Bias & Variance


What are the concise meaning and interpretation of bias and variance in machine learning and statistics?


Graphical interpretation of Bias - Variance.
Let’s understand this image. This is bull’s eye diagram. Assume that center of the target(Red colored) is a model that perfectly predict the correct values. As we move away from the bull’s eye, our prediction goes worse. Imagine we can repeat our entire model building process to get a number of separate hits on the target. Each hit represents an individual realization of our model, given the chance variability in the training data we gather. Sometimes we will get a good distribution of training data so we predict very well and we are close to the bulls-eye, while sometimes our training data might be full of outliers or non-standard values resulting in poorer predictions. These different realizations result in a scatter of hits on the target.
Let’s look at the definition of Bias and Variance :
Bias - Bias means how far off our predictions are from real values. Generally parametric algorithms have a high bias making them fast to learn and easier to understand but generally less flexible. In turn they are have lower predictive performance on complex problems that fail to meet the simplifying assumptions of the algorithms bias.
  • Low Bias: Suggests more assumptions about the form of the target function.
  • High-Bias: Suggests less assumptions about the form of the target function.
Examples of low-bias machine learning algorithms include: Decision Trees, k-Nearest Neighbors and Support Vector Machines.
Examples of high-bias machine learning algorithms include: Linear Regression, Linear Discriminant Analysis and Logistic Regression.
Variance - Change in predictions across different data sets. Again, imagine you can repeat the entire model building process multiple times. The variance is how much the predictions for a given point vary between different realizations of the model. In other words,
Variance is the amount that the estimate of the target function will change if different training data was used.
The target function is estimated from the training data by a machine learning algorithm, so we should expect the algorithm to have some variance. Ideally, it should not change too much from one training dataset to the next, meaning that the algorithm is good at picking out the hidden underlying mapping between the inputs and the output variables.
Machine learning algorithms that have a high variance are strongly influenced by the specifics of the training data. This means that the specifics of the training have influences the number and types of parameters used to characterize the mapping function.
  • Low Variance: Suggests small changes to the estimate of the target function with changes to the training dataset.
  • High Variance: Suggests large changes to the estimate of the target function with changes to the training dataset.
Generally nonparametric machine learning algorithms that have a lot of flexibility have a high variance. For example decision trees have a high variance, that is even higher if the trees are not pruned before use.
Examples of low-variance machine learning algorithms include: Linear Regression, Linear Discriminant Analysis and Logistic Regression.
Examples of high-variance machine learning algorithms include: Decision Trees, k-Nearest Neighbors and Support Vector Machines.
Understanding Over- and Under-Fitting
At its root, dealing with bias and variance is really about dealing with over- and under-fitting. Bias is reduced and variance is increased in relation to model complexity. As more and more parameters are added to a model, the complexity of the model rises and variance becomes our primary concern while bias steadily falls. For example, as more polynomial terms are added to a linear regression, the greater the resulting model's complexity will be. In other words, bias has a negative first-order derivative in response to model complexity while variance has a positive slope.
Understanding bias and variance is critical for understanding the behavior of prediction models, but in general what you really care about is overall error, not the specific decomposition. The sweet spot for any model is the level of complexity at which the increase in bias is equivalent to the reduction in variance. Mathematically:
dBiasd/Complexity=−dVariance/dComplexity
If our model complexity exceeds this sweet spot, we are in effect over-fitting our model; while if our complexity falls short of the sweet spot, we are under-fitting the model. In practice, there is not an analytical way to find this location. Instead we must use an accurate measure of prediction error and explore differing levels of model complexity and then choose the complexity level that minimizes the overall error.

Comments

Post a Comment

Popular posts from this blog

Support Vector Machines

Image
Support Vector Machines A Support Vector Machine (SVM) is a powerful supervised machine learning model used for classification. An SVM makes classifications by defining a decision boundary and then seeing what side of the boundary an unclassified point falls on. Decision boundaries get defined,  by using a training set of classified points.     Decision boundaries exist even when your data has more than two features. If there are three features, the decision boundary is now a plane rather than a line.   As the number of dimensions grows past 3, it becomes very difficult to visualize these points in space. Nonetheless, SVMs can still find a decision boundary. However, rather than being a separating line, or a separating plane, the decision boundary is called a separating hyperplane . Optimal Decision Boundaries In general, we want our decision boundary to be as far away from training points as possible. Maximizing the dis...
Read more

ACCURACY, RECALL, PRECISION, F1 SCORE

ACCURACY, RECALL, PRECISION, F1 SCORE Classifying a single point can result in a true positive ( truth = 1 , guess = 1 ), a true negative ( truth = 0 , guess = 0 ), a false positive ( truth = 0 , guess = 1 ), or a false negative ( truth = 1 , guess = 0 ). Accuracy measures how many classifications your algorithm got correct out of every classification it made. Recall measures the percentage of the relevant items your classifier was able to successfully find. Precision measures the percentage of items your classifier found that were actually relevant. Precision and recall are tied to each other. As one goes up, the other will go down. F1 score is a combination of precision and recall. F1 score will be low if either precision or recall is low. The decision to use precision, recall, or F1 score ultimately comes down to the context of your classification. Maybe you don’t care if your classifier has a lot of false positives. If that’s the case, precision doesn’t matter as m...
Read more

Random Forest

RANDOM FOREST A random forest is an ensemble machine learning model. It makes a classification by aggregating the classifications of many decision trees. Random forests are used to avoid overfitting. By aggregating the classification of multiple trees, having overfitted trees in a random forest is less impactful. Every decision tree in a random forest is created by using a different subset of data points from the training set. Those data points are chosen at random with replacement , which means a single data point can be chosen more than once. This process is known as bagging . When creating a tree in a random forest, a randomly selected subset of features are considered as candidates for the best splitting feature. If your dataset has n features, it is common practice to randomly select the square root of n features. Boosting Steps : Draw a random subset of training samples d1 without replacement from the training set D to train a weak learner C1 ...
Read more