How do you handle outliers or noisy data when using loss functions for regression problems?

Handle outliers by robust loss functions like Huber loss. These downplay the impact of extreme data points, making regression models more resilient to noisy inputs.

Data can be tricky sometimes! Imagine you're studying for a test and one person got a weirdly high score that throws off the class average. That high score might be an outlier, a data point way outside the norm. It could be a mistake, or maybe that one person just aced the material! Similarly, noisy data is like static on a bad connection. It's random fuzz that messes with the actual information you're trying to see. Both outliers and noisy data can mess up our analysis, kind of like wonky data points messing up the curve on a test. That's why it's important to clean our data before using it – gotta make sure we're working with the clearest picture possible!

Speaking from experience, I believe that outliers, stemming from measurement or data entry errors, and noisy data, characterized by random fluctuations, can distort the distribution of data, leading to skewed, non-linear, or heteroscedastic patterns. These irregularities can violate the assumptions of regression models and loss functions, compromising the reliability of analytical outcomes. Addressing outliers and noisy data through robust data preprocessing techniques, such as outlier detection and noise reduction methods, is essential to ensure the quality and validity of data-driven insights.

From my undesrtanding these mathematical functions aggregate individual errors into a single value that is minimized during the model training process. Loss functions are pivotal as they influence how effectively a model learns from data and its resilience to outliers and noisy data. By selecting appropriate loss functions tailored to the specific characteristics of the data and modeling objectives, practitioners can optimize model training, enhance predictive accuracy, and mitigate the impact of outliers and noise. Understanding the significance of loss functions in guiding model optimization and generalization is essential for building robust and reliable regression models that yield accurate and meaningful insights from complex datasets

A small addition: There are multiple ways in defining loss functions. One example is the difference between predicted output and actual output. Some losses force the output to have a certain behavior, e.g. follow a distribution. Sometimes losses are used in the middle of a network, not just in the output of the network.

The robustness of MAE (Mean Absolute Error) compared to MSE (Mean Squared Error) on outliers can be illustrated with a simple example. Consider the following: ground truth = [1, 2, 3, 4, 100] model predictions = [0, 3, 7, 4, 80] The MAE is calculated as mean of absolute difference between Ground truth and predictions MAE = ( |1-0| + |2 - 3| + |3 - 7| + |4 - 4| + |100 - 80|)/5 MAE = 5.2 On the other hand, MSE is calculated by taking the mean of squared differences: MSE = ( (1-0)^2 + (2 - 3)^2 + (3 - 7)^2 + (4 - 4)^2 + (100 - 80)^2)/5 MSE = 83.6 In this example, MAE assigns a lower weight (20/26) to outliers compared to MSE (400/418) due to the absolute differences used in its calculation, making it more robust to extreme values.

MSE: Squares errors, making it sensitive to outliers. Best for normally distributed data where large errors need penalizing. MAE: Uses absolute errors, making it less sensitive to outliers. Ideal for skewed data or when outliers are present. Huber Loss: Combines MSE and MAE, penalizing small errors like MSE and large ones like MAE. Suitable for data with some outliers, offering a balance between sensitivity and robustness. Quantile Loss: Targets specific quantiles, useful for modeling varying uncertainty or skewed. Log-Cosh Loss: A smoother alternative to Huber, robust to outliers and easy to optimize. Choose MSE for normal data, MAE for robustness, Huber for balance, Quantile for distribution tails, and Log-Cosh smooth performance.

Speaking from what I understand in my own company, common loss functions such as mean squared error (MSE), mean absolute error (MAE), and Huber loss each offer distinct advantages and considerations based on the characteristics of your data. MSE is ideal for normally distributed, symmetric, and homoscedastic data, emphasizing the penalty for large errors. In contrast, MAE is more suitable for skewed, asymmetric, or heteroscedastic data, as it is robust to outliers and noise. Huber loss strikes a balance between MSE and MAE, making it a valuable choice for datasets with a mix of outliers and inliers, utilizing the strengths of both functions for small and large errors, respectively.

There is always a trade off between Mean Squared Error (MSE) and Mean Absolute Error (MAE). One can consider Huber loss, which is the combination of MAE and MSE. This loss function can better identify outliers or noisy data.

One note that I think worth noting is that the outliers which are harmful are the ones that come due to error. If the outlier in the data is merely because naturally, they are less common, they should be removed with more care. Sometimes, we should find ways to increase their repetition instead of eliminating them.

Firstly, I will try utilizing descriptive statistics such as mean, median, standard deviation, quartiles, and interquartile range can help identify data points that deviate significantly from the central tendency or normal range of the data. Visual exploratory tools like box plots, scatter plots, histograms, and density plots offer insights into the data distribution and can highlight isolated or extreme observations. Furthermore, leveraging machine learning techniques such as clustering, classification, or anomaly detection enables the grouping or labeling of data points based on similarity or dissimilarity, facilitating the identification and removal of abnormal or inconsistent data points.

In real world, identifying outliers can be tricky. Instead, using methods like Marginalization with MCMC helps estimate parameters without bias from arbitrary outlier thresholds. This approach offers a better understanding of complex real-world data. Sometimes, keeping outliers can actually improve accuracy rather than getting rid of them.

To handle outliers and noisy data without removing them, you can transform or modify the data to minimize their impact. Use scaling methods like min-max scaling or standardization to adjust the range and distribution of the data. Apply transformations such as log transformation to reduce the influence of extreme values. Employ smoothing techniques like moving averages or median filters to stabilize the data. For missing or erroneous values, use imputation methods like mean, median, or k-nearest neighbors imputation to replace them with reasonable estimates.

Often times, outliers are important but represent the tail in the long-tail distribution of data. Synthetic data generation using GANs and/or algorithms like auto-sampling can help in augmenting / balancing the number of data points available per category, this technique is particularly useful when we wish to model the outliers too and not remove them.

AI might seem super complicated, but guess what? It's all about asking the right questions! Think of it like tackling a tough math problem. You gotta figure out what you're trying to solve, then break it down into steps. Same with AI! The more you understand the problem you're trying to solve, the better you can choose the right AI tools and techniques. It's all about using your brain and your knowledge to make the most of this awesome technology!

Undue influence of outliers & noise hampers an ANN's training process. Imputation can help with outliers. Loss functions like Huber loss & Tukey loss are robust to outliers which penalize large errors less severely than MSE & other squared loss functions. Data normalization & standardization helps. SMOTE & other sampling tools reduce noise & outliers in training data. PCA & SVD help in tackling outliers & noise. For outlier detection & noise reduction, robust regression, outlier detection algorithms like Isolation Forest, Local Outlier Factor, & denoising methods like wavelet denoising & median filtering) are used. Ensemble methods like gradient boosting & random forest, & regularization techniques like L1, L2 (lasso) are also used.

I would like to share a project experience related to this topic of interest. We were working on a graph data related project, where the aim was to identify molecular properties based on the chemical formula of the molecule. It was a complex typical regression problem, where the input is graph modality and the output is a continuous number. While experimenting with multiple regressors and loss functions, we found out the huber regressor (linear regressor with huber loss function) had performed the best, after graph feature extraction. This was because it works like MSE for small errors and MAE for large errors, hence combining the benefits of both loss functions.