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.
Related
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.
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!
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'm working on binary classification problem using Apache Mahout. The algorithm I use is OnlineLogisticRegression and the model which I currently have strongly tends to produce predictions which are either 1 or 0 without any middle values.
Please suggest a way to tune or tweak the algorithm to make it produce more intermediate values in predictions.
Thanks in advance!
What is the test error rate of the classifier? If it's near zero then being confident is a feature, not a bug.
If the test error rate is high (or at least not low), then the classifier might be overfitting the training set: measure the difference between of the training error and the test error. In that case, increasing regularization as rrenaud suggested might help.
If your classifier is not overfitting, then there might be an issue with the probability calibration. Logistic Regression models (e.g. using the logit link function) should yield good enough probability calibrations (if the problem is approximately linearly separable and the label not too noisy). You can check the calibration of the probabilities with a plot as explained in this paper. If this is really a calibration issue, then implementing a custom calibration based on Platt scaling or isotonic regression might help fix the issue.
From reading the Mahout AbstractOnlineLogisticRegression docs, it looks like you can control the regularization parameter lambda. Increasing lambda should mean your weights are closer to 0, and hence your predictions are more hedged.
I've learned the Logistic Regression for some days, and i think the logistic regression's dataset's labels needs to be 1 or 0, is it right ?
But when i lookup the libSVM library's regression dataset, i see the label values are continues number(e.g. 1.0086,1.0089 ...), did i miss something ?
Note that the libSVM library could be used for regression problem.
Thanks so much !
Contrary to its name, logistic regression is a classification algorithm and it outputs class probability conditioned on the data point. Therefore the training set labels need to be either 0 or 1. For the dataset you mentioned, logistic regression is not a suitable algorithm.
SVM is a classification algorithm and it uses the input labels -1 or 1. It is not a probabilistic algorithm and it doesn't output class probabilities. It also can be adapted to regression.
Are you using a 3rd party library or programming this yourself? Generally the labels are used as ground truth so you can see how effective your approach was.
For example if your algo is trying to predict what a particular instance is it might output -1, the ground truth label will be +1 which means you did not successfully classify that particular instance.
Note that "regression" is a general term. To say someone will perform regression analysis doesn't necessarily tell you what algorithm they will be using, nor all of the nature of the data sets. All it really tells you is that you have a set of samples with features which you want to use to predict a single outcome value (a model for conditional probability).
One major difference between logistic regression and linear regression is that the former is usually trained on categorical, binary-labeled sample sets; while the latter is trained on real-labeled (ℝ) sample sets.
Any time your labels are real valued, it means you're probably going to use linear regression or similar, or else convert those real valued labels to categorical labels (e.g. via thresholds or bins) if you want to in fact use logistic regression. There is potentially a big difference in the quality and interpretation of your results though, if you try to convert from one such problem setup to another.
See also Regression Analysis.