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Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Big Data to Small Data – Welcome to the World of Reservoir Sampling

Sreenath
Sreenath Last Updated : 24 Nov, 2020
3 min read

This article was published as a part of the Data Science Blogathon.

Introduction

Big Data refers to a combination of structured and unstructured data that may be measured in petabytes or exabytes. Usually, we make use of 3Vs to characterize big data 3Vs, being, the volume of data, the variety of types of data, and the velocity at which it is processed.

These three characteristics make it difficult to handle big data. Big data is hence expensive in terms of investment in a whole lot of server storage, sophisticated analytics machines, and data mining methodologies. Many organizations are finding this cumbersome both technically as well as economically and hence are thinking about how to achieve similar results can be achieved using much fewer sophistications. Hence they are trying to convert big data to small data, which consists of usable chunks of data. The following figure [1] shows a comparison.

 

Volume vs Effectiveness

Let’s try to explore a simple statistical technique, which can be used to create a usable chunk of data from big data. The sample which is basically a subset of the population should be selected in such a way that it represents the population properly. This can be ensured by employing statistical testing.

 

Introduction to Reservoir Sampling

The key idea behind reservoir sampling is to create a ‘reservoir’ from a big ocean of data. Let ‘N’ be the population size and ‘n’ be the sample size. Each element of the population has an equal probability of being present in the sample and that probability is (n/N). With this key idea, we have to create a subsample. It has to be noted, when we create a sample, the distributions should be identical not only row-wise but also column-wise.

Usually, we focus only on the rows, but it is important to maintain the distribution of the columns as well. Columns are the features from which the training algorithm learns. Hence, we have to perform statistical tests for each feature as well to ensure the distribution is identical.

The algorithm goes this way: Initialize the reservoir with first ‘n’ elements of the population of size ‘N’. Then read each row of your dataset (i > n). At each iteration, compute (n/i). We replace the elements of the reservoir from the next set of ‘n’ elements with a gradually decreasing probability.

for i = 1 to n:

R[i] = S[i] 

for i = n+1 to N:

j = U ~ [1, i]

if j <= n:

R[j] = S[i]

 

Statistical Tests

As I mentioned, earlier we have to ensure that all the columns(features) in the reservoir are distributed identically to the population. We shall use the Kolmogorov-Smirnov test for continuous features and Pearson’s chi-square test for categorical features.

Kolmogorov-Smirnov test is used to check whether the cumulative distribution functions (CDF) of the population and sample are the same. We compare the CDFs of population F_N (x) with that of the sample F_n(x).

𝐹𝑁𝑥

Reservoir sampling - Kolmogorov-Smirnov test

As n -> N, D_n -> 0, if the distributions are identical. This test has to be performed for all the features of the data set that are continuous.

For the categorical features, we can perform Pearson’s chi-square test. Let O_i be the number of observations of the category ‘i’ and ne be the number of samples. Let E_i be the expected count of category ‘i’. Then E_i = N p_i, where p_i is the probability from being of the category ‘i’. Then chi-square value is given by the following relation:

Reservoir sampling - Chi-square test

If chi-square = 0, then that means observed values and expected values are the same. If the p-value of the statistical test is greater than the significance level, then we say that the sample is statistically significant.

 

End Notes

Reservoir sampling can be used to create a useful chunk of data from big data provided that both the tests – Kolmogorov-Smirnov and Pearson’s chi-square is successful. The recent buzz is of course big data. Centralized models as in big data architecture come along with big difficulties. To decentralize things and thus making the work modular we have to create useful small chunks of data and then get meaningful insights from them. I think more efforts should come in this direction, rather than investing in architecture to support big data!

 

References

1. https://www.bbvaopenmind.com/en/technology/digital-world/small-data-vs-big-data-back-to-the-basics/

Big datablogathonreservoir samplingSamplingstatistics
Sreenath
Sreenath

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Responses From Readers

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Mona
Mona

Statistic is a real life. Traditional and non-traditional methods. Please keep be updated with all statistics new subjects. My personal regards Dr/ Mona

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Top 100 Data Science Interview Questions & Answers 2024
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What is big data and how is big data architecture designed?
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