Adaptive Synthetic Sampling (ADASYN) is a technique used to address imbalanced datasets in machine learning, improving classification performance for underrepresented classes. Imbalanced datasets are common in real-world applications, such as medical research, network intrusion detection, and fraud detection in credit card transactions. These datasets have a majority class with many samples and minority classes with few samples, causing machine learning algorithms to be biased towards the majority class. ADASYN is an oversampling method that generates synthetic samples for minority classes, balancing the dataset and improving classification accuracy. Recent research has explored various applications and improvements of ADASYN. For example, ADASYN has been combined with the Random Forest algorithm for intrusion detection, resulting in better performance and generalization ability. Another study proposed WOTBoost, which combines a Weighted Oversampling Technique and ensemble Boosting method to improve classification accuracy for minority classes. Researchers have also compared ADASYN with other oversampling techniques, such as SMOTE, in multi-class text classification tasks. Practical applications of ADASYN include: 1. Intrusion detection: ADASYN can improve the classification accuracy of network attack behaviors, making it suitable for large-scale intrusion detection systems. 2. Medical research: ADASYN can help balance datasets in medical research, improving the performance of machine learning models for diagnosing diseases or predicting patient outcomes. 3. Fraud detection: By generating synthetic samples for rare fraud cases, ADASYN can improve the accuracy of fraud detection models in credit card transactions or other financial applications. A company case study involves using ADASYN for unsupervised fault diagnosis in bearings. Researchers integrated expert knowledge with domain adaptation in a synthetic-to-real framework, generating synthetic fault datasets and adapting models from synthetic faults to real faults. This approach was evaluated on laboratory and real-world wind-turbine datasets, demonstrating its effectiveness in encoding fault type information and robustness against class imbalance. In conclusion, ADASYN is a valuable technique for addressing imbalanced datasets in various applications. By generating synthetic samples for underrepresented classes, it helps improve the performance of machine learning models and enables more accurate predictions in diverse fields.

# Adjusted R-Squared

## What is the difference between R-squared and adjusted R-squared?

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variables in a regression model. It ranges from 0 to 1, with higher values indicating a better fit. However, R-squared has a limitation: it tends to increase as more predictors are added to the model, even if those predictors do not contribute significantly to the model's performance. Adjusted R-squared, on the other hand, is a modification of R-squared that takes into account the number of predictors in the model. It penalizes models with a large number of predictors to avoid overfitting. Adjusted R-squared is generally considered a more reliable metric for model evaluation, as it provides a more accurate representation of the model's performance when multiple predictors are used.

## How do you interpret adjusted R-squared in regression?

Adjusted R-squared is interpreted as the proportion of the variance in the dependent variable that can be explained by the independent variables in the model, after accounting for the number of predictors. It ranges from 0 to 1, with higher values indicating a better fit. An adjusted R-squared value close to 1 suggests that the model explains a large portion of the variance in the dependent variable, while a value close to 0 indicates that the model does not explain much of the variance. When comparing different regression models, a higher adjusted R-squared value generally indicates a better model, as it suggests that the model is capturing more of the underlying relationships between the variables while avoiding overfitting.

## Should I use R-squared or adjusted R-squared?

In most cases, it is recommended to use adjusted R-squared instead of R-squared when evaluating the performance of a regression model. This is because adjusted R-squared takes into account the number of predictors in the model and penalizes models with a large number of predictors, helping to avoid overfitting. R-squared, on the other hand, tends to increase as more predictors are added to the model, even if those predictors do not contribute significantly to the model's performance. Using adjusted R-squared can provide a more accurate representation of the model's performance, especially when multiple predictors are used.

## What does it mean when adjusted R-squared is high?

A high adjusted R-squared value indicates that the regression model explains a large portion of the variance in the dependent variable, after accounting for the number of predictors used. This suggests that the model is capturing the underlying relationships between the variables effectively and is likely to be a good fit for the data. However, it is important to note that a high adjusted R-squared value does not guarantee that the model is perfect or that it will perform well on new, unseen data. It is always essential to validate the model using other evaluation metrics and techniques, such as cross-validation, to ensure its robustness and generalizability.

## How is adjusted R-squared calculated?

Adjusted R-squared is calculated using the following formula: Adjusted R-squared = 1 - [(1 - R-squared) * (n - 1) / (n - k - 1)] where n is the number of observations in the dataset, k is the number of predictors in the model, and R-squared is the unadjusted R-squared value. The formula adjusts the R-squared value by taking into account the number of predictors used in the model, penalizing models with a large number of predictors to avoid overfitting.

## Can adjusted R-squared be negative?

Yes, adjusted R-squared can be negative, although it is relatively rare. A negative adjusted R-squared value indicates that the model performs worse than a simple mean model, which predicts the mean of the dependent variable for all observations. This can happen when the model is overfitting the data or when the predictors used in the model do not have a significant relationship with the dependent variable. In practice, a negative adjusted R-squared value is a strong indication that the model should be re-evaluated and potentially improved by using different predictors, removing irrelevant predictors, or applying regularization techniques.

## Adjusted R-Squared Further Reading

1.A Prediction Model for System Testing Defects using Regression Analysis http://arxiv.org/abs/1401.5830v1 Muhammad Dhiauddin Mohamed Suffian, Suhaimi Ibrahim2.Upper bounds on the minimum coverage probability of confidence intervals in regression after variable selection http://arxiv.org/abs/0711.0993v1 Paul Kabaila, Khageswor Giri3.Bounds for Bias-Adjusted Treatment Effect in Linear Econometric Models http://arxiv.org/abs/2203.12431v1 Deepankar Basu4.Hedonic Models of Real Estate Prices: GAM and Environmental Factors http://arxiv.org/abs/2210.14266v1 Jason R. Bailey, Davide Lauria, W. Brent Lindquist, Stefan Mittnik, Svetlozar T. Rachev5.Evaluating the Data Quality of Eye Tracking Signals from a Virtual Reality System: Case Study using SMI's Eye-Tracking HTC Vive http://arxiv.org/abs/1912.02083v1 Dillon J. Lohr, Lee Friedman, Oleg V. Komogortsev6.An Empirical Study of Capital Asset Pricing Model based on Chinese A-share Trading Data http://arxiv.org/abs/2305.04838v1 Kai Ren7.Quantitative Relationship between Population Mobility and COVID-19 Growth Rate based on 14 Countries http://arxiv.org/abs/2006.02459v1 Benjamin Seibold, Zivjena Vucetic, Slobodan Vucetic8.A non-inferiority test for R-squared with random regressors http://arxiv.org/abs/2002.08476v2 Harlan Campbell9.Analysis of variance, coefficient of determination and $F$-test for local polynomial regression http://arxiv.org/abs/0810.4808v1 Li-Shan Huang, Jianwei Chen10.Generalized R-squared for Detecting Dependence http://arxiv.org/abs/1604.02736v3 Xufei Wang, Bo Jiang, Jun S. Liu## Explore More Machine Learning Terms & Concepts

Adaptive Synthetic Sampling (ADASYN) Adversarial Autoencoders (AAE) Adversarial Autoencoders (AAE) are a powerful technique for learning deep generative models of data, with applications in various domains such as image synthesis, semi-supervised classification, and data visualization. Adversarial Autoencoders (AAE) are a type of deep learning model that combines the strengths of autoencoders and generative adversarial networks (GANs). Autoencoders are neural networks that learn to compress and reconstruct data, while GANs consist of two networks, a generator and a discriminator, that compete against each other to generate realistic samples from a given data distribution. AAEs use the adversarial training process from GANs to impose a specific prior distribution on the latent space of the autoencoder, resulting in a more expressive generative model. Recent research in AAEs has explored various applications and improvements. For instance, the Doubly Stochastic Adversarial Autoencoder introduces a stochastic function space to encourage exploration and diversity in generated samples. The PATE-AAE framework incorporates AAEs into the Private Aggregation of Teacher Ensembles (PATE) for privacy-preserving spoken command classification, achieving better performance than alternative privacy-preserving solutions. Another study uses AAEs and adversarial Long Short-Term Memory (LSTM) networks to improve urban air pollution forecasts by reducing the divergence from the underlying physical model. Practical applications of AAEs include semi-supervised classification, where the model can learn from both labeled and unlabeled data, disentangling style and content in images, and unsupervised clustering, where the model can group similar data points without prior knowledge of the group labels. AAEs have also been used for dimensionality reduction and data visualization, allowing for easier interpretation of complex data. One company case study involves using AAEs for wafer map pattern classification in semiconductor manufacturing. The proposed method, an Adversarial Autoencoder with Deep Support Vector Data Description (DSVDD) prior, performs one-class classification on wafer maps, helping manufacturers identify defects and improve yield rates. In conclusion, Adversarial Autoencoders offer a powerful and flexible approach to learning deep generative models, with applications in various domains. By combining the strengths of autoencoders and generative adversarial networks, AAEs can learn expressive representations of data and generate realistic samples, making them a valuable tool for developers and researchers alike.