What Is the Difference Between Bias and Variance?

Understanding bias and variance, which have roots in statistics, is essential for data scientists involved in machine learning. Bias and variance are used in supervised machine learning, in which an algorithm learns from training data or a sample data set of known quantities. The correct balance of bias and variance is vital to building machine-learning algorithms that create accurate results from their models.

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During development, all algorithms have some level of bias and variance. The models can be corrected for one or the other, but each aspect cannot be reduced to zero without causing problems for the other. That’s where the concept of bias-variance trade-off becomes important. Data scientists must understand the tensions in the model and make the proper trade-off in making bias or variance more prominent.

The Importance of Bias and Variance

Machine learning algorithms use mathematical or statistical models with inherent errors in two categories: reducible and irreducible error. Irreducible error, or inherent uncertainty, is due to natural variability within a system. In comparison, reducible error is more controllable and should be minimized to ensure higher accuracy.

Bias and variance are components of reducible error. Reducing errors requires selecting models that have appropriate complexity and flexibility, as well as suitable training data. Data scientists must thoroughly understand the difference between bias and variance to reduce error and build accurate models.

What Is Bias?

Also called “error due to squared bias,” bias is the amount that a model’s prediction differs from the target value, compared to the training data. Bias error results from simplifying the assumptions used in a model so the target functions are easier to approximate. Bias can be introduced by model selection. Data scientists conduct resampling to repeat the model building process and derive the average of prediction values. Resampling data is the process of extracting new samples from a data set in order to get more accurate results. There are a variety of ways to resample data including:

  • K fold resampling, in which a given data set is split into a K number of sections, or folds, where each fold is used as a testing set.
  • Bootstrapping, which involves iteratively resampling a dataset with replacement.

Resampling can affect bias. If the average prediction values are significantly different from the true value based on the sample data, the model has a high level of bias.

Every algorithm starts with some level of bias, because bias results from assumptions in the model that make the target function easier to learn. A high level of bias can lead to underfitting, which occurs when the algorithm is unable to capture relevant relations between features and target outputs. A high bias model typically includes more assumptions about the target function or end result. A low bias model incorporates fewer assumptions about the target function.

A linear algorithm often has high bias, which makes them learn fast. In linear regression analysis, bias refers to the error that is introduced by approximating a real-life problem, which may be complicated, by a much simpler model. Though the linear algorithm can introduce bias, it also makes their output easier to understand. The simpler the algorithm, the more bias it has likely introduced. In contrast, nonlinear algorithms often have low bias.

What Is Variance?

Variance indicates how much the estimate of the target function will alter if different training data were used. In other words, variance describes how much a random variable differs from its expected value. Variance is based on a single training set. Variance measures the inconsistency of different predictions using different training sets — it’s not a measure of overall accuracy.

Variance can lead to overfitting, in which small fluctuations in the training set are magnified. A model with high-level variance may reflect random noise in the training data set instead of the target function. The model should be able to identify the underlying connections between the input data and variables of the output.

A model with low variance means sampled data is close to where the model predicted it would be. A model with high variance will result in significant changes to the projections of the target function.

Machine learning algorithms with low variance include linear regression, logistics regression, and linear discriminant analysis. Those with high variance include decision trees, support vector machines and k-nearest neighbors.

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The Bias-Variance Trade-Off

Data scientists building machine learning algorithms are forced to make decisions about the level of bias and variance in their models. Ultimately, the trade-off is well known: increasing bias decreases variance, and increasing variance decreases bias. Data scientists have to find the correct balance.

When building a supervised machine-learning algorithm, the goal is to achieve low bias and variance for the most accurate predictions. Data scientists must do this while keeping underfitting and overfitting in mind. A model that exhibits small variance and high bias will underfit the target, while a model with high variance and little bias will overfit the target.

A model with high variance may represent the data set accurately but could lead to overfitting to noisy or otherwise unrepresentative training data. In comparison, a model with high bias may underfit the training data due to a simpler model that overlooks regularities in the data.

The trade-off challenge depends on the type of model under consideration. A linear machine-learning algorithm will exhibit high bias but low variance. On the other hand, a non-linear algorithm will exhibit low bias but high variance. Using a linear model with a data set that is non-linear will introduce bias into the model. The model will underfit the target functions compared to the training data set. The reverse is true as well — if you use a non-linear model on a linear dataset, the non-linear model will overfit the target function.

To deal with these trade-off challenges, a data scientist must build a learning algorithm flexible enough to correctly fit the data. However, if the algorithm has too much flexibility built in, it may be too linear and provide results with a high variance from each training data set.

In characterizing the bias-variance trade-off, a data scientist will use standard machine learning metrics, such as training error and test error, to determine the accuracy of the model. The Mean Square Error (MSE) can be used in a linear regression model with the training set to train the model with a large portion of the available data and act as a test set to analyze the accuracy of the model with a smaller sample of the data. A small portion of data can be reserved for a final test to assess the errors in the model after the model is selected.

There is always tension between bias and variance. In fact, it’s difficult to create a model that has both low bias and variance. The goal is a model that reflects the linearity of the training data but will also be sensitive to unseen data used for predictions or estimates. Data scientists must understand the difference between bias and variance so they can make the necessary compromises to build a model with acceptably accurate results.

Total Error

The total error of a machine-learning model is the sum of the bias error and variance error.

The goal is to balance bias and variance, so the model does not underfit or overfit the data. As the complexity of the model rises, the variance will increase and bias will decrease. In a simple model, there tends to be a higher level of bias and less variance. To build an accurate model, a data scientist must find the balance between bias and variance so that the model minimizes total error.

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Learning how to manage the bias-variance trade-off and truly understanding the difference between bias and variance is one example of the challenges data scientists face. If you’re intrigued by the complexities of bias and variance, then a data science career could be a good fit for you. To learn more about data science careers, explore the resources available through Master’s in Data Science.

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