# What is the difference between bias and inductive bias?

Inductive bias is, according to Wikipedia, "the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered".

Bias, in the context of the bias-variance tradeoff, is "erroneous assumptions in the learning algorithm".

These seem equivalent to me, yet I never hear the term "inductive bias" when discussing bias/variance. Is there something I'm missing?

To explore the differences between inductive bias and bias, particularly as bias-variance tradeoff, I propose an examination of these two concepts in the context of a regression exercise to produce forecasts out-of-sample. The latter estimated prediction model may possess coefficients that required bias correction due to say a measurement error issue in the explanatory variables.

As background commencing from the same Wikipedia source on inductive bias, to repeat:

The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered.[1]

which is consistent with forecasting out-of-sample. Further, an interesting cited example of inductive bias includes:

A classical example of an inductive bias is Occam's razor, assuming that the simplest consistent hypothesis about the target function is actually the best.

As such, in the hypothetical context of the regression model best practices for out-of-sample forecasting, consistent with inductive bias would be continuing to assume say Normal distribution based errors (based upon say the prevalence of the Normal distribution error model) and a simple model (that is, something other than the best-fitting model with many variables) comprised of a parsimonious set of key variables. The latter depiction would appear to be generally consistent with the inductive bias approach.

Continuing, on the other hand, with Wikipedia on the bias-variance tradeoff, to quote:

The bias-variance tradeoff is a central problem in supervised learning. Ideally, one wants to choose a model that both accurately captures the regularities in its training data, but also generalizes well to unseen data. Unfortunately, it is typically impossible to do both simultaneously. High-variance learning methods may be able to represent their training set well but are at risk of overfitting to noisy or unrepresentative training data. In contrast, algorithms with high bias typically produce simpler models that don't tend to overfit but may underfit their training data, failing to capture important regularities.

Interestingly, the application of the above in the context of a regression prediction model appears to even more precisely imply the same path of best practices as was suggested previously by inductive bias. As such, I would agree the concepts appear to be generally related, but the bias, in the context of the bias-variance tradeoff, is contextually more specific.