Explained variance

Definition

Explained variance is a statistical measure that indicates the proportion of the total variance in a dataset that can be attributed to a particular model or set of variables. This concept is crucial for assessing how well a model captures the underlying patterns in the data, and it's particularly relevant in techniques such as matrix factorizations, where understanding how much information is retained is essential for evaluating model performance.

5 Must Know Facts For Your Next Test

1. Explained variance is often represented as a percentage, indicating how much of the total variance in the dataset can be accounted for by the model.
2. In matrix factorizations, maximizing explained variance helps in creating more accurate and efficient representations of large datasets.
3. A high explained variance suggests that the model is effective at capturing essential patterns, whereas low explained variance indicates that important information may be overlooked.
4. Explained variance can be used to compare different models, allowing data scientists to choose the best performing one based on how much variance it captures.
5. Techniques like PCA and SVD leverage explained variance to reduce dimensionality while maintaining as much information as possible from the original dataset.

Review Questions

• How does explained variance impact the evaluation of models derived from matrix factorizations?
  • Explained variance is critical when evaluating models derived from matrix factorizations because it quantifies how much of the original data's variability is captured by the model. A higher explained variance implies that the model closely represents the underlying data structure, which is especially important in applications dealing with large datasets. By focusing on explained variance, one can determine whether a simpler model might suffice or if a more complex one is necessary to capture intricate patterns in the data.
• Discuss how techniques like PCA utilize explained variance in their methodology and outcomes.
  • PCA employs explained variance to determine how many principal components should be retained during dimensionality reduction. Each principal component captures a certain amount of variance from the original dataset, and by analyzing these values, one can decide which components contribute most significantly to explaining variability. Retaining components that account for high explained variance ensures that the reduced dataset still contains most of the important information from the original data, enhancing analysis and interpretation.
• Evaluate the importance of explained variance when comparing different models in big data applications and its implications for decision-making.
  • Explained variance serves as a key criterion when comparing different models in big data applications because it highlights each model's effectiveness in capturing the data's underlying structure. Models with higher explained variances are generally preferred as they provide more reliable predictions and insights. In decision-making contexts, relying on models that maximize explained variance can lead to better-informed strategies and actions, ultimately improving outcomes in fields such as finance, healthcare, and marketing.

Related terms

variance: Variance measures the extent to which data points differ from their mean, providing insight into the data's spread or dispersion.

principal component analysis (PCA):

PCA is a dimensionality reduction technique that transforms data into a new coordinate system, where the greatest variances by any projection lie on the first coordinates, effectively summarizing data while preserving explained variance.

singular value decomposition (SVD):

SVD is a mathematical technique used to factorize matrices into their constituent components, playing a significant role in applications like noise reduction and data compression while preserving explained variance.