Practical Mathematics for AI and Deep Learning: A Concise yet In-Depth Guide on Fundamentals of Computer Vision, NLP, Complex Deep Neural Networks and Machine Learning by Tamoghna Ghosh & Shravan Kumar Belagal Math

Author:Tamoghna Ghosh & Shravan Kumar Belagal Math [Ghosh, Tamoghna & Math, Shravan Kumar Belagal]
Language: eng
Format: epub
Publisher: BPB Publications
Published: 2023-01-15T00:00:00+00:00

Points to remember

A statistic T is a function of samples from a population and is generally used to estimate a population parameter from the sample values. We can view a prediction model as a statistic and an estimator of the true population behavior. The training data can be viewed as a sample that can be used to estimate the true population behavior.

Bias-variance decomposition: The Mean-Squared Error (MSE) of T in estimating parameter can be decomposed as:

Bias-variance tradeoff: High bias model indicted our model is oversimplified and is underfitting and thus prediction from these models have high variance. Similarly, low bias implies overfitting and also prediction from this model will have low variance.

If MVU exists for a statistic, then the MLE procedure will give that estimator.

MLE estimates are consistent and efficient, but need not be unbiased.

MLE estimates are prone to overfitting, and this can be mitigated by Bayesian estimation with MAP or with regularization techniques.

Linear models discussed here should not be visualized only as lines or planes. Remember, linear means linear coefficients, and by using non-linear basis functions like polynomial or radial basis functions, we can represent very complex multivariable non-linear functions (fixed basis function models).

The probabilistic view of linear, logistic and Poisson regression helps us reduce the classification and regression problem as a convex optimization problem that can be solved by iterative gradient-based optimization methods.

The interpretability of linear models makes them more useful for solving business problems. Testing of the statistical hypothesis for whether the coefficient is actually zero helps analyze the significance of the coefficients. Lower p-value indicates low chances of rejecting the hypothesis that the coefficient is zero, and hence, the corresponding feature must be an important feature.

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