Arnab Chattopadhyay’s Post

Here’s what most people get wrong about correlation 🧩 . . Correlation measures how two features vary with one another linearly (or monotonically). This makes the correlation symmetric: corr(A, B) = corr(B, A). Yet, associations are often asymmetric. For instance, given a date, it is easy to tell the month. But given a month, you can never tell the date. But correlation, being symmetric, entirely ignores this notion. What’s more, it is not meant to quantify how well a feature can predict the outcome. Yet, at times, it is misinterpreted as a measure of “predictiveness”. Lastly, correlation is mostly limited to numerical data. But categorical data is equally important for predictive models. The Predictive Power Score (PPS) addresses each of these limitations. As the name suggests, it measures the predictive power of a feature. PPS(a → b) is calculated as follows: - If target (b) is numeric: Train a Decision Tree Regressor that predicts b using a. Find PPS by comparing its MAE to the MAE baseline model (median prediction). - If target (b) is categorical: Train a Decision Tree Classifier that predicts b using a. Find PPS by comparing its F1 to the F1 of a baseline model (random or most frequent prediction). Thus, PPS: - is asymmetric, meaning PPS(a, b) != PPS(b,a). - can be used on categorical data. - can be used to measure the predictive power of categorical features (a). - works well for linear and non-linear relationships. - works well for monotonic and non-monotonic relationships. Its effectiveness is evident from the image below. For all three datasets: - correlation is low. - PPS (x → y) is high. - PPS (y → x) is zero. That being said, it is important to note that correlation has its place. When selecting between PPS and correlation, first set a clear objective about what you wish to learn about the data: - Do you want to know the general monotonic trend between two variables? Correlation will help. - Do you want to know the predictiveness of a feature? PPS will help. -- 👉 Get a Free Data Science PDF (550+ pages) with 320+ posts by subscribing to my daily newsletter today: https://lnkd.in/gzfJWHmu -- 👉 Over to you: What other points will you add here about PPS vs. Correlation?

In the realm of data analysis, adjusted R-squared stands as a vital tool, helping us navigate the complexity of statistical models. But what exactly is it, and how can it guide our decisions? 🔍 Understanding Adjusted R-squared: - It's a statistical measure that evaluates the goodness of fit of a regression model. - Unlike plain R-squared, adjusted R-squared considers the number of predictors in the model, offering a more accurate reflection of model performance. ✅ Pros: - Takes Complexity into Account: Adjusted R-squared adjusts for the number of predictors, guarding against overfitting. - Better Model Comparison: It facilitates fair comparisons between models with different numbers of predictors. - Reflects Model Fit: Provides insights into how well the model fits the data, aiding in interpretation. ❌ Cons: - Can't Detect Overfitting Completely: While it helps mitigate overfitting, it doesn't eradicate the risk entirely. - May Penalize Complexity: In some cases, overly penalizing complex models may lead to overly simplistic conclusions. 🤔 When to Use Adjusted R-squared to Determine Variable Removal: - When assessing whether additional variables significantly improve model fit. - When aiming to strike a balance between model complexity and explanatory power. - When comparing models with different numbers of predictors. Consider the graph below, illustrating two different regression models. Based on the adjusted R-squared and model complexity, I would choose the second model, which excludes the 'life' and 'generosity' predictors. This model has a slightly lower adjusted R-squared but maintains a good fit while being less complex, striking a better balance between explanatory power and model simplicity. Note: Adjusted R-squared isn't considered state-of-the-art due to the emergence of more advanced statistical techniques and machine learning algorithms that offer greater complexity and flexibility in model evaluation and prediction. However, it remains valuable due to its simplicity, quick insights, and historical context. Its ease of interpretation and ability to aid in fair model comparison make it a practical choice for initial model evaluation and decision-making. Explore my webinar titled "Data Analysis & Visualization in R," where I delve into regression model comparison and explain the nuances of adjusted R-squared. More details are available at this link: https://lnkd.in/eVXD2x78 #datastructure #bigdata #visualanalytics #statisticsclass #datascienceeducation #rstats

Why 1-model fits them all (demand/product) will fail! Do this 4-step Approach instead to boost Demand Predictability This is the second post in this week's series with focus on Forecasting Demand. (You want a summary: sign up here: https://scmsync.com/) Today I dissect and reconstruct the narrative that no singular model can master the diversity of product demand. The Premise: Conventional wisdom may suggest a universal approach to demand prediction, yet the nuanced stages of a product's lifecycle—introduction, growth, maturity, and decline—demand tailored analytical frameworks. A singular forecasting model is inadequate to address the varying degrees of data availability and predictability inherent to each phase. Do it better with this 4-step approach, following the attached graph: 1st-step - Lifecycle-Dependent Data Characteristics: During the introductory phase, sparse data and erratic demand patterns predominate, rendering high predictability elusive and often necessitating more fundamental, adaptive models. Contrastingly, the growth and maturity stages, characterized by data enrichment, allow for the deployment of advanced predictive models such as LightGBM, XGBoost, and LSTM networks, which promise enhanced accuracy. 2nd-step - Feature Identification and Lifecycle Correlation: As indicated in the accompanying figure (Table), specific features such as volatility and intermittency serve as indicators of lifecycle stages. The initial phase may exhibit heightened volatility, while regularity could signify a transition into the growth phase. It is essential to quantify these features as indicators of predictability. 3rd-step - Clustering for Enhanced Model Discrimination: Cluster analysis emerges as a potent tool for discerning distinct demand profiles, laying the groundwork for developing bespoke models for each cluster. This granular approach ensures that each model is finely attuned to the specific demand signals of its cluster. 4th-step - Constructing Cluster-Specific Models and Ensembling: The subsequent step involves architecting predictive models tailored to the identified clusters. The crescendo of this symphony is the assembly of these models into an ensemble—a 'superlearner' that synthesizes the disparate predictive strengths of each model into a cohesive, overarching forecasting mechanism. The transition from a monolithic to a multi-model approach model not only mirrors the heterogeneity of product demand but also capitalizes on it, engendering a substantial return on investment. === Have you experienced the limitations of one-size-fits-all models? Comment below. Follow me, if you like such content. Share, if you know people who like it. Sign up, to my newsletter: scmsync.com #DemandForecasting #Analytics #SCM #SupplyChain #ProductLifecycle #MachineLearning #Forecasting #Optimization #EnsembleLearning #Prediction #DataScience #Finance #ROI #Energy #Clustering #Ensemble #inventory #planning 🔥 Matt Dancho 🔥

In the realm of data analysis, adjusted R-squared stands as a vital tool, helping us navigate the complexity of statistical models. But what exactly is it, and how can it guide our decisions? 🔍 Understanding Adjusted R-squared: - It's a statistical measure that evaluates the goodness of fit of a regression model. - Unlike plain R-squared, adjusted R-squared considers the number of predictors in the model, offering a more accurate reflection of model performance. ✅ Pros: - Takes Complexity into Account: Adjusted R-squared adjusts for the number of predictors, guarding against overfitting. - Better Model Comparison: It facilitates fair comparisons between models with different numbers of predictors. - Reflects Model Fit: Provides insights into how well the model fits the data, aiding in interpretation. ❌ Cons: - Can't Detect Overfitting Completely: While it helps mitigate overfitting, it doesn't eradicate the risk entirely. - May Penalize Complexity: In some cases, overly penalizing complex models may lead to overly simplistic conclusions. 🤔 When to Use Adjusted R-squared to Determine Variable Removal: - When assessing whether additional variables significantly improve model fit. - When aiming to strike a balance between model complexity and explanatory power. - When comparing models with different numbers of predictors. Consider the graph below, illustrating two different regression models. Based on the adjusted R-squared and model complexity, I would choose the second model, which excludes the 'life' and 'generosity' predictors. This model has a slightly lower adjusted R-squared but maintains a good fit while being less complex, striking a better balance between explanatory power and model simplicity. Note: Adjusted R-squared isn't considered state-of-the-art due to the emergence of more advanced statistical techniques and machine learning algorithms that offer greater complexity and flexibility in model evaluation and prediction. However, it remains valuable due to its simplicity, quick insights, and historical context. Its ease of interpretation and ability to aid in fair model comparison make it a practical choice for initial model evaluation and decision-making. Explore my webinar titled "Data Analysis & Visualization in R," where I delve into regression model comparison and explain the nuances of adjusted R-squared. Learn more by visiting this link: https://lnkd.in/dcW8Wq9u #bigdata #dataviz #advancedanalytics #datavisualization #analysisskills #datastructure #rprogramminglanguage

 🚀Exploring Affinity Propagation for High-Dimensional Data Clustering 🚀 Recently, I had the opportunity to dive deep into the world of clustering algorithms and discovered a gem that seems to be flying under the radar: Affinity Propagation. For those who might not be familiar, Affinity Propagation is a unique algorithm that doesn't require the number of clusters to be pre-specified, unlike traditional methods such as k-means. Instead, it automatically identifies the optimal number of clusters by passing messages between data points until convergence. In my recent project, I used Affinity Propagation on high-dimensional text embeddings. Here’s what I found: - Number of Clusters Identified: Affinity Propagation suggested around 40 clusters for my dataset. - Comparison with K-Means: When I applied k-means (using methods to determine the optimal number of clusters), it identified only 12 clusters. What's intriguing is that the clusters formed by Affinity Propagation provided a much better representation of the high-dimensional data, capturing nuances and complexities that k-means seemed to overlook. This is particularly crucial when dealing with text data, where subtle differences can carry significant meaning. 💡 Key Takeaways: -Flexibility: No need to pre-define the number of clusters. The algorithm determines it for you! -High-Dimensional Suitability: Excels in handling complex, high-dimensional datasets like text embeddings. -Enhanced Clustering Quality: Identifies more nuanced clusters, which can lead to better insights. I encourage data enthusiasts to explore Affinity Propagation as an alternative to k-means, especially for high-dimensional data. It might just uncover the hidden structures in your dataset that you didn't know existed!

The model that will result in the best profit, that model that can gain more customer, and that model that will result in a higher year-end bonus.... 💅🥰

🎯 𝗙𝗲𝗮𝘁𝘂𝗿𝗲 𝗦𝗲𝗹𝗲𝗰𝘁𝗶𝗼𝗻: 𝗠𝗮𝗸𝗶𝗻𝗴 𝗖𝗹𝗲𝗮𝗿 𝗖𝗵𝗼𝗶𝗰𝗲𝘀 𝗳𝗼𝗿 𝗬𝗼𝘂𝗿 𝗠𝗼𝗱𝗲𝗹𝘀! 🔍 Ever felt overwhelmed by a sea of features in your dataset? 🌊 It’s time to bring some clarity with Feature Selection! This critical step in data preprocessing helps you finding the most relevant features, ensuring your model performs at its best without unnecessary complexity. Let’s dive into the essentials of Feature Selection and why it’s a game-changer in your data science journey. 🚀 🔷 𝗪𝗵𝗮𝘁 𝗜𝘀 𝗙𝗲𝗮𝘁𝘂𝗿𝗲 𝗦𝗲𝗹𝗲𝗰𝘁𝗶𝗼𝗻? Feature Selection is the process of identifying and selecting the most important features (variables) in your dataset. By focusing on the most relevant features, you can improve model performance, reduce overfitting, and make your model easier to interpret. 🎯 🔷 𝗪𝗵𝘆 𝗜𝘁’𝘀 𝗜𝗺𝗽𝗼𝗿𝘁𝗮𝗻𝘁? Reduces Overfitting: By eliminating irrelevant features, your model is less likely to fit noise in the data. 🛡️ Improves Accuracy: Relevant features enhance the model’s ability to make accurate predictions. 📈 Boosts Efficiency: Fewer features mean faster training and prediction times. ⏱️ Enhances Interpretability: Simpler models are easier to understand and interpret. 🔍 🔷 𝗠𝗲𝘁𝗵𝗼𝗱𝘀 𝗳𝗼𝗿 𝗙𝗲𝗮𝘁𝘂𝗿𝗲 𝗦𝗲𝗹𝗲𝗰𝘁𝗶𝗼𝗻 Filter Methods: Use statistical techniques to score features independently of the model. Examples include: Correlation Coefficient: Measure the relationship between features and target. Chi-Square Test: Assess the independence of categorical variables. ANOVA: Evaluate the variance between groups of features. 📊 Wrapper Methods: Use a predictive model to evaluate feature subsets. Examples include: Forward Selection: Start with no features and add one at a time. Backward Elimination: Start with all features and remove one at a time. Recursive Feature Elimination (RFE): Repeatedly fit the model and remove the least important features. 🔄 Embedded Methods: Incorporate feature selection as part of the model training process. Examples include: Lasso Regression: Regularization technique that penalizes less important features. Tree-Based Methods: Algorithms like Random Forest and Gradient Boosting inherently perform feature selection. 🌳 🔷 𝗧𝗵𝗲 𝗣𝗿𝗮𝗰𝘁𝗶𝗰𝗮𝗹 𝗔𝗽𝗽𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻 Start with a Large Set: Begin with all features to ensure you don’t miss any potentially valuable ones. Apply Feature Selection Methods: Use a combination of filter, wrapper, and embedded methods to identify the best features. Validate Your Model: Check if feature selection improves model performance using cross-validation. 🎬 𝗧𝗵𝗲 𝗙𝗶𝗻𝗮𝗹 𝗦𝗰𝗲𝗻𝗲 Feature Selection is like fine-tuning a musical instrument—getting rid of the noise and focusing on the notes that truly matter. Whether you’re dealing with hundreds of features or just a handful, applying the right feature selection techniques can lead to more accurate and efficient models.

In the realm of data analysis, adjusted R-squared stands as a vital tool, helping us navigate the complexity of statistical models. But what exactly is it, and how can it guide our decisions? 🔍 Understanding Adjusted R-squared: - It's a statistical measure that evaluates the goodness of fit of a regression model. - Unlike plain R-squared, adjusted R-squared considers the number of predictors in the model, offering a more accurate reflection of model performance. ✅ Pros: - Takes Complexity into Account: Adjusted R-squared adjusts for the number of predictors, guarding against overfitting. - Better Model Comparison: It facilitates fair comparisons between models with different numbers of predictors. - Reflects Model Fit: Provides insights into how well the model fits the data, aiding in interpretation. ❌ Cons: - Can't Detect Overfitting Completely: While it helps mitigate overfitting, it doesn't eradicate the risk entirely. - May Penalize Complexity: In some cases, overly penalizing complex models may lead to overly simplistic conclusions. 🤔 When to Use Adjusted R-squared to Determine Variable Removal: - When assessing whether additional variables significantly improve model fit. - When aiming to strike a balance between model complexity and explanatory power. - When comparing models with different numbers of predictors. Consider the graph below, illustrating two different regression models. Based on the adjusted R-squared and model complexity, I would choose the second model, which excludes the 'life' and 'generosity' predictors. This model has a slightly lower adjusted R-squared but maintains a good fit while being less complex, striking a better balance between explanatory power and model simplicity. Note: Adjusted R-squared isn't considered state-of-the-art due to the emergence of more advanced statistical techniques and machine learning algorithms that offer greater complexity and flexibility in model evaluation and prediction. However, it remains valuable due to its simplicity, quick insights, and historical context. Its ease of interpretation and ability to aid in fair model comparison make it a practical choice for initial model evaluation and decision-making. Join me on May 7 for my webinar, "Data Analysis & Visualization in R," where I'll also delve into regression model comparison and explain the nuances of adjusted R-squared: https://lnkd.in/eVXD2x78 #rstats #statisticalanalysis #datascience

I am already a huge fan because this is the kind of information that would have been so helpful on some past projects that I’ve been on and some past programs And I guess other #DATA scientist out there could come in on this, but since this is about forecasting and the afterthought on, it is really about customer lifetime valuation. It be really interesting to see the correlation in the forecast versus the information from a customer lifetime valuation.

Balancing Imbalanced Datasets: Metrics and Methods (1) Imbalanced datasets occur when one class significantly outnumbers the other. To address this, we use techniques to balance the data: * Undersampling Reduces the number of instances in the majority class. Risk: Information loss, especially if removed instances are crucial. Methods: Random undersampling, Tomek Links for Undersampling, cluster-based undersampling. * Oversampling Increases the number of instances in the minority class. Risk: Overfitting, as the model might learn the minority class too well. Methods: Random oversampling, SMOTE. SMOTE (Synthetic Minority Over-sampling Technique) SMOTE is an oversampling technique used to address imbalanced datasets. It specifically focuses on the minority class. How it works: Identify minority class instances: It selects examples from the minority class. Find nearest neighbors: For each minority class instance, it finds its nearest neighbors (usually k-nearest neighbors). Create synthetic instances: It generates new synthetic data points along the line segments joining the original minority class instance and its neighbors. Key points: It creates new, synthetic data points for the minority class. Helps to balance the dataset without overfitting. Improves model performance on the minority class. In essence, SMOTE increases the number of instances in the minority class by creating new, similar instances, making the dataset more balanced and improving the model's ability to learn from the underrepresented class. Benefits: Generates diverse synthetic data, reducing overfitting risk compared to random oversampling. Understanding Tomek Links for Undersampling Tomek links are pairs of instances where one instance is from the majority class and the other is from the minority class, and they are the nearest neighbors of each other. In simpler terms, they are instances from different classes that are very close together. The idea behind using Tomek links for undersampling is to remove noisy or borderline majority class instances. These instances are often misclassified and can negatively impact the model's performance. Here's how it works: Identify Tomek Links: The algorithm scans the dataset to find pairs of instances that meet the Tomek link criteria. Remove Majority Class Instance: For each Tomek link identified, the instance from the majority class is removed from the dataset. Iterate: This process continues until no more Tomek links can be found. By removing these borderline instances, the dataset becomes more balanced, and the model can potentially achieve better performance. (Might not be sufficient for heavily imbalanced datasets) Choosing the right technique depends on: Severity of imbalance Size of the dataset Desired outcome (e.g., precision, recall) Computational resources Often, a combination of techniques or other approaches (e.g., class weighting) is used for optimal results.