Variance, in the context of statistics and machine learning, refers to the variability or spread of data points around the mean or expected value. It measures the extent to which individual data points deviate from the average.
In statistics, it is calculated as the average of the squared differences between each data point and the mean. It quantifies the dispersion or scatter of the data points and provides an indication of how spread out the data is.
In machine learning, it is often used to assess the performance and generalization ability of a model. Specifically, it is related to the concept of bias-variance trade-off.
High Variance: A model with high variance is overly sensitive to the training data and tends to fit the noise or random fluctuations in the training set. This results in poor performance on unseen data or the test set. High variability is often an indication of overfitting, where the model captures the training set’s idiosyncrasies but fails to generalize to new examples.
Low Variance: On the other hand, a model with low variability is less sensitive to the training data and produces more consistent predictions. It generalizes well to unseen data and has better performance. Low variance is associated with underfitting, where the model is too simplistic and fails to capture the underlying patterns in the data.
Balancing bias and variance is crucial in machine learning. While bias represents the model’s ability to capture the true underlying relationship in the data, variance measures its sensitivity to the noise or randomness. The goal is to find an optimal trade-off that minimizes both bias and variance, leading to a well-performing model that generalizes well.
Various techniques can be used to address high variance, such as regularization, increasing the size of the training data, or using ensemble methods like random forests or gradient boosting. These techniques aim to reduce the model’s sensitivity to the training data and improve its generalization ability.
Overall, variance provides insight into the variability and performance of a model. By managing and minimizing variance, one can build models that make accurate predictions on unseen data and generalize well beyond the training set.
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