I Need help with understanding these two algorithm questions Please :)

1. 2

The blood sugar level (BSL) is defined as the concentration of sugar in our blood. This value should remain constant, around 100 mg/, indeed both a high value and a low value are dangerous, and can potentially lead to death. During a meal, we ingest glucose, and our BSL tends to increase. In a healthy individual, the homeostatic mechanism immediately counteracts the increase of BSL by releasing insulin, that brings the level down.

Paula is a patient affected by diabetes type 2, and for her the homeostatic mech- anism does not work. After a meal, she needs to guess the BLS increase (), and take the corresponding quantity of insulin to bring her BLS down to the normal level. If she guesses incorrectly, e.g., takes too little insulin, then her BLS will remain high, and this will cause her physiological stress.

Luckily, Paula is very methodical and was able to collect a training dataset with 80 meals and the corresponding exact increase in after each meal, y1, y2, . . . , y80. Note that the increase in BLS is a discrete value, so each BLS increase can assume only in {1,2,3,19,20}.

Today she wants to try a new meal, and she needs to guess the exact BLS increase (unknown), so she can take the right dose of insulin.

1. (a)Paula will have no problem if she guesses the BLS increase exactly right. However, an incorrect prediction can cause problems. She hopes to use the training dataset and no outside knowledge prediction.
2. Based on the dataset of 80 meals, what strategy should Paula use in order to maximize the probability of guessing the exact value of the BLS increase? Explain how this question relates to what we have learned in class about loss functions and making predictions. Be sure to discuss each of the following,
5. )
6. ) is minimized the minimum value of Lh)
7. (b)Assuming we could quantify physiological stress that a human body faces, then let an incorrect BLS increase prediction cause a stress which is - to the square of the difference between the prediction and the actual value. What strategy should Paula use to least impact her physiologically? Include an explanation with all of the components listed above.

2. Low BSL is dangerous

As in the previous problem, we are helping Paula predict her BLS increase (y) after her new meal. Low BSL gives the human body lesser energy to work with and can potentially be fatal. Overestimating the BLS increase (thus taking a higher dose of insulin) will cause a low BSL level, which can be very dangerous. Overestimating the BLS increase is much worse than underestimating the BLS increase.

Keeping this in mind, we now model the physiological stress in the case in which we are underestimating the BLS increase (so if h y) as the distance between the hypothesis (h) and the actual value of the BLS increase (y). Overestimating the BLS increase is a more serious problem, so we model the physiological stress in the case in which we are underestimating the BLS increase (so if > y) as 3 times the distance between

(a) What loss function L) Write down Lh) using mathematical notation.

(b) Let us assume that the training set is ordered, i.e., y1 y2 with = 80. Find the value(s) of h that minimizes L) and prove that is minimized at the value(s) of h that you claim. Explain how these results can be used to help you make predictions.

Hint: if the estimation is = 9 and the actual value of the BLS increase is = 14 (this is a case of underestimation of the BLS increase), the physiological stress is (9 14); while if = 14 (overestimation of the BLS increase), the physiological stress is 3 (19 14).