The bias-variance tradeoff is a fundamental concept in machine learning and statistics. In this post, learn about bias and variance, possible errors, and other notable aspects that guide you right in, and learn how to go about it.
Table of Contents:
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What is Bias?
Bias is basically how far a machine learning model’s predictions deviate from the actual values. It is defined as the discrepancy between the correct values and the values predicted by the model. High bias causes significant inaccuracies in both training and testing data. Therefore, to prevent underfitting, an algorithm should always have low bias.
- High bias: We say the bias is too high if the average predictions are far from the actual values. High bias causes the algorithm to miss dominant patterns or relationships between the input and output variables. When the bias is excessively large, the model is thought to be too simple and needs to be fed the complexity of the data to identify the link, leading to underfitting.
- Low bias: Low bias means the model’s average predictions are very close to the actual values. In the case of low bias, the model is typically highly complex and adaptable, allowing it to capture even subtle patterns and intricate relationships within the input and output variables. When bias is low, the model excels in both fitting the training data and making accurate predictions on new, unseen data. This situation is linked to a well-balanced level of model complexity, resulting in strong generalization capabilities and the avoidance of underfitting.
What is Variance?
Variance is a measure of how scattered a machine learning model’s predictions are from the actual values. It is typically estimated on an unseen independent data or validation set. When a model performs worse on the validation set than it does on the training set, it is possible that the model has high variance.
- High variance: High variance in a model means it has learned the noise and irrelevant data in the training set, leading to overfitting. When a model has high variance, it is very flexible and makes strong predictions for new data points, but it is also more likely to make mistakes.
- Low variance: Low variance in a model means that it has learned the underlying patterns in the training data and is not too sensitive to noise. When a model has low variance, its predictions are more consistent and reliable, but it may not be able to capture complex relationships in the data.
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What is Bias Variance Tradeoff?
Finding the right balance between the bias and variance of the model is called Bias Variance Tradeoff. It is basically a way to ensure that the model is neither overfitted nor under-fitted in any case. If the model is too simple and has very few parameters, it will suffer from high bias and low variance. On the other hand, if the model has a large number of parameters, it will have high variance and low bias.
So, this tradeoff should result in a perfectly balanced relationship between the two, and ideally, low bias with low bias and low variance is the target for any machine learning.
In terms of model complexity, we can use the following diagram to decide on the optimal complexity of our model.
Examples:
Let’s look at a real-world instance of a regression model to illustrate the bias-variance tradeoff.
Consider creating a model to forecast home values based on characteristics like square footage, the number of bedrooms, and location. A house price dataset with associated attributes is available:
High Bias (Underfitting):
Model Description: With the assumption that there is a linear relationship between price and square footage, you choose to employ a basic linear regression and it’s model.
Bias: Because it oversimplifies the connection between the input features and house prices, the model exhibits a high level of bias.
Result: Throughout the dataset, the model continuously overestimates or underestimates house prices. Poor predictions are the consequence because they need to plan for the housing market’s complexity.
High Variance (Overfitting):
Model Description: You choose to employ a sophisticated polynomial regression model with numerous degrees in an effort to attain high accuracy on the training set of data
Bias: The model’s large variance results from its excessive flexibility and attempts to fit exactly each data point in the training dataset.
Result: The model does a mediocre job on fresh, unused data but matches the training data incredibly well. It cannot generalize to other homes or locations because it has virtually memorized the training data, including its noise.
Balanced Trade-Off:
Model Description: You select a somewhat sophisticated model, such as a decision tree with some depth or multiple linear regression.
Bias Variance Tradeoff: Bias-Variance Tradeoff model balances accurately capturing important house price patterns and preventing overfitting.
Result: As a result, the model can predict data from both the training set and the incoming data with some degree of accuracy. It is useful for calculating housing values because it generalizes well to various homes and localities.
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Errors in Bias and Variance
Bias and variance represent core principles within the domain of machine learning, offering valuable insights into the efficacy of a model’s performance. The consideration of bias and variance errors constitutes a pivotal facet during the development and evaluation phases of machine learning models. The errors in bias and variance are:
- Underfitting: Underfitting happens in supervised learning when a model falls short of capturing the underlying pattern of the data. These models often have high bias and low variance. It occurs when we attempt to develop a linear model with nonlinear data or when we have very little data on which to base an appropriate model. Additionally, these kinds of models, including logistic and linear regression, are quite straightforward to capture the complicated patterns in data.
In underfitting, we have either a high bias with low variance or a high bias with high variance.
- Overfitting: Overfitting occurs in supervised learning when our model includes both the background noise and the underlying pattern. This occurs when we train our model repeatedly on noisy data. These models have large variance and little bias. These models are extremely complex and prone to overfitting, like decision trees.
In overfitting, we have low bias with high variance.
Whenever there is a combination of low bias with low variance in a model (when test error is low), we call it a Generalized model. These models give the best results to make predictions.
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How does it Affect your Model?
The efficiency and ability to generalize a machine learning model are significantly impacted by bias and variance mistakes. In order to build reliable and accurate predictive models, an in-depth knowledge of the effects of these errors is important.
- High Variable + High Bias = It needs to be more consistent and accurate on average.
- Low Variable + High Bias = It is consistent but low on average.
- High Variance + Low Bias = It is inconsistent but is accurate on average.
- Low Variance + Low Bias = Consistent and accurate on average. (This is the ideal scenario and is the target for any machine.)
The below bulls-eye diagram explains the tradeoff better:
While detecting is easy, the real task is to reduce it to a minimum, and in that case, we do the following steps:
- Add more input features.
- Add more complexity by introducing the polynomial feature.
- We can decrease the regularization term and get more training data to reduce bias and variance.
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Total Error
In order to create a strong model, we have to achieve a balance between bias and variance. This can be accomplished by reducing the total error.
Total Error = Bias^2 + Variance
The Mathematical derivation of total error is:
Also, learn about the Gradient of a Function from our blog!
Conclusion
In order to wrap up, the bias-variance tradeoff shows the difficult balance between model simplicity and complexity. It is a basic idea in machine learning. High-bias models underfit the data and ignore core patterns, whereas high-variance models overfit and acquire noise. Building models that generalize well to unknown data involves finding the ideal balance between bias and variance. The choice of a model must be made after careful evaluation of this trade-off, using methods like cross-validation and regularization. The bias-variance tradeoff must ultimately be mastered in order to produce reliable and accurate machine-learning solutions for a range of domains and applications.
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