Lasso, Ridge and Elastic Net Regularization

Regularization techniques in Generalized Linear Models (GLM) are used during a modeling process for many reasons. A regularization technique helps in the following main ways-

  1. Doesn’t assume any particular distribution of the dependent variable ( DV). The DV can follow any distribution such as normal, binomial, possison etc. Hence the name Generalized Linear Models (GLMs)
  2. Address Variance-Bias Tradeoffs. Generally will lower the variance from the model
  3. More robust to handle multicollinearity
  4. Better sparse data (observations < features) handling
  5. Natural feature selection
  6. More accurate prediction on new data as it minimizes overfitting on the train data
  7. Easier interpretation of the output

And so on

What is a regularization technique you may ask? A regularization technique is in simple terms a penalty mechanism which applies shrinkage (driving them closer to zero) of coefficient to build a more robust and parsimonious model. Although there are many ways to regularize a model, few of the common ones are-

  1. L1 Regularization aka Lasso Regularization– This add regularization terms in the model which are function of absolute value of the coefficients of parameters. The coefficient of the paratmeters can be driven to zero as well during the regularization process. Hence this technique can be used for feature selection and generating more parsimonious model
  2. L2 Regularization aka Ridge Regularization – This add regularization terms in the model which are function of square of coefficients of parameters. Coefficient of parameters can approach to zero but never become zero and hence
  3. Combination of the above two such as Elastic Nets– This add regularization terms in the model which are combination of both L1 and L2 regularization.

For more on the regularization techniques you can visit this paper.

Scikit help on Lasso Regression

Here is a working example code on the Boston Housing data. Please note, generally before doing regularized GLM regression it is advised to scale variables. However, in the below example we are working with the variables on the original scale to demonstrate each algorithms working.



Ensemble Modeling using Python

Ensemble models are a great tool to fix the variance-bias trade-off which a typical machine learning model faces, i.e. when you try to lower bias, variance will go higher and vice-versa. This generally results in higher error rates.

Total Error in Model = Bias + Variance + Random Noise

Variance and Bias Trade-off

Variance and Bias Trade-off

Ensemble models typically combine several weak learners to build a stronger model, which will reduce variance and bias at the same time. Since ensemble models follow a community learning or divide and conquer approach, output from ensemble models will be wrong only when the majority of underlying learners are wrong.

One of the biggest flip side of ensemble models is that they may become “Black Box” and not very explainable as opposed a simple machine learning model. However, the gains in model performances generally outweigh any loss in transparency. That is the reason why you will see top performing models in many high ranking competitions will be generally an ensemble model.

Ensemble models can be broken down into the following three main categories-

  1. Bagging
  2. Boosting
  3. Stacking

Let’s look at each one of them-


  • One good example of such model is Random Forest
  • These types of ensemble models work on reducing the variance by removing instability in the underlying complex models
  • Each learner is asked to do the classification or regression independently and in parallel and then either a voting or averaging of the output of all the learners is done to create the final output
  • Since these ensemble models are predominantly focuses on reducing the variance, the underlying models are fairly complex ( such as Decision Tree or Neural Network) to begin with low bias
  • An underlying decision tree will have higher depth and many branches. In other words, the tree will be deep and dense and with lower bias


  • Some good examples of these types of models are Gradient Boosting Tree, Adaboost, XGboost among others.
  • These ensemble models work with weak learners and try to improve the bias and variance simultaneously by working sequentially.
  •  These are also called adaptive learners, as learning of one learner is dependent on how other learners are performing. For example, if a certain set of the data has higher mis-classification rate, this sample’s weight in the overall learning will be increased so that the other learners focus more on correctly classifying the tougher samples.
  • An underlying decision tree will shallow and a weak learner with higher bias

There are various approaches for building a bagging model such as- pasting, bagging, random subspaces, random patches etc. You can find all details over here.


  • These meta learning models are what the name suggest. They are stacked models. Or in other words, a particular learner’s output will become an input to another model and so on.

Working examples-

Coming soon….



Deep Learning- Convolution Neural Network (CNN) in Python

Convolution Neural Network (CNN) are particularly useful for spatial data analysis, image recognition, computer vision, natural language processing, signal processing and variety of other different purposes. They are biologically motivated by functioning of neurons in visual cortex to a visual stimuli.

What makes CNN much more powerful compared to the other feedback forward networks for image recognition is the fact that they do not require as much human intervention and parameters as some of the other networks such as MLP do. This is primarily driven by the fact that CNNs have neurons arranged in three dimensions.

CNNs make all of this magic happen by taking a set of input and passing it on to one or more of following main hidden layers in a network to generate an output.

  • Convolution Layers
  • Pooling Layers
  • Fully Connected Layers

Click here to see a live demo of a CNN

Let’s dig deeper into utility of each of the above layers.

Convolution Layers– Before we move this discussion any further, let’s remember that any image or similar object can be represented as a matrix of numbers ranging between 0-255. Size of this matrix will be determined by the size the image in the following fashion-

Height X Width X Channels

Channels =1 for grey-scale images

Channels =3 for colored images

For example, if we feed an image which is 28 by 28 square in pixels and on the grey scale. This image will be a matrix of numbers in the below fashion-

28*28*1. Each of the 784 pixels can any values between 0-255 depending on the intensity of grey-scale.

Now let’s talk about what happens in a convolution layer. The main objective of this layer is to derive features of an image by sliding smaller matrix called kernel or filter over the entire image through convolution.

What is convolution? Convolution is taking a dot product between the filter and the local regions

Kernels can be many types such as edge detection, blob of color, sharpening, blurring etc. You can find some main kernels over here.  Please note that we can specify the number of filters during the network training process, however network will learn the filters on its own.

As a result of this convolution layers, the network creates numbers of features maps. The size of feature maps depends on the # of filters (kernels), size of filters, padding (zero padding to preserve size), and strides (steps by which a filter scans the original image). Please note that a non linear activation function such Relu or Tanh is applied at each convolution layer to generate modified feature maps.



Pooling Layer– The arrays generated from the convolution layers are generally very big and hence pooling layer is used predominantly to reduce the feature maps and retain the most important aspect.  In other words this facilitate “Downsampling” using algorithms such as max pooling or average pooling etc. Moreover, as the numbers of parameters in the network are truncated, this layer also helps in avoiding over fitting.  It is common to have pooling layers in between different convolution layers.

Fully Connected Layer– This enables every neuron in the layers to be interconnected to the neurons from the previous and next layer to take the matrix inputs from the previous layers and flatten it to pass on to the output layer. Which in turn will make prediction such as classification probability.

Here is an excellent write-up which provides further details on all of the above steps.

Since we know enough about how a CNN works, let’s code now-

In this example, we will be working with MNIST dataset and build a CNN to recognize handwritten digits from 0-9. We will be using classification accuracy as a metric to evaluate the model’s performance. Please see link for MNIST CNN working

Please note that CNN need very high amount of computational power and memory and hence it’s recommended that you run this in GPUs or Cloud. CPUs may not be able to fit the model.  Furthermore, you may need to reduce batch size to a lower level to ensure algorithm runs successfully.



As you can see, the above model gives 99%+ accuracy in the classification.


Time-series Forecasting Using Facebook Prophet Package

Forecasting is a technique that is used for a variety of different purposes and situations such as sales forecasting, operational and budget planning etc. Similarly there are a variety of different techniques such as moving averages, smoothening, ARIMA etc to statistically make a forecast.

In this article we will talk about an open source package called “Prophet” from Facebook which takes away the complexity of other techniques without compromising on accuracy of the forecast. The guiding principle of this approach is General Additive Models (GAMs). More on which can be found over here.

Let’s look at an example of how to deploy Prophet in Python.



How to Start Jupyter Notebook From Anaconda Prompt

Jupyter Notebook can be started using many ways, most common ones are-

  1. From the Windows or Mac search interface. Type “Jupyter Notebook” and it should show you to application to start
  2. From Anaconda prompt by typing “jupyter notebook” at the anaconda prompt
  3. For high graphics display such as with plotly package, you are advised to start the jupyter notebook using the following command- “jupyter notebook –NotebookApp.iopub_data_rate_limit=1e10”
Jupyter Notebook Start from Anaconda

Jupyter Notebook Start from Anaconda for High Resolution Graphics

otherwise you can get an error message similar to the one shown below-

IOPub data rate exceeded. The notebook server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--NotebookApp.iopub_data_rate_limit`.

Python Error Message for High Graphics Images


Markov Chains and Markov Model

Markov chains or Markov models are statistical sequential models leveraging probability concepts to predict outcome. This model is named after a Russian mathematician Andrey Markov.  The main guiding principle for Markov chains is that the probability of certain events to happen in the future depend on past events. They can be broken down into different categories-

  • First order Markov model- probability of next event depends on the current event
  • Second order Markov model- probability of the next event depends on the current and the previous event
  • A Hidden Markov Model ( HMM) is where the previous states from which the current state is generated are hidden or unobserved or unknown.

and so on…

Markov models have been proven to be very effective in sequential modeling such as-

  • Speech recognition
  • Handwriting recognition
  • Stock market forecasting
  • Online sales attribution to channels


Here is a pictorial depiction of HMM-



This link has a very good visual explanation of the Markov Models and guiding principles.

R has an in built package called “ChannelAttribution” for solving online multi channel attribution. This package has also an excellent explanation of the Markov Model and working example.

Python also has a library to build Markov models in Python.


Price Elasticity of Demand

Price elasticity of demand (PED) is a measure that has been used in econometric to show how demand of a particular product changes when the price of the product is changed. More particularly, it measures the % change in demand of a product when the price changes by 1%.

It can be expressed as the following formula-


Let’s look at example- Let’s say that demand of a particular Bluetooth headset decreases by 2% when the price is increased by 1%. In this case the PED will be defined as = -2%/1% or -2.

Now, let’s talk about how we interpret PED-

PED of greater than 1 (absolute value) shows highly elastic product. In other words, the change in price will cause a more than proportionate change in demand. This is generally the case with non-essential or luxury products such as the example shown above. On the other hand, PED of less than 1 shows relatively inelastic products such as groceries and daily necessities. Furthermore, for most product PED will be negative, i.e. when the price is increased demand falls.

There are few other practical applications of PED that we should be aware of-

  • PED for a given product or product category can change over time and hence it’s imperative to measure PED over of time.
  • PED for a given product or product category can vary by customer segments. For example, low income customers may have higher PED for the same product
  • Pricing of a product should be optimized taking in account the PED. For example, if a product is showing lower price elasticity or inelasticity, pricing can be increased on the product to maximize revenue

Here is an article that gives some examples from the retail world.

Let’s now step into how we can estimate PED in Python. For this, we will working with the beef price and demand data from USDA Red Meat Yearbook-

You can download the data from here

We will be building a log-log linear model to estimate PED. Please see here for the theoretical discussion on this topic. The coefficient from the log-log linear model shows the PED between two factors.

Let the Python show begin! In the below example PED comes out to be -0.53. It shows that when the price of beef is increased by 1% the demand for beef falls by 0.53%





Recommender Engines

Recommendation engines or systems are all around us. Few common examples are-

  • Amazon- People who buy this also buy this or who viewed this also viewed this
  • Facebook- Friends recommendation
  • Linkedin- Jobs that match you or network recommendation or who viewed this profile also viewed this profile
  • Netflix- Movies recommendation
  • Google- news recommendation, youtube videos recommendation

and so on…

The main objective of these recommendation systems is to do following-

  • Customization or personalizaiton
  • Cross sell
  • Up sell
  • Customer retention
  • Address the “Long Tail” phenomenon seen in Online stores vs Brick and Mortar stores


There are three main approaches for building any recommendation system-

  • Collaborative Filtering

Users and items matrix is built. Normally this matrix is sparse, i.e. most of the cells will be empty. The goal of any recommendation system is to find similarities among the users and items and recommend items which have high probability of being liked by a user given the similarities between users and items.

Similarities between users and items can be assessed using several similarity measures such as Correlation, Cosine Similarities, Jaccard Index, Hamming Distance. The most commonly used similarity measures are Cosine Similarity and Jaccard Index in a recommendation engine

  • Content Based-

This type of recommendation engine focuses on finding the characteristics, attributes, tags or features of the items and recommend other items which have some of the same features. Such as recommend another action movie to a viewer who likes action movies.

  • Hybrid- 

These recommendation systems combine both of the above approaches.

Read more here

Build Recommendation System in Python using ” Scikit – Surprise”-

Now let’s switch gears and see how we can build recommendation engines in Python using a special Python library called Surprise.

This library offers all the necessary tools such as different algorithms (SVD, kNN, Matrix Factorization),  in built datasets, similarity modules (Cosine, MSD, Pearson), sampling and models evaluations modules.

Here is how you can get started

  • Step 1- Switch to Python 2.7 Kernel, I couldn’t make it work in 3.6 and hence needed to install 2.7 as well in my Jupyter notebook environment
  • Step 2- Make sure you have Visual C++ compilers installed on your system as this package requires Cython Wheels. Here are couple of links to help you in this effort

Please note that if you don’t do the Step 2 correctly, you will get errors such as shown below – ” Failed building wheel for Scikit-surprise” or ” Microsoft Visual C++ 14 is required”c1c2

  • Step 3- Install Scikit- Surprise. Please make sure that you have Numpy installed before this

pip install numpy

pip install scikit-surprise

  • Step 4- Import scikit-surprise and make sure it’s correctly loaded

from surprise import Dataset

  • Step 5- Follow along the below examples


Getting Started

Movie Example



Market Basket Analysis or Association Rules or Affinity Analysis or Apriori Algorithm

First of all, if you are not familiar with the concept of Market Basket Analysis (MBA), Association Rules or Affinity Analysis and related metrics such as Support, Confidence and Lift, please read this article first.

Here is how we can do it in Python. We will look at two examples-

Example 1-

Data used for this example can be found here Retail_Data.csv


Example 2-



Linear Discriminant Analysis ( LDA) with Scikit

Linear Discriminant Analysis (LDA) is similar to Principal Component Analysis (PCA) in reducing the dimensionality. However, there are certain nuances with LDA that we should be aware of-

  • LDA is supervised (needs categorical dependent variable) to provide the best linear combination of original variables while providing the maximum separation among the different groups. On the other hand, PCA is unsupervised
  • LDA can be used for classification also, whereas PCA is generally used for unsupervised learning
  • LDA doesn’t need the numbers of discriminant to be passed on ahead of time. Generally speaking the number of discriminant will be lower of the number of variables or number of categories-1.
  • LDA is more robust and can be conducted without even standardizing or normalizing the variables in certain cases
  • LDA is preferred for bigger data sets and machine learning

Let the action begin now-