An estimator $\hat{\theta}_m$ is called unbiased if $$\textrm{bias}(\hat{\theta}_m) = 0$$. 

By the definition of bias, $\mathrm{bias}(\hat \theta_m) = \mathbb{E}(\hat \theta_m) - \theta$, this implies $\mathbb{E}(\hat{\theta}_m) = \theta$. In other words, when a estimator is unbiased, the expected value of the estimator $\hat{\theta}_m$ is equal to the actual value of the parameter used to generate the data, $\theta$. 


Unbiased Estimators

$\mathrm{bias}(\hat \theta_m) = \mathbb{E}(\hat \theta_m) - \theta$, 

where $\hat{\theta}_m$ is the the estimator of a paramter, $\theta$ is the true value of that parameter, and $m$ is the sample size/number of data points. 

The bias of an estimator for a parameter is the difference between the expected value that the estimator will take when trained on data and the actual value of the parameter used to generate the data.

Johns Hopkins University

Bias is a systematic error in the estimate of an association between cause and effect. It may result from poor diagnosis/diagnostic criteria, poor case choice, poor choice of controls or variation in the way risk exposure is measured in case and controls.

Bias (Scientific)

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

- Recall bias
- Selection bias
- Collider bias
- Omitted variable bias

Types of Bias

http://approximatelycorrect.com/2016/11/07/the-foundations-of-algorithmic-bias/http://approximatelycorrect.com/2016/11/07/the-foundations-of-algorithmic-bias/

The Foundations of Algorithmic Bias



This article talks about how algorithms make decisions, how does machine learning relate to it, and it dissects many foundation ways algorithm and ML can go wrong and cause biases. It is a good indepth article on this topic.

algorithm and bias

Mathematical Defintion of Bias

A point estimator is a function that returns an estimate denoted by $\hat\theta$, using a given set of data as an input 

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