Publications by Betsy Rosalen

CUNY MSDS DATA609 HW6

15.11.2021

Ex. 1 Use a data set such as PlantGrowth in R to calculate three different distance metrics and discuss the results. Without thinking much about it I calculated the distance using both variables, independent and dependent, (you can see the results below), but then the numbers didn’t really make sense. For the Manhattan distance it is just doub...

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CUNY MSDS DATA609 HW5

07.11.2021

Ex. 1 Carry out the logistic regression (Example 22 on Page 94 in the book, Introduction to Algorithms for Data Mining and Machine Learning, by Xin-She Yang), in R using the data. x 0.1 0.5 1.0 1.5 2.0 2.5 y 0 0 1 1 1 0 The formula is \[y(x) = \frac{1}{1+exp[-(a+bx)]}\] First we use the glm function with family = 'binomial' to cr...

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CUNY MSDS DATA609 HW4

17.10.2021

Ex. 1 For Example 19 on Page 79 in the book (Introduction to Algorithms for Data Mining and Machine Learning, by Xin-She Yang), carry out the regression using R. x -0.98 1.00 2.02 3.03 4.00 y 2.44 -1.51 -0.47 2.54 7.52 I always plot the data first to see if it gives me any insight into what type of model I might need. In this case i...

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CUNY MSDS DATA609 HW2

20.09.2021

Ex. 1 Show \(x^2 + exp(x) + 2x^4 + 1\) is convex. A function is defined as convex if: \[ f(\alpha x+\beta y) \le \alpha f(x) + \beta f(y), \quad \forall \:x,\: y \in \Omega, \quad \text{where } \alpha \ge 0,\ \beta \ge 0,\ \alpha + \beta = 1. \] Substituting in our expression we get: \[ \begin{align} (\alpha x+\beta y)^2 + exp(\alpha x + \beta y...

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CUNY MSDS DATA609 HW1

19.09.2021

Ex. 1 Find the minimum of \(f(x,y) = x^2 + xy + y^2\) in \((x, y) \in\mathbb{R}^2\). There are two first partial derivatives \(\frac{\partial f}{\partial x}\) and \(\frac{\partial f}{\partial y}\), thus the stationary conditions are: \(\frac{\partial f}{\partial x} = 2x + y = 0\) and \(\frac{\partial f}{\partial y} = x + 2y = 0\). From \(2x + y ...

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CUNY MSDS DATA609 HW3

04.10.2021

Ex. 1 Write down Newton’s formula for finding the minimum of \[f(x) = (3x^4 - 4x^3)/12\] in the range of \([-10, 10]\). Then implement it in R. Newton’s Formula: \[ \begin{align} x_{k+1} = x_k - \frac{f'(x_k)}{f''(x_k)} \end{align} \] Inserting the first two derivatives of \(f(x) = \frac{3x^4 - 4x^3}{12}\) we get: \[ \begin{align} x_{k+1} ...

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