 logistic regression in python - building classifier - tutorialspoint

It is not required that you have to build the classifier from scratch. Building classifiers is complex and requires knowledge of several areas such as Statistics, probability theories, optimization techniques, and so on. There are several pre-built libraries available in the market which have a fully-tested and very efficient implementation of these classifiers. We will use one such pre-built model from the sklearn.

Once the classifier is created, you will feed your training data into the classifier so that it can tune its internal parameters and be ready for the predictions on your future data. To tune the classifier, we run the following statement logistic regression

Despite having regression in its name, a logistic regression is actually a widely used binary classifier (i.e. the target vector can only take two values). In a logistic regression, a linear model (e.g. $\beta_{0}+\beta_{1}x$) is included in a logistic (also called sigmoid) function, ${\frac{1}{1+e^{-z}}}$, such that:

where $P(y_i=1 \mid X)$ is the probability of the $i$th observations target value, $y_i$, being class 1, $X$ is the training data, $\beta_0$ and $\beta_1$ are the parameters to be learned, and $e$ is Eulers number. logistic regression r | introduction to logistic regression

Every machine learning algorithm works best under a given set of conditions. Making sure your algorithm fits the assumptions/requirements ensures superior performance. You cant use any algorithm in any condition. For example: Have you ever tried using linear regression on a categorical dependent variable? Dont even try! Because you wont be appreciated for getting extremely low values of adjusted R and F statistic.

Instead, in such situations, you should try using algorithms such as Logistic Regression, Decision Trees, SVM, Random Forest etc. To get a quick overview of these algorithms, Ill recommend reading Essentials of Machine Learning Algorithms.

With this post, Igive you usefulknowledge on Logistic Regression in R. After youve mastered linear regression, this comes as the natural following step in your journey. Its also easy to learn and implement, but you must know the science behind this algorithm.

However, the collection, processing, and analysis of data have been largely manual, and given the nature of human resources dynamics and HR KPIs, the approach has been constraining HR. Therefore, it is surprising that HR departments woke up to the utility of machine learning so late in the game. Here is an opportunity to try predictive analytics in identifying the employees most likely to get promoted.

Logistic Regression is a classification algorithm. It is used to predict a binary outcome (1 / 0, Yes / No, True / False) given a set of independent variables. To represent binary/categorical outcome, we use dummy variables. You can also think of logistic regression as a special case of linear regression when the outcome variable is categorical, where we are using log of odds as dependent variable. In simple words, it predicts the probability of occurrence of an event by fitting data to a logit function.

Logistic Regression is part of a larger class of algorithms known as Generalized Linear Model (glm). In 1972, Nelder and Wedderburn proposed this model with an effort to provide a means of using linear regression to the problems which were not directly suited for application of linear regression. Infact, they proposed a class of different models (linear regression, ANOVA, Poisson Regression etc) which included logistic regression as a special case.

Here, g() is the link function, E(y) is the expectation of target variable and +x1 +x2 is the linear predictor (,, to be predicted). The role of link function is to link the expectation of y to linear predictor.

We are provided a sample of 1000 customers. We need to predict the probability whether a customer will buy (y) a particular magazine or not. As you can see, weve a categorical outcome variable, well use logistic regression.

In logistic regression, we are only concerned about the probability of outcome dependent variable ( success or failure). As described above, g() is the link function. This function is established usingtwo things: Probability of Success(p) and Probability of Failure(1-p). p should meet following criteria:

This is the equation used in Logistic Regression. Here (p/1-p) is the odd ratio. Whenever the log of odd ratio is found to be positive, the probability of success is always more than 50%. A typical logistic model plot is shown below. You can see probability never goes below 0 and above 1.

1. AIC (Akaike Information Criteria) The analogous metric of adjusted Rin logistic regression is AIC. AIC is the measure of fit which penalizes model for the number of model coefficients. Therefore, we always prefer model with minimum AIC value.

2. Null Deviance and Residual Deviance Null Deviance indicates the response predicted by a model with nothing but an intercept. Lower the value, better the model. Residual deviance indicates the response predicted by a model on adding independent variables. Lower the value, better the model.

4. ROC Curve:Receiver Operating Characteristic(ROC) summarizes the models performance by evaluating the trade offs between true positive rate (sensitivity) and false positive rate(1- specificity). For plotting ROC, it is advisable to assume p > 0.5 since we are more concerned about success rate. ROC summarizes the predictive power for all possible values of p > 0.5. The area under curve (AUC), referred to as index of accuracy(A) or concordance index, is a perfect performance metric for ROC curve. Higher the area under curve, better the prediction power of the model. Below is a sample ROC curve. The ROC of a perfect predictive model has TP equals 1 and FP equals 0. This curve will touch the top left corner of the graph.

Note: For model performance, you can also consider likelihood function. It is called so, because it selects the coefficient values which maximizes the likelihood of explaining the observed data. It indicates goodness of fit as its value approaches one, and a poor fit of the data as its value approaches zero.

This data require lots of cleaning and feature engineering. The scope of this article restricted me to keep the example focused on building logistic regression model. This data is available for practice. Id recommend you to work on this problem. Theres a lot to learn.

By now, you would know the science behind logistic regression. Ive seen many times that people know the use of this algorithm without actually having knowledge about its core concepts. Ive tried my best to explain this part in simplest possible manner. The example above only shows the skeleton of using logistic regression in R. Before actually approaching to this stage, you must invest your crucial time in feature engineering.

And the minimum AIC is the better the model is going to be that we know; Can you suggest some way to say whether this AIC is good enough and how do we justify that there will not be any good possible model having lower AIC; And also I want to know some more details about this criterion to check the model;

Thanks for your appreciation. Kudos to my team indeed. You should not consider AIC criterion in isolation. Like, youve run this model and got some AIC value. You must be thinking, what to do next? You cant do anything unless you build another model and then compare their AIC values. Model with lower AIC should be your choice. Always.

Number of Fisher Scoring iterations is a derivative of Newton-Raphson algorithm which proposes how the model was estimated. In your case, it can be interpreted as, Fisher scoring algorithm took 18 iterations to perform the fit. This metric doesnt tell you anything which you must know. It just confirms the model convergence. Thats it.

I am working on a project where I am building a model on transaction-wise data; there are some 5000 customer and among them 1200 churned till data; and total transaction is 4.5 Lacs out of that 1 lacs is for the churned and rest is for non churned; Now i am trying to build the model marking those 1 Lacs as 1 and rest all as 0; and took some sample of that; say of 120000 rows; here 35 K rows have marked as 1 and rest all 0; the ratio > 15% so we can go for logistic; (as i know) now when i built the model transaction wise this accuracy from confusion matrix is coming as 76% and when we applt the model in the entire dataset, and aggregated customerwise by doing customerwise averaging the predicted transaction probabilities; and in this case out of 5000 customer, A1P1=950, A1P0=250, A0P0= 3600, A0P1=200 and hence accuracy is 91%; do u think i can feel that this model is pretty good?? in this case i made 5-6 models and the minimum AIC and corresponding tests gave me the confidence to select this model;

For example I have 10 k customers demographic data; credit number age salary income # ofchildren 2323323232 32 23k 3l 2 545433433 27 45k 6l 3 so on I am not sure how to use macro economic factors like un-employment rate , GDP,. in this logistic model. because the macro eco data is time dependent. PLease help me to work on this type of data. Thanks in advance Rajanna

You can also add Wald statistics used to test the significance of the individual coefficients and pseudo R sqaures like R^2 logit = {-2LL(of null model) (-2LL(of proposed model)}/ (-2LL (of null model)) used to check the overall significance of the model.

I ran 10 fold Cross validation on titanic survivor data using logit model. I got varying values of accuracy (computed using confusion matrix) and their respective AIC: Accuracy AIC 1 0.797 587.4 2 0.772 577.3 3 0.746 587.7 4 0.833 596.1 5 0.795 587.7 6 0.844 600.3 7 0.811 578.8 8 0.703 568.4 9 0.768 584.6 10 0.905 614.8

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SGDClassifier is a generalized linear classifier that will use Stochastic Gradient Descent as a solver. As it is mentionned here http://scikit-learn.org/stable/modules/sgd.html : "Even though SGD has been around in the machine learning community for a long time, it has received a considerable amount of attention just recently in the context of large-scale learning." It is easy to implement and efficient. For example, this is one of the solvers that is used for Neural Networks.

With SGDClassifier you can use lots of different loss functions (a function to minimize or maximize to find the optimum solution) that allows you to "tune" your model and find the best sgd based linear model for your data. Indeed, some data structures or some problems will need different loss functions.

In your example, the SGD classifier will have the same loss function as the Logistic Regression but a different solver. Depending on your data, you can have different results. You may try to find the best one using cross validation or even try a grid search cross validation to find the best hyper-parameters.

Basically, SGD is like an umbrella capable to facing different linear functions. SGD is an approximation algorithm like taking single single points and as the number of point increases it converses more to the optimal solution. Therefore, it is mostly used when the dataset is large. Logistic Regression uses Gradient descent by default so its slower (if compared on large dataset) To make SGD perform well for any particular linear function, lets say here logistic Regression we tune the parameters called hyperparameter tuning

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Text classification is the automatic process of predicting one or more categories given a piece of text. For example, predicting if an email is legit or spammy. Thanks to Gmails spam classifier, I dont see or hear from spammy emails!

Other than spam detection, text classifiers can be used to determine sentiment in social media texts, predict categories of news articles, parse and segment unstructured documents, flag the highly talked about fake news articles and more.

Text classifiers work by leveraging signals in the text to guess the most appropriate classification. For example, in a sentiment classification task, occurrences of certain words or phrases, like slow,problem,wouldn't and not can bias the classifier to predict negative sentiment.

The nice thing about text classification is that you have a range of options in terms of what approaches you could use. From unsupervised rules-based approaches to more supervised approaches such as Naive Bayes, SVMs, CRFs and Deep Learning.

In this article, we are going to learn how to build and evaluate a text classifier using logistic regression on a news categorization problem. The problem while not extremely hard, is not as straightforward as making a binary prediction (yes/no, spam/ham).

Heres the full source code with accompanying dataset for this tutorial. Note that this is a fairly long tutorial and I would suggest that you break it down to several sessions so that you completely grasp the concepts.

The dataset that we will be using for this tutorial is from Kaggle. It contains news articles from Huffington Post (HuffPost) from 2014-2018 as seen below. This data set has about ~125,000 articles and 31 different categories.

Without the actual content of the article itself, the data that we have for learning is actually pretty sparse a problem you may encounter in the real world. But lets see if we can still learn from it reasonably well. We will not use the author field because we want to test it on articles from a different news organization, specifically from CNN.

In this tutorial, we will use the Logistic Regression algorithm to implement the classifier. In my experience, I have found Logistic Regression to be very effective on text data and the underlying algorithm is also fairly easy to understand. More importantly, in the NLP world, its generally accepted that Logistic Regression is a great starter algorithm for text related classification.

Features are attributes (signals) that help the model learn. This can be specific words from the text itself (e.g. all words, top occurring terms, adjectives) or additional information inferred based on the original text (e.g. parts-of-speech, contains specific phrase patterns, syntactic tree structure).

For this task, we have text fields that are fairly sparse to learn from. Therefore, we will try to use all words from several of the text fields. This includes the description, headline and tokens from the url. The more advanced feature representation is something you should try as an exercise.

Not all words are equally important to a particular document / category. For example, while words like murder, knife and abduction are important to a crime related document, words like news and reporter may not be quite as important.

In this tutorial, we will be experimenting with 3 feature weighting approaches. The most basic form of feature weighting, is binary weighting. Where if a word is present in a document, the weight is 1 and if the word is absent the weight is 0.

There are of course many other methods for feature weighting. The approaches that we will experiment with in this tutorial are the most common ones and are usually sufficient for most classification tasks.

One of the most important components in developing a supervised text classifier is the ability to evaluate it. We need to understand if the model has learned sufficiently based on the examples that it saw in order to make correct predictions.

For this particular task, even though the HuffPost dataset lists one category per article, in reality, an article can actually belong to more than one category. For example, the article in Figure 4 could belong to COLLEGE (the primary category) or EDUCATION.

If the classifier predicts EDUCATION as its first guess instead of COLLEGE, that doesnt mean its wrong. As this is bound to happen to various other categories, instead of looking at the first predicted category, we will look at the top 3 categories predicted to compute (a) accuracy and (b) mean reciprocal rank (MRR).

Accuracy evaluates the fraction of correct predictions. In our case, it is the number of times the PRIMARY category appeared in the top 3 predicted categories divided by the total number of categorization tasks.

where Q here refers to all the classification tasks in our test set and rank_{i} is the position of the correctly predicted category. The higher the rank of the correctly predicted category, the higher the MRR.

Since we are using the top 3 predictions, MRR will give us a sense of where the PRIMARY category is at in the ranks. If the rank of the PRIMARY category is on average 2, then the MRR would be ~0.5 and at 3, it would be ~0.3. We want to get the PRIMARY category higher up in the ranks.

Next, we will be creating different variations of the text we will use to train the classifier. This is to see how adding more content to each field, helps with the classification task. Notice that we create a field using only the description, description + headline, and description + headline + url (tokenized).

Earlier, we talked about feature representation and different feature weighting schemes. In extract_features() from above, is where we extract the different types of features based on the weighting schemes.

First, note that cv.fit_transform(...) from the above code, snippet creates a vocabulary based on the training set. Next, cv.transform() takes in any text (test or unseen texts) and transforms it according to the vocabulary of the training set, limiting the words by the specified count restrictions (min_df, max_df) and applying necessary stop words if specified. It returns a term-document matrix where each column in the matrix represents a word in the vocabulary while each row represents the documents in the dataset. The values could either be binary or counts. The same concept also applies to tfidf_vectorizer.fit_transform(...) and tfidf_vectorizer.transform().

The code below shows how we start the training process. When you instantiate the LogisticRegression module, you can vary the solver, the penalty, the C value and also specify how it should handle the multi-class classification problem (one-vs-all or multinomial). By default, a one-vs-all approach is used and thats what were using below:

In a one-vs-all approach that we are using above, a binary classification problem is fit for each of our 31 labels. Since we are selecting the top 3 categories predicted by the classifier (see below), we will leverage the estimated probabilities instead of the binary predictions. Behind the scenes, we are actually collecting the probability of each news category being positive.

You can see that the accuracy is 0.59 and MRR is 0.48. This means that only about 59% of the PRIMARY categories are appearing within the top 3 predicted labels. The MRR also tells us that the rank of the PRIMARY category is between positions 2 and 3. Lets see if we can do better. Lets try a different feature weighting scheme.

This second model uses tf-idf weighting instead of binary weighting using the same description field. You can see that the accuracy is 0.63 and MRR is 0.51 a slight improvement. This is a good indicator that the tf-idf weighting works better than binary weighting for this particular task.

How else can we improve our classifier? Remember, we are only using the description field and it is fairly sparse. What if we used the description, headline and tokenized URL, would this help? Lets try it.

Now, look! As you can see in Figure 8, the accuracy is 0.87 and MRR is 0.75, a significant jump. Now we have about 87% of the primary categories appearing within the top 3 predicted categories. In addition, more of the PRIMARY categories are appearing at position 1. This is good news!

Overall, not bad, huh? The predicted categories make a lot of sense. Note that in the above predictions, we used the headline text. To further improve the predictions, we can enrich the text with the URL tokens and description.

Once we have fully developed the model, we want to use it later on unseen documents. Doing this is actually straightforward with sklearn. First, we have to save the transformer to later encode/vectorize any unseen document. Next, we also need to save the trained model so that it can make predictions using the weight vectors. Heres how you do it:

Heres the full source code with the accompanying dataset for this tutorial. I hope this article has given you the confidence in implementing your very own high-accuracy text classifier.Keep in mind that text classification is an art as much as it is a science. Your creativity when it comes to text preprocessing, evaluation and feature representation will determine the success of your classifier.A one-size-fits-all approach is rare. What works for this news categorization task, may very well be inadequate for something like bug detection in source code.

Right now, we are at 87% accuracy. How can we improve the accuracy further? What else would you try? Leave a comment below with what you tried, and how well it worked. Aim for a 90-95% accuracy and let us all know what worked!

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