Optimal SVM parameters for high recall - python

I'm using scikit-learn to perform classification using SVM. I'm performing a binary classification task.
0: Does not belong to class A
1: Belongs to class A
Now, I want to optimize the parameters such that I get high recall. I don't care much about a few false positives but the objects belonging to class A should not be labelled as not belonging to A often.
I use a SVM with linear kernel.
from sklearn import svm
clf = svm.SVC(kernel='linear')
clf.fit(X,Y)
clf.predict(...)
How should I choose other SVM parameters like C? Also, what is the difference between SVC with a linear kernel and LinearSVC?

The choice of the kernel is really dependent on the data, so picking the kernel based on a plot of the data might be the way to go. This could be automated by running through all kernel types and picking the one that gives you either high/low recall or bias, whatever you're looking for. You can see for yourself the visual difference of the kernels.
Depending on the kernel different arguments of the SVC constructor are important, but in general the C is possibly the most influential, as it's the penalty for getting it wrong. Decreasing C would increase the recall.
Other than that there's more ways to get a better fit, for example by adding more features to the n_features of the X matrix passed on to svm.fit(X,y).
And of course it can always be useful to plot the precision/recall to get a better feel of what the parameters are doing.

Generally speaking you can tackle this problem by penalizing the two types of errors differently during the learning procedure. If you take a look at the loss function, in particular in the primal/parametric setting, you can think of scaling the penalty of false-negatives by alpha and penalty of false-positives by (1 - alpha), where alpha is in [0 1]. (To similar effect would be duplicating the number of positive instances in your training set, but this makes your problem unnecessarily larger, which should be avoided for efficiency)

You can choose the SVM parameter C, which is basically your penalty term, by cross-validation. Here you can use K-Fold cross-validation. You can also use a sklearn class called gridsearchCV in which you can pass your model and then perform cross-validation on it using the cv parameter.
According to linearSVC documentation -
Similar to SVC with parameter kernel=’linear’, but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples.

Related

xgboost: Sample Weights for Imbalanced Data?

I have a highly unbalanced dataset of 3 classes. To address this, I applied the sample_weight array in the XGBClassifier, but I'm not noticing any changes in the modelling results? All of the metrics in the classification report (confusion matrix) are the same. Is there an issue with the implementation?
The class ratios:
military: 1171
government: 34852
other: 20869
Example:
pipeline = Pipeline([
('bow', CountVectorizer(analyzer=process_text)), # convert strings to integer counts
('tfidf', TfidfTransformer()), # convert integer counts to weighted TF-IDF scores
('classifier', XGBClassifier(sample_weight=compute_sample_weight(class_weight='balanced', y=y_train))) # train on TF-IDF vectors w/ Naive Bayes classifier
])
Sample of Dataset:
data = pd.DataFrame({'entity_name': ['UNICEF', 'US Military', 'Ryan Miller'],
'class': ['government', 'military', 'other']})
Classification Report
First, most important: use a multiclass eval_metric. eval_metric=merror or mlogloss, then post us the results. You showed us ['precision','recall','f1-score','support'], but that's suboptimal, or outright broken unless you computed them in a multi-class-aware, imbalanced-aware way.
Second, you need weights. Your class ratio is military: government: other 1:30:18, or as percentages 2:61:37%.
You can manually set per-class weights with xgb.DMatrix..., weights)
Look inside your pipeline (use print or verbose settings, dump values), don't just blindly rely on boilerplate like sklearn.utils.class_weight.compute_sample_weight('balanced', ...) to give you optimal weights.
Experiment with manually setting per-class weights, starting with 1 : 1/30 : 1/18 and try more extreme values. Reciprocals so the rarer class gets higher weight.
Also try setting min_child_weight much higher, so it requires a few exemplars (of the minority classes). Start with min_child_weight >= 2(* weight of rarest class) and try going higher. Beware of overfitting to the very rare minority class (this is why people use StratifiedKFold crossvalidation, for some protection, but your code isn't using CV).
We can't see your other parameters for xgboost classifier (how many estimators? early stopping on or off? what was learning_rate/eta? etc etc.). Seems like you used the defaults - they'll be terrible. Or else you're not showing your code. Distrust xgboost's defaults, esp. for multiclass, don't expect xgboost to give good out-of-the-box results. Read the doc and experiment with values.
Do all that experimentation, post your results, check before concluding "it doesn't work". Don't expect optimal results from out-of-the-box. Distrust or double-check the sklearn util functions, try manual alternatives. (Often, just because sklearn has a function to do something, doesn't mean it's good or best or suitable for all use-cases, like imbalanced multiclass)

Linear regression: Good results for training data, horrible for test data

I am working with a dataset of about 400.000 x 250.
I have a problem with the model yielding a very good R^2 score when testing it on the training set, but extremely poorly when used on the test set. Initially, this sounds like overfitting. But the data is split into training/test set at random and the data set i pretty big, so I feel like there has to be something else.
Any suggestions?
Splitting dataset into training set and test set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(df.drop(['SalePrice'],
axis=1), df.SalePrice, test_size = 0.3)
Sklearn's Linear Regression estimator
from sklearn import linear_model
linReg = linear_model.LinearRegression() # Create linear regression object
linReg.fit(X_train, y_train) # Train the model using the training sets
# Predict from training set
y_train_linreg = linReg.predict(X_train)
# Predict from test set
y_pred_linreg = linReg.predict(X_test)
Metric calculation
from sklearn import metrics
metrics.r2_score(y_train, y_train_linreg)
metrics.r2_score(y_test, y_pred_linreg)
R^2 score when testing on training set: 0,64
R^2 score when testing on testing set: -10^23 (approximatly)
While I agree with Mihai that your problem definitely looks like overfitting, I don't necessarily agree on his answer that neural network would solve your problem; at least, not out of the box. By themselves, neural networks overfit more, not less, than linear models. You need somehow to take care of your data, hardly any model can do that for you. A few options that you might consider (apologies, I cannot be more precise without looking at the dataset):
Easiest thing, use regularization. 400k rows is a lot, but with 250 dimensions you can overfit almost whatever you like. So try replacing LinearRegression by Ridge or Lasso (or Elastic Net or whatever). See http://scikit-learn.org/stable/modules/linear_model.html (Lasso has the advantage of discarding features for you, see next point)
Especially if you want to go outside of linear models (and you probably should), it's advisable to first reduce the dimension of the problem, as I said 250 is a lot. Try using some of the Feature selection techniques here: http://scikit-learn.org/stable/modules/feature_selection.html
Probably most importantly than anything else, you should consider adapting your input data. The very first thing I'd try is, assuming you are really trying to predict a price as your code implies, to replace it by its logarithm, or log(1+x). Otherwise linear regression will try very very hard to fit that single object that was sold for 1 Million $ ignoring everything below $1k. Just as important, check if you have any non-numeric (categorical) columns and keep them only if you need them, in case reducing them to macro-categories: a categorical column with 1000 possible values will increase your problem dimension by 1000, making it an assured overfit. A single column with a unique categorical data for each input (e.g. buyer name) will lead you straight to perfect overfitting.
After all this (cleaning data, reducing dimension via either one of the methods above or just Lasso regression until you get to certainly less than dim 100, possibly less than 20 - and remember that this includes any categorical data!), you should consider non-linear methods to further improve your results - but that's useless until your linear model provides you at least some mildly positive R^2 value on test data. sklearn provides a lot of them: http://scikit-learn.org/stable/modules/kernel_ridge.html is the easiest to use out-of-the-box (also does regularization), but it might be too slow to use in your case (you should first try this, and any of the following, on a subset of your data, say 1000 rows once you've selected only 10 or 20 features and see how slow that is). http://scikit-learn.org/stable/modules/svm.html#regression have many different flavours, but I think all but the linear one would be too slow. Sticking to linear things, http://scikit-learn.org/stable/modules/sgd.html#regression is probably the fastest, and would be how I'd train a linear model on this many samples. Going truly out of linear, the easiest techniques would probably include some kind of trees, either directly http://scikit-learn.org/stable/modules/tree.html#regression (but that's an almost-certain overfit) or, better, using some ensemble technique (random forests http://scikit-learn.org/stable/modules/ensemble.html#forests-of-randomized-trees are the typical go-to algorithm, gradient boosting http://scikit-learn.org/stable/modules/ensemble.html#gradient-tree-boosting sometimes works better). Finally, state-of-the-art results are indeed generally obtained via neural networks, see e.g. http://scikit-learn.org/stable/modules/neural_networks_supervised.html but for these methods sklearn is generally not the right answer and you should take a look at dedicated environments (TensorFlow, Caffe, PyTorch, etc.)... however if you're not familiar with those it is certainly not worth the trouble!

scikit-learn: what is the difference between SVC and SGD?

SVM: http://scikit-learn.org/stable/modules/svm.html#classification
SGD: http://scikit-learn.org/stable/modules/sgd.html#classification
seem to do pretty much the same to my eyes,as they write "an SGD implements a linear model". Can someone explain the differences between them?
SVM is a support-vector machine which is a special linear-model. From a theoretical view it's a convex-optimization problem and we can get the global-optimum in polynomial-time. There are many different optimization-approaches.
In the past people used general Quadratic Programming solvers. Nowadays specialized approaches like SMO and others are used.
sklearn's specialized SVM-optimizers are based on liblinear and libsvm. There are many documents and research papers if you are interested in the algorithms.
Keep in mind, that SVC (libsvm) and LinearSVC (liblinear) make different assumptions in regards to the optimization-problem, which results in different performances on the same task (linear-kernel: LinearSVC much more efficient than SVC in general; but some tasks can't be tackled by LinearSVC).
SGD is an Stochastic Gradient Descent-based (this is a general optimization method!) optimizer which can optimize many different convex-optimization problems (actually: this is more or less the same method used in all those Deep-Learning approaches; so people use it in the non-convex setting too; throwing away theoretical-guarantees).
sklearn says: Stochastic Gradient Descent (SGD) is a simple yet very efficient approach to discriminative learning of linear classifiers under convex loss functions. Now it's actually even more versatile, but here it's enough to note that it subsumes (some) SVMs, logistic-regression and others.
Now SGD-based optimization is very different from QP and others. If one would take QP for example, there are no hyper-parameters to tune. This is a bit simplified, as there can be tuning, but it's not needed to guarantee convergence and performance! (theory of QP-solvers, e.g. Interior-point method is much more robust)
SGD-based optimizers (or general first-order methods) are very very hard to tune! And they need tuning! Learning-rates or learning-schedules in general are parameters to look at as convergence depends on these (theory and practice)!
It's a very complex topic, but some simplified rules:
Specialized SVM-methods
scale worse with the number of samples
do not need hyper-parameter tuning
SGD-based methods
scale better for huge-data in general
need hyper-parameter tuning
solve only a subset of the tasks approachable by the the above (no kernel-methods!)
My opinion: use (the easier to use) LinearSVC as long as it's working, given your time-budget!
Just to make it clear: i highly recommend grabbing some dataset (e.g. from within sklearn) and do some comparisons between those candidates. The need for param-tuning is not a theoretical-problem! You will see non-optimal (objective / loss) results in the SGD-case quite easily!
And always remember: Stochastic Gradient Descent is sensitive to feature scaling docs. This is more or less a consequence of first-order methods.
SVC(SVM) uses kernel based optimisation, where, the input data is transformed to complex data(unravelled) which is expanded thus identifying more complex boundaries between classes. SVC can perform Linear and Non-Linear classification
SVC can perform Linear classification by setting the kernel parameter to 'linear'
svc = SVC(kernel='linear')
SVC can perform non-linear classification by setting the kernel parameter to 'poly' , 'rbf'(default)
svc = SVC(kernel='poly')
svc = SVC(kernel='rbf')
SGDClassifier uses gradient descent optimisation technique, where, the optimum coefficients are identified by iteration process. SGDClassifier can perform only linear classification
SGDClassifer can use Linear SVC(SVM) model when the parameter loss is set to 'hinge'(which is the default) i.e SGDClassifier(loss='hinge')

How to do regression as opposed to classification using logistic regression and scikit learn

The target variable that I need to predict are probabilities (as opposed to labels). The corresponding column in my training data are also in this form. I do not want to lose information by thresholding the targets to create a classification problem out of it.
If I train the logistic regression classifier with binary labels, sk-learn logistic regression API allows obtaining the probabilities at prediction time. However, I need to train it with probabilities. Is there a way to do this in scikits-learn, or a suitable Python package that scales to 100K data points of 1K dimension.
I want the regressor to use the structure of the problem. One such
structure is that the targets are probabilities.
You can't have cross-entropy loss with non-indicator probabilities in scikit-learn; this is not implemented and not supported in API. It is a scikit-learn's limitation.
In general, according to scikit-learn's docs a loss function is of the form Loss(prediction, target), where prediction is the model's output, and target is the ground-truth value.
In the case of logistic regression, prediction is a value on (0,1) (i.e., a "soft label"), while target is 0 or 1 (i.e., a "hard label").
For logistic regression you can approximate probabilities as target by oversampling instances according to probabilities of their labels. e.g. if for given sample class_1 has probability 0.2, and class_2 has probability0.8, then generate 10 training instances (copied sample): 8 withclass_2as "ground truth target label" and 2 withclass_1`.
Obviously it is workaround and is not extremely efficient, but it should work properly.
If you're ok with upsampling approach, you can pip install eli5, and use eli5.lime.utils.fit_proba with a Logistic Regression classifier from scikit-learn.
Alternative solution is to implement (or find implementation?) of LogisticRegression in Tensorflow, where you can define loss function as you like it.
In compiling this solution I worked using answers from scikit-learn - multinomial logistic regression with probabilities as a target variable and scikit-learn classification on soft labels. I advise those for more insight.
This is an excellent question because (contrary to what people might believe) there are many legitimate uses of logistic regression as.... regression!
There are three basic approaches you can use if you insist on true logistic regression, and two additional options that should give similar results. They all assume your target output is between 0 and 1. Most of the time you will have to generate training/test sets "manually," unless you are lucky enough to be using a platform that supports SGD-R with custom kernels and X-validation support out-of-the-box.
Note that given your particular use case, the "not quite true logistic regression" options may be necessary. The downside of these approaches is that it is takes more work to see the weight/importance of each feature in case you want to reduce your feature space by removing weak features.
Direct Approach using Optimization
If you don't mind doing a bit of coding, you can just use scipy optimize function. This is dead simple:
Create a function of the following type:
y_o = inverse-logit (a_0 + a_1x_1 + a_2x_2 + ...)
where inverse-logit (z) = exp^(z) / (1 + exp^z)
Use scipy minimize to minimize the sum of -1 * [y_t*log(y_o) + (1-y_t)*log(1 - y_o)], summed over all datapoints. To do this you have to set up a function that takes (a_0, a_1, ...) as parameters and creates the function and then calculates the loss.
Stochastic Gradient Descent with Custom Loss
If you happen to be using a platform that has SGD regression with a custom loss then you can just use that, specifying a loss of y_t*log(y_o) + (1-y_t)*log(1 - y_o)
One way to do this is just to fork sci-kit learn and add log loss to the regression SGD solver.
Convert to Classification Problem
You can convert your problem to a classification problem by oversampling, as described by #jo9k. But note that even in this case you should not use standard X-validation because the data are not independent anymore. You will need to break up your data manually into train/test sets and oversample only after you have broken them apart.
Convert to SVM
(Edit: I did some testing and found that on my test sets sigmoid kernels were not behaving well. I think they require some special pre-processing to work as expected. An SVM with a sigmoid kernel is equivalent to a 2-layer tanh Neural Network, which should be amenable to a regression task structured where training data outputs are probabilities. I might come back to this after further review.)
You should get similar results to logistic regression using an SVM with sigmoid kernel. You can use sci-kit learn's SVR function and specify the kernel as sigmoid. You may run into performance difficulties with 100,000s of data points across 1000 features.... which leads me to my final suggestion:
Convert to SVM using Approximated Kernels
This method will give results a bit further away from true logistic regression, but it is extremely performant. The process is the following:
Use a sci-kit-learn's RBFsampler to explicitly construct an approximate rbf-kernel for your dataset.
Process your data through that kernel and then use sci-kit-learn's SGDRegressor with a hinge loss to realize a super-performant SVM on the transformed data.
The above is laid out with code here
Instead of using predict in the scikit learn library use predict_proba function
refer here:
http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression.predict_proba

What are good metrics to evaluate the performance of a multi-class classifier?

I'm trying to run a classifier in a set of about 1000 objects, each with 6 floating point variables. I've used scikit-learn's cross validation features to generate an array of the predicted values for several different models. I've then used sklearn.metrics to compute the accuracy of my classifiers, and the confusion table. Most classifiers have around 20-30% accuracy. Below is the confusion table for the SVC classifier (25.4% accuracy).
Since I'm new to machine learning, I'm not sure how to interpret that result, and whether there are other good metrics to evaluate the problem. Intuitively speaking, even with 25% accuracy, and given that the classifier got 25% of the predictions right, I believe it is at least somewhat effective, right? How can I express that with statistical arguments?
If this table is a confusion table, I think that your classifier predicts in majority of the time the class E. I think that your class E is overrepresented in your dataset, accuracy is not a good metric if your classes have not the same number of instances,
Example, If you have 3 classes, A,B,C and in the test dataset the class A is over represented (90%) if your classifier predicts all time class A, you will have 90% of accuracy,
A good metric is to use log loss, logistic regression is a good algorithm that optimize this metric
see https://stats.stackexchange.com/questions/113301/multi-class-logarithmic-loss-function-per-class
An other solution, is to do oversampling of your small classes
First of all, I find it very difficult to look at confusion tables. Plotting it as an image would give a lot better intuitive understanding about what is going on.
It is advisory to have single number metric to optimize since it is easier and faster. When you find that your system doesn't perform as you expect it to, revise your selection of metric.
Accuracy is usually a good metric to use if you have same amount of examples in every class. Otherwise (which seems to be the case here) I'd advise to use F1 score which takes into account both precision and recall of your estimator.
EDIT: However it is up to you to decide if the ~25% accuracy, or whatever metric is "good enough". If you are classifying if robot should shoot a person you should probably revise your algorithm but if you are deciding if it is a pseudo-random or random data, 25% percent accuracy could be more than enough to prove the point.

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