Functions of Two Variables A function \(f\) of two variables is a rule that assigns each ordered pair of real numbers \((x,y)\) in a set \(D\) to a unique real number denoted by \(f(x,y)\). Th...

Length of a Curve Suppose a curve has the vector equation \(r(t) = \left\langle f(t), g(t), h(t) \right\rangle,\ a \leq t \leq b\), or, equivalently, the parametric equations \(x=f(t), y=g(t),...

Keywords [1] If the square matrix \(A\) has an inverse, then \(A^{-1}A=I\) and \(AA^{-1}=I\) [2] The algorithm to test invertibility is elimination: \(A\) must have \(n\) nonzero pivots [3] ...

Derivatives stewart-calculus-8th-edition The derivative \(r'\) of a vector function \(r\) is [\frac{dr}{dt}=r’(t)=\lim_{h \rightarrow 0}\frac{r...

Vector functions and space curves Vector function is a function whose domain is a set of real numbers and whose range is a set of vectors. We’re interested in vector function \(r\). For every ...

Introduction When real-time inference is not required, ensembling different models can bring about performance boost. Some of popula ensembling methods for object detection include non-maximum...

Maximum Likelihood Estimation (MLE) Likelihood Function In the last post link, we’ve seen common estimators and some of their properties. But, how do we systematically choose good estimators ...

Point Estimation Point estimation is an estimation to provide the single best prediction of some quantity of interest. The quantity of interest might be a single parameter or a vector of param...

Hyperparameters deeplearningbook.org Most machine learning algorithms have hyperparamters that are not modified by the learning algorithm itself...

Train and Test set The central goal in machine learning is that our model must perform well on the previously unseen inputs not the data we trained for. This ability is known as generalization...