linear discriminant analysis? Since I already have the mean and covariance matrices obtained from the GMM. But wouldn't I have to calculate the score for each combination of features then?
Would be nice to get some help if this is a unrewarding approach and I'm on the wrong track and/or any other suggestions?
One way of finding "informative" features is to use the features that will maximise the log likelihood. You could do this with cross validation.
https://www.cs.cmu.edu/~kdeng/thesis/feature.pdf
Another idea might be to use another unsupervised algorithm that automatically selects features such as an clustering forest
http://research.microsoft.com/pubs/155552/decisionForests_MSR_TR_2011_114.pdf
In that case the clustering algorithm will automatically split the data based on information gain.
Fisher LDA will not select features but project your original data into a lower dimensional subspace. If you are looking into the subspace method
another interesting approach might be spectral clustering, which also happens
in a subspace or unsupervised neural networks such as auto encoder.
I have a binary logistic regression model (0/1), built over binary features. The feature coefficients are usually in the range (-1, 1). After training, can I use the feature coefficients as a proxy for the 'importance' of a feature? If the coefficient is < 0, does that mean the presence of the feature is a negative for the class (i.e., reduces the probability of the output being 1)?
Right; a negative coefficient means that the feature contra-indicates that class. The magnitude is, indeed, the relative importance. -1 and +1 are imperatives: all members of the class do not / do have that feature.
You absolutely can. In fact, this idea of important or 'blame' is the main concept behind machine learning algorithms. The coefficients change many times during the training process through gradient descent. How much the weights update by is actually determined by each weight's contribution towards the cost.
That is, the more a weight is to be blamed for a high cost the more extreme the update will be. Therefore, more extreme values (high positives or low negatives) are an indication of how impactful the respective feature is when the model is making its decision.
The motivating idea behind neural nets seems to be that they learn the "right" features to apply logistic regression to. Is there a similar approach for linear regression? (or just regression problems in general?)
Would doing the obvious thing of removing the application of a sigmoid function for all neurons (ie, including the hidden layers) make sense/work? (ie, each neuron is performing linear regression instead of logistic regression).
Alternatively, would doing the (maybe even more obvious) thing of just scaling output values to [0,1] work? (intuitively I would think not, as the sigmoid function seems like it would cause the net to arbitrarily favor extreme values) (edit: though I was just searching around some more, and saw that one technique is to scale based on mean and variance, which seems like it might deal with this issue -- so maybe this is more viable than I thought).
Or is there some other technique for doing "feature learning" for regression problems?
Check out this applet. Try to learn different functions. When you dictate linear activation functions at both hidden and output layers, it even fails to learn the quadratic function. At least one layer needs to be set to sigmoid function, see figures below.
There are different kinds of scaling. Standard scaling, as you mentioned, eliminates the impact of mean and standard deviation of the training sample, is most often used in machine learning. Just make sure you are using the same mean and std value from training sample in the test sample.
The reason why scaling is required is because the output of sigmoid function ranges at (0,1). I didn't try, but I think it is better to scale the output even if you select linear function at output layer. Otherwise large input at hidden layer (with sigmoid) won't lead to drastic output (the sigmoid function is approximately linear when the input is at a small range, out of such range will make the output changes much slowly). You can try this by yourself in your own data.
Besides, if you have various features, the feature normalization that makes different features in the same scale is also recommended. The scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features take on much larger values than the rest.
As #Ray mentioned, deep learning that many levels of features are involved can help you with the feature learning, it's not all linear combinations though.
I have some problems with understanding the kernels for non-linear SVM.
First what I understood by non-linear SVM is: using kernels the input is transformed to a very high dimension space where the transformed input can be separated by a linear hyper-plane.
Kernel for e.g: RBF:
K(x_i, x_j) = exp(-||x_i - x_j||^2/(2*sigma^2));
where x_i and x_j are two inputs. here we need to change the sigma to adapt to our problem.
(1) Say if my input dimension is d, what will be the dimension of the
transformed space?
(2) If the transformed space has a dimension of more than 10000 is it
effective to use a linear SVM there to separate the inputs?
Well it is not only a matter of increasing the dimension. That's the general mechanism but not the whole idea, if it were true that the only goal of the kernel mapping is to increase the dimension, one could conclude that all kernels functions are equivalent and they are not.
The way how the mapping is made would make possible a linear separation in the new space.
Talking about your example and just to extend a bit what greeness said, RBF kernel would order the feature space in terms of hyperspheres where an input vector would need to be close to an existing sphere in order to produce an activation.
So to answer directly your questions:
1) Note that you don't work on feature space directly. Instead, the optimization problem is solved using the inner product of the vectors in the feature space, so computationally you won't increase the dimension of the vectors.
2) It would depend on the nature of your data, having a high dimensional pattern would somehow help you to prevent overfitting but not necessarily will be linearly separable. Again, the linear separability in the new space would be achieved because the way the map is made and not only because it is in a higher dimension. In that sense, RBF would help but keep in mind that it might not perform well on generalization if your data is not locally enclosed.
The transformation usually increases the number of dimensions of your data, not necessarily very high. It depends. The RBF Kernel is one of the most popular kernel functions. It adds a "bump" around each data point. The corresponding feature space is a Hilbert space of infinite dimensions.
It's hard to tell if a transformation into 10000 dimensions is effective or not for classification without knowing the specific background of your data. However, choosing a good mapping (encoding prior knowledge + getting right complexity of function class) for your problem improves results.
For example, the MNIST database of handwritten digits contains 60K training examples and 10K test examples with 28x28 binary images.
Linear SVM has ~8.5% test error.
Polynomial SVM has ~ 1% test error.
Your question is a very natural one that almost everyone who's learned about kernel methods has asked some variant of. However, I wouldn't try to understand what's going on with a non-linear kernel in terms of the implied feature space in which the linear hyperplane is operating, because most non-trivial kernels have feature spaces that it is very difficult to visualise.
Instead, focus on understanding the kernel trick, and think of the kernels as introducing a particular form of non-linear decision boundary in input space. Because of the kernel trick, and some fairly daunting maths if you're not familiar with it, any kernel function satisfying certain properties can be viewed as operating in some feature space, but the mapping into that space is never performed. You can read the following (fairly) accessible tutorial if you're interested: from zero to Reproducing Kernel Hilbert Spaces in twelve pages or less.
Also note that because of the formulation in terms of slack variables, the hyperplane does not have to separate points exactly: there's an objective function that's being maximised which contains penalties for misclassifying instances, but some misclassification can be tolerated if the margin of the resulting classifier on most instances is better. Basically, we're optimising a classification rule according to some criteria of:
how big the margin is
the error on the training set
and the SVM formulation allows us to solve this efficiently. Whether one kernel or another is better is very application-dependent (for example, text classification and other language processing problems routinely show best performance with a linear kernel, probably due to the extreme dimensionality of the input data). There's no real substitute for trying a bunch out and seeing which one works best (and make sure the SVM hyperparameters are set properly---this talk by one of the LibSVM authors has the gory details).