Joachim Schork’s Post

When building predictive models, overfitting is a common challenge. Shrinkage methods, such as Ridge Regression, Lasso, and Elastic Net, help address this by adding a penalty term to the objective function during training, which discourages large coefficients. This results in more robust models that generalize better to new data. ✔️ Ridge Regression shrinks coefficients by penalizing their squared values, making it great when all features matter. ✔️ Lasso forces some coefficients to zero, effectively performing feature selection, ideal when only a subset of features is important. ✔️ Elastic Net combines the strengths of Ridge and Lasso, providing a balance between regularization and feature selection, especially useful when features are correlated. However, there are some challenges to consider: ❌ Loss of interpretability: Excessive shrinkage can make it difficult to interpret the model coefficients, as important predictors may have their effects reduced. ❌ Tuning required: These methods require careful tuning of hyperparameters (like λ and α) to find the right balance between bias and variance. Poor tuning can lead to either underfitting or overfitting. ❌ Not suitable for all situations: In some cases, simpler models like OLS (Ordinary Least Squares) might perform just as well or even better, especially when the sample size is large and multicollinearity isn’t an issue. 🔹 In R: Use the glmnet package to apply Ridge, Lasso, and Elastic Net. 🔹 In Python: Leverage the sklearn.linear_model module for all three shrinkage methods. Want to dive deeper into these methods and learn how to apply them? Join my online course on Statistical Methods in R, where we explore this and other key techniques in further detail. See this link for additional information: https://lnkd.in/ed7XyXQm #Rpackage #coding #Statistical

Automatic variable selection is a powerful technique for simplifying models, reducing overfitting, and improving interpretability. It enables you to efficiently identify the most important predictors from a large set of variables. However, it’s important to recognize that automatic variable selection involves random processes. The same algorithm may select different variables across multiple runs, and different algorithms can yield entirely different selections, even when applied to the same data set. The graph below illustrates how different automatic variable selection methods perform across 200 simulation runs. Each box represents one method, with rows corresponding to variables and columns to simulation runs. Black indicates selected variables, while white indicates excluded ones. 🔹 Stepwise Selection: Highly inconsistent, with patterns that often appear random. Very few variables are consistently selected across all runs. 🔹 Regression Tree: Most variables are rarely selected, with only a small subset chosen consistently across simulations. The small median model size reflects this focused selection. 🔹 Random Forest: Demonstrates improved stability compared to regression trees, with more consistently selected variables, though variability persists for weaker predictors. This method tends to include a broader set of variables compared to regression trees. 🔹 Lasso and Elastic Net: Both methods exhibit relatively stable variable selection, with Elastic Net slightly outperforming Lasso due to its larger model size, allowing for broader inclusion of important variables. While no method achieves perfect consistency, Random Forest, Lasso, and Elastic Net generally provide more stable and reliable variable selection results, whereas Stepwise Selection tends to be the least reliable. I published these results in a working paper back in 2018, but they remain highly relevant today. If you're interested, you can read the full paper here: https://lnkd.in/enUh7vnD. If you enjoy insights like these, subscribe to my free email newsletter for regular tips on data science, statistics, Python, and R programming. Learn more: http://eepurl.com/gH6myT #research #datavisualization #database #rprogramminglanguage #datascientists #data #visualanalytics

Mean imputation is a straightforward method for handling missing values in numerical data, but it can significantly distort the relationships between variables. By replacing missing values with the mean of observed data, this approach artificially reduces variability and weakens correlations, leading to misleading results in analysis. Why Does Mean Imputation Distort Correlations? ❌ No variability in imputed values: Mean imputation assigns the same value to all missing entries, failing to reflect the natural variability of the data. ❌ Weakens relationships: The imputed values introduce artificial uniformity that diminishes or masks the strength of correlations between variables. ❌ Biased downstream analyses: Statistical tests and predictive models relying on the data's correlation structure may produce inaccurate or unreliable results. A Visual Example: The attached image demonstrates how mean imputation can disrupt correlations between variables. The black points represent the original observed values, showing the natural relationship between variables X1 and X2. The red and green points represent imputed values for X1 and X2, respectively, placed at their mean values. This disrupts the overall pattern, artificially aligning the data along the mean and weakening the true correlation between X1 and X2. A Better Approach: To preserve relationships between variables, predictive mean matching is a superior alternative. This method selects observed values closest to the predicted value for a missing entry, maintaining variability and the natural correlation structure. When combined with multiple imputation, it also accounts for uncertainty, ensuring more robust and reliable results for downstream analyses. For a detailed explanation of mean imputation, its drawbacks, and better alternatives, check out my full tutorial here: https://lnkd.in/d2vfiSmf Sign up for my free email newsletter to stay informed about data science, statistics, Python, and R. More info: http://eepurl.com/gH6myT #RStats #Data #datasciencetraining #Python #StatisticalAnalysis #DataAnalytics

I'm excited to share my latest data science project: Handwritten Digit Classification using the classic MNIST dataset! This was a fantastic foundational project in image classification. My goal was to build and compare several machine learning models to see which one could most accurately identify the digits (0-9). Here's a quick overview of the process: 🔹 Exploration & Preprocessing: Loaded the 70,000 images, visualized the data, and scaled all 784 pixel-features using StandardScaler. 🔹 Model Comparison: Trained and evaluated three different models: Logistic Regression (as a baseline), K-Nearest Neighbors (KNN), and a Random Forest Classifier. 🔹 Results: The Random Forest Classifier was the top performer, achieving ~97% accuracy on the 10,000-image test set! The most interesting part was diving deeper than just accuracy. By analyzing the confusion matrix and the specific images the model got wrong, I could see exactly where its weaknesses were (like confusing a '4' with a '9' or a '3' with an '8'). This project was a great hands-on experience with: ✅ Feature Scaling ✅ Model Evaluation (Accuracy, Precision, Recall, Confusion Matrices) ✅ Error Analysis ✅ Scikit-learn, NumPy, and Matplotlib You can find the full Python script, my analysis, and all the output plots on my GitHub. https://lnkd.in/dVzHpzq2 I'd love to hear your feedback! #DataScience #MachineLearning #Python #ScikitLearn #MNIST #Portfolio #DataAnalysis #Classification #Developer

Binary logistic regression is a powerful statistical method used to model the relationship between a binary target variable and one or more predictor variables. It's commonly used in situations where the outcome is categorical, such as predicting whether a customer will buy a product (yes/no) or whether a patient has a disease (present/absent). When properly implemented, binary logistic regression offers several benefits: ✔️ Accurate Predictions: It helps in making precise predictions about binary outcomes, which can be crucial for decision-making in fields like marketing, healthcare, and finance. ✔️ Variable Impact: By examining the coefficients, you can understand the impact of different variables on the probability of the outcome. ✔️ Flexibility: Logistic regression can handle multiple predictor variables, making it suitable for complex models. However, if not handled correctly, there can be drawbacks: ❌ Overfitting: Using too many predictor variables can cause the model to become overly complex and perform poorly on new data. ❌ Misinterpretation: The model's output probabilities need careful interpretation, as incorrect conclusions can lead to faulty decisions. ❌ Assumption Dependence: Logistic regression relies on certain assumptions, such as the linear relationship between predictors and the log odds of the target variable. Violating these assumptions can reduce model reliability. To implement binary logistic regression in practice, you can use these tools: 🔹 R: Use the glm() function from the base package to fit a logistic regression model. The ggplot2 package can be used to visualize the data and model predictions. 🔹 Python: Use LogisticRegression from the scikit-learn library to create a logistic regression model. Libraries like matplotlib or seaborn can help visualize the results. The visualization of this post demonstrates a logistic regression model, showcasing how the model predicts probabilities for a binary outcome based on a continuous predictor. It includes a curve that represents the predicted probabilities, helping us understand how changes in the predictor variable affect the likelihood of different outcomes. If you want to dive deeper into this topic and learn how to apply these techniques in R, check out my online course on Statistical Methods in R. It covers binary logistic regression and many other related topics in detail. See this link for additional information: https://lnkd.in/d-UAgcYf #research #rprogramminglanguage #datavisualization #ggplot2 #dataanalytic #bigdata #datavisualization #dataanalytics #tidyverse

Now, I just trained a Logistic Regression model on the Iris dataset! Quite Interesting 🤔 Steps I followed: •Loaded & explored data •Split into train/test sets •Scaled features •Trained & predicted 1. Import libraries import pandas as pd from sklearn.datasets import load_iris from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.linear_model import LogisticRegression from sklearn.metrics import accuracy_score 2. Load dataset iris = load_iris() 3.Create combined DataFrame df = pd.DataFrame(data=iris.data, columns=iris.feature_names) df["target_class"] = iris.target 4. Split input (X) and output (y) X = df[iris.feature_names] y = df["target_class"] 5. Split into train and test X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42) 6. Scale the data scaler = StandardScaler() X_train_scaled = scaler.fit_transform(X_train) X_test_scaled = scaler.transform(X_test) 7. Train logistic regression model model = LogisticRegression() model.fit(X_train_scaled, y_train) 8. Predict and check accuracy y_pred = model.predict(X_test_scaled) acc = accuracy_score(y_test, y_pred) print(f"Model Accuracy: {acc * 100:.2f}%") Logistic Regression predicts probabilities for categories, not logistics! #MachineLearning #DataScience #Python #LogisticRegression #IrisDataset #LMES #UPTOR #MohanSivaraman

Understanding the power of a statistical test is essential for designing effective experiments and making confident decisions. Power is the probability of correctly identifying a true effect, and it plays a critical role in determining whether a study can detect meaningful differences and avoid misleading conclusions. ✔️ A well-powered test increases the chances of identifying meaningful results, leading to accurate and actionable insights. ✔️ Proper planning ensures efficient use of resources, avoiding underpowered or overpowered studies. ❌ Low power makes it more likely to miss true effects, resulting in missed opportunities and weak conclusions. ❌ Overpowered studies can highlight trivial differences, leading to wasted resources or unnecessary focus on insignificant findings. The visualization below illustrates the concept of power in a two-sided test. The blue area shows the probability of incorrectly rejecting a true null hypothesis, while the red area represents the likelihood of correctly identifying a true effect. Image credit to Wikipedia: https://lnkd.in/eQbnPFyz Carefully balancing effect size, sample size, and significance level is key to conducting robust and efficient analyses. Tools like power curves can further aid in refining these parameters for optimal study design. 🔹 In R, the pwr package provides tools for power calculations, including estimating the required sample size for t-tests and ANOVA. It also includes functions to visualize power curves, aiding in better planning. Additionally, the pwrss package provides additional options for calculating sample sizes across a broader range of tests. 🔹 In Python, the statsmodels library includes modules like TTestIndPower for t-tests and FTestAnovaPower for ANOVA. The scipy.stats module can be used for customized power calculations when needed. For more insights into Statistics, Data Science, R, and Python, subscribe to my email newsletter! Learn more: http://eepurl.com/gH6myT #datasciencetraining #Rpackage #datascienceenthusiast

The mclust R package is a widely used tool for model-based clustering, classification, and density estimation. It fits Gaussian finite mixture models and can automatically select the best model and number of clusters using the Bayesian Information Criterion (BIC). It also supports hierarchical model-based clustering and provides tools for classification of new observations. ✔️ Reveals patterns in complex data sets ✔️ Produces probabilistic cluster assignments for improved interpretation ✔️ Provides uncertainty measures to assess classification reliability ✔️ Offers rich visualization options for exploring clustering structure The visualizations below are from the mclust package website and show example plots generated with mclust. For more details, visit the package website: https://lnkd.in/d2rZime4 Want more practical tips and examples on Statistics, Data Science, R, and Python? Subscribe to my email newsletter for exclusive insights. Take a look here for more details: http://eepurl.com/gH6myT #datasciencetraining #data #rstudio #analytics #dataviz #datavisualization #database #package

I see a number and ask, "Is it lying?" Your 'average' is almost always lying to you, skewed by outliers and misleading. Presenting it as fact is a common mistake. Starting a 'Back to Basics' series for those valuing accuracy over speed. 𝗣𝗮𝗿𝘁 1️⃣: 𝗗𝗼𝗻'𝘁 𝗧𝗿𝘂𝘀𝘁 𝗬𝗼𝘂𝗿 '𝗔𝘃𝗲𝗿𝗮𝗴𝗲' → THE MEAN (Average) - Easily skewed by one big number. → THE MEDIAN (Middle) - Ignores outliers, revealing the actual typical value. → THE MODE (Most Frequent) - Applicable in different scenarios, not with numbers. 🏁 𝗧𝗵𝗲 𝗧𝗮𝗸𝗲𝗮𝘄𝗮𝘆: - Avoid misleading 'averages'. - Opt for the Median with skewed data. - It's about being smart, not just looking smart. For a full deep dive with Python examples, check out my Medium article: https://lnkd.in/giaTJAci ♻️ Found this useful? Repost this. #BackToBasics #DataScience #Statistics #DataAnalytics #Infographic

Understanding the power of a statistical test is essential for designing effective experiments and making confident decisions. Power is the probability of correctly identifying a true effect, and it plays a critical role in determining whether a study can detect meaningful differences and avoid misleading conclusions. ✔️ A well-powered test increases the chances of identifying meaningful results, leading to accurate and actionable insights. ✔️ Proper planning ensures efficient use of resources, avoiding underpowered or overpowered studies. ❌ Low power makes it more likely to miss true effects, resulting in missed opportunities and weak conclusions. ❌ Overpowered studies can highlight trivial differences, leading to wasted resources or unnecessary focus on insignificant findings. The visualization below illustrates the concept of power in a two-sided test. The blue area shows the probability of incorrectly rejecting a true null hypothesis, while the red area represents the likelihood of correctly identifying a true effect. Image credit to Wikipedia: https://lnkd.in/ejzgNUHw Carefully balancing effect size, sample size, and significance level is key to conducting robust and efficient analyses. Tools like power curves can further aid in refining these parameters for optimal study design. 🔹 In R, the pwr package provides tools for power calculations, including estimating the required sample size for t-tests and ANOVA. It also includes functions to visualize power curves, aiding in better planning. Additionally, the pwrss package provides additional options for calculating sample sizes across a broader range of tests. 🔹 In Python, the statsmodels library includes modules like TTestIndPower for t-tests and FTestAnovaPower for ANOVA. The scipy.stats module can be used for customized power calculations when needed. For more insights into Statistics, Data Science, R, and Python, subscribe to my email newsletter! Learn more by visiting this link: http://eepurl.com/gH6myT #package #rprogramminglanguage #datasciencetraining