I'm following a TensorFlow example that takes a bunch of features (real estate related) and "expensive" (ie house price) as the binary target.
I was wondering if the target could take more than just a 0 or 1. Let's say, 0 (not expensive), 1 (expensive), 3 (very expensive).
I don't think this is possible as the logistic regression model has asymptotes nearing 0 and 1.
This might be a stupid question, but I'm totally new to ML.
I think I found the answer myself. From Wikipedia:
First, the conditional distribution y|x is a Bernoulli distribution rather than a Gaussian distribution, because the dependent variable is binary. Second, the predicted values are probabilities and are therefore restricted to (0,1) through the logistic distribution function because logistic regression predicts the probability of particular outcomes.
Logistic Regression is defined for binary classification tasks.(For more details, please logistic_regression. For multi-class classification problems, you can use Softmax Classification algorithm. Following tutorials shows how to write a Softmax Classifier in Tensorflow Library.
Softmax_Regression in Tensorflow
However, your data set is linearly non-separable (most of the time this is the case in real-world datasets) you have to use an algorithm which can handle nonlinear decision boundaries. Algorithm such as Neural Network or SVM with Kernels would be a good choice. Following IPython notebook shows how to create a simple Neural Network in Tensorflow.
Neural Network in Tensorflow
Good Luck!
Related
I have used resnet50 to solve a multi-class classification problem. The model outputs probabilities for each class. Which loss function should I choose for my model?
After choosing binary cross entropy :
After choosing categorical cross entropy:
The above results are for the same model with just different loss functions.This model is supposed to classify images into 26 classes so categorical cross entropy should work.
Also, in the first case accuracy is about 96% but losses are so high. Why?
edit 2:
Model architecture:
You definitely need to use categorical_crossentropy for a multi-classification problem. binary_crossentropy will reduce your problem down to a binary classification problem in a way that's unclear without further looking into it.
I would say that the reason you are seeing high accuracy in the first (and to some extent the second) case is because you are overfitting. The first dense layer you are adding contains 8 million parameters (!!! to see that do model.summary()), and you only have 70k images to train it with 8 epochs. This architectural choice is very demanding both in computing power and in data requirement. You are also using a very basic optimizer (SGD). Try to use a more powerful Adam.
Finally, I am a bit surprised at your choice to take a 'sigmoid' activation function in the output layer. Why not a more classic 'softmax'?
For a multi-class classification problem you use the categorical_crossentropy loss, as what it does is match the ground truth probability distribution with the one predicted by the model.
This is exactly what is used for multi-class classification, you have a misconception of you think you can't use this loss.
I am trying to use machine learning to predict a dataset. It is a regression problem with 180 input features and 1 continuously-valued output. I try to compare deep neural networks, random forest regression, and linear regression.
As I expect, 3-hidden-layer deep neural networks outperform other two approaches with a root mean square error (RMSE) of 0.1. However, I unexpected to see that random forest even performs worse than linear regression (RMSE 0.29 vs. 0.27). In my expectation, the random forest can discover more complex dependencies between features to decrease error. I have tried to tune the parameters of random forest (number of trees, maximum features, max_depth, etc.). I also tried different K-cross validation, but the performance is still less than linear regression.
I searched online, and one answer says linear regression may perform better if features have a smooth, nearly linear dependence on the covariates. I do not fully get the point because if that is the case, should not deep neural networks give much performance gain?
I am struggling to give an explanation. Under what situation, random forest is worse than linear regression, but deep neural networks can perform much better?
If your features explain linear relation to the target variable then a Linear Model usually performs well than a Random Forest Model. It totally depends on the linear relations between your features.
That said, Linear models are not superior or the Random Forest is any inferior one.
Try scaling and transforming the data using MinMaxScaler() from scikit-learn to see if the linear model improves further
Pro Tips
If linear model is working like a charm you need to ask your self Why? and How? And get into the basics of both the models to understand why it worked on your data. These questions will lead you to feature engineer better. And as a matter of fact, Kaggle Grand Masters do use Linear Models in stacking to get that top 1% score by capturing the linear relations in the dataset.
So at the end of the day, linear models could wonders too.
If a dataset contains multi categories, e.g. 0-class, 1-class and 2-class. Now the goal is to divide new samples into 0-class or non-0-class.
One can
combine 1,2-class into a unified non-0-class and train a binary classifier,
or train a multi-class classifier to do binary classification.
How is the performance of these two approaches?
I think more categories will bring about a more accurate discriminant surface, however the weights of 1- and 2- classes are both lower than non-0-class, resulting in less samples be judged as non-0-class.
Short answer: You would have to try both and see.
Why?: It would really depend on your data and the algorithm you use (just like for many other machine learning questions..)
For many classification algorithms (e.g. SVM, Logistic Regression), even if you want to do a multi-class classification, you would have to perform a one-vs-all classification, which means you would have to treat class 1 and class 2 as the same class. Therefore, there is no point running a multi-class scenario if you just need to separate out the 0.
For algorithms such as Neural Networks, where having multiple output classes is more natural, I think training a multi-class classifier might be more beneficial if your classes 0, 1 and 2 are very distinct. However, this means you would have to choose a more complex algorithm to fit all three. But the fit would possibly be nicer. Therefore, as already mentioned, you would really have to try both approaches and use a good metric to evaluate the performance (e.g. confusion matrices, F-score, etc..)
I hope this is somewhat helpful.
My colleague and I are trying to wrap our heads around the difference between logistic regression and an SVM. Clearly they are optimizing different objective functions. Is an SVM as simple as saying it's a discriminative classifier that simply optimizes the hinge loss? Or is it more complex than that? How do the support vectors come into play? What about the slack variables? Why can't you have deep SVM's the way you can't you have a deep neural network with sigmoid activation functions?
I will answer one thing at at time
Is an SVM as simple as saying it's a discriminative classifier that simply optimizes the hinge loss?
SVM is simply a linear classifier, optimizing hinge loss with L2 regularization.
Or is it more complex than that?
No, it is "just" that, however there are different ways of looking at this model leading to complex, interesting conclusions. In particular, this specific choice of loss function leads to extremely efficient kernelization, which is not true for log loss (logistic regression) nor mse (linear regression). Furthermore you can show very important theoretical properties, such as those related to Vapnik-Chervonenkis dimension reduction leading to smaller chance of overfitting.
Intuitively look at these three common losses:
hinge: max(0, 1-py)
log: y log p
mse: (p-y)^2
Only the first one has the property that once something is classified correctly - it has 0 penalty. All the remaining ones still penalize your linear model even if it classifies samples correctly. Why? Because they are more related to regression than classification they want a perfect prediction, not just correct.
How do the support vectors come into play?
Support vectors are simply samples placed near the decision boundary (losely speaking). For linear case it does not change much, but as most of the power of SVM lies in its kernelization - there SVs are extremely important. Once you introduce kernel, due to hinge loss, SVM solution can be obtained efficiently, and support vectors are the only samples remembered from the training set, thus building a non-linear decision boundary with the subset of the training data.
What about the slack variables?
This is just another definition of the hinge loss, more usefull when you want to kernelize the solution and show the convexivity.
Why can't you have deep SVM's the way you can't you have a deep neural network with sigmoid activation functions?
You can, however as SVM is not a probabilistic model, its training might be a bit tricky. Furthermore whole strength of SVM comes from efficiency and global solution, both would be lost once you create a deep network. However there are such models, in particular SVM (with squared hinge loss) is nowadays often choice for the topmost layer of deep networks - thus the whole optimization is actually a deep SVM. Adding more layers in between has nothing to do with SVM or other cost - they are defined completely by their activations, and you can for example use RBF activation function, simply it has been shown numerous times that it leads to weak models (to local features are detected).
To sum up:
there are deep SVMs, simply this is a typical deep neural network with SVM layer on top.
there is no such thing as putting SVM layer "in the middle", as the training criterion is actually only applied to the output of the network.
using of "typical" SVM kernels as activation functions is not popular in deep networks due to their locality (as opposed to very global relu or sigmoid)
I want to build a machine learning model to regression on continuous output given binary valued features(0,1). the dimension of my problem is around 200.
which of the flowing methods seems suitable for this kind of problem ?
SVR with different Kernels
Regression random forest
MARS
Gradient boosting with regression tree
Kernel regression (Nadya-Watson Kernel regression)
LSR and LARS
Stochastic gradient boosting
Intuitively speaking, anything requiring the calculation of a gradient is going to struggle on binary values. From your list, SVR and Forests would be the first place I'd look for a benchmark solution.
You can also look at expectation maximization for Bernoully mixture models.
It deals with binary input sets. You can find theory in book:
Christopher M. Bishop. "Pattern Recognition and Machine Learning".