LINEAR REGRESSION

 

https://tinyurl.com/AML-2021-ASSIGNMENT1
1. (0.5 points) Give an example of a finite hypothesis class H with VCdim(H) = 2021.
Justify your choice.
2. (0.5 points) Consider Hballs to be the set of all balls in R2
:
Hballs = {B(x,r), x ∈ ℝ2
, r ≥ 0 }, where B(x,r) = {y ∈ ℝ2
| || y – x ||2 ≤ r}
view Hballs as the set of indicator functions of
the balls B(x,r) in the plane: Hballs ={ ℎ!.!: ℝ! → 0,1 , ℎ!.! = �!(!,!), � ∈ ℝ!, � > 0}.
Can you give an example of a set A in R2 of size 4 that is shattered by Hballs? Give
such an example or justify why you cannot find a set A of size 4 shattered by Hballs.
3. (1 point) Let X = R2 and consider Hα the set of concepts defined by the area inside a
right triangle ABC with the two catheti AB and AC parallel to the axes (Ox and Oy)
and with AB/AC = α (fixed constant > 0). Consider the realizability assumption. Show
that the class Hα can be (�, �) − PAC learned by giving an algorithm A and
determining an upper bound on the sample complexity mH( �, �) such that the
definition of PAC-learnability is satisfied.
4. (1 point) Consider H to be the class of all centered in origin sphere classifiers in the
3D space. A centered in origin sphere classifier in the 3D space is a classifier hr that
assigns the value 1 to a point if and only if it is inside the sphere with radius r > 0 and
center given by the origin O(0,0,0). Consider the realizability assumption.
a. show that the class H can be (�, �) − PAC learned by giving an algorithm A and
determining an upper bound on the sample complexity mH(�, �) such that the
definition of PAC-learnability is satisfied. (0.5 points)
b. compute VCdim(H). (0.5 points)
5. (1 point) Let H = {ℎ!: ℝ → 0,1 , ℎ! � = � !,!!! ∪[!!!,!!) � , � ∈ ℝ}. Compute
VCdim(H).
6. (1 point) Let X be an instance space and consider H ⊆ {0,1}! a hypothesis space with
finite VC dimension. For each � ∈ X, we consider the function zx: H →{0,1} such
that zx(h) = h(x) for each ℎ ∈ H. Let Z = {zx: H →{0,1}, � ∈ X}. Prove that
VCdim(Z) < 2VCdim(H)+1.
Ex-officio: 0.5 points

 

 

 

 

 

 

 

Sample Solution

 

 

Reasons for a Cold

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interpretive paper sampleSummer is gone, and now it is the center of fall. In spite of that it is a delightful season, supported by writers and inventive individuals by and large, it is additionally when the climate changes, and gets colder. Numerous individuals in harvest time may wake up and find their noses are full, and their throats throb; the most unfortunate of them feel fever and chills. These are the most well-known side effects of the basic cold, and since it is just getting colder, it is helpful to make sense of what precisely aims the normal virus to have the option to dodge it.

A great many people think the regular virus is brought about by chilly climate, since it sounds sensible and self-evident. Be that as it may, cold itself doesn’t cause affliction, which is effectively demonstrated by individuals who can swim in super cold water, or by the individuals who are less touchy to chilly climate. The most commonplace reason for the cold, be that as it may, is a group of infections called rhinoviruses (HowStuffWorks). A rhinovirus is transmitted through air, so when a tainted individual sniffles, and you breathe noticeable all around close by, you may get contaminated too (this is one reason why specialists now and again prescribe to wear face covers in broad daylight places when it is cold outside). The infection can be transmitted in some different manners too, as through handshakes (and contacting when all is said in done).

Another sort of infection answerable for individuals getting the basic virus is a group of supposed coronaviruses. It is accepted these infections ordinarily cause around 20 percent of colds. Coronaviruses as a rule influence the nose, sinuses, and additionally upper throat. Despite the fact that this kind of infection isn’t excessively hazardous, there have been situations when it has caused genuine peril and passing. For instance, in 2012, near 100 individuals in the Middle East kicked the bucket based on what was called MERS (Middle East respiratory disorder). Coronaviruses are likewise known to have caused extreme intense respiratory disorder, and some different sicknesses that have deadly outcomes (WebMD).

The respiratory syncytial infection is additionally among the fundamental driver of the virus. RSV typically influences newborn children, and in most of cases doesn’t prompt much else genuine than the regular virus. However, it can cause pneumonia in uncommon cases, so guardians ought to know about this infection (WebMD).

Overall, the normal virus isn’t a risk to current humankind. On the off chance that an individual has a solid safe framework, their body can even arrangement with the disease all alone; notwithstanding, this is uncommon, and it is still strongly prescribed to visit a specialist in the wake of seeing the indications of a virus. Infections causing the normal virus are typically transmitted through air, and as a rule don’t cause genuine disorder. Notwithstanding, a few sorts of coronavirus, for example, MERS or SARS, are known to have caused passings previously. RSV specifically can be a danger for newborn children, because of its capacity to cause pneumonia in uncommon cases. In any case, when all is said in done, convenient treatment dispenses with all the manifestations and the ailment itself.

References

“What Causes the Common Cold?” HowStuffWorks. N.p., n.d. Web. 01 Oct. 2014. .

“Coronavirus Symptoms, Causes, Treatments, Types.” WebMD. WebMD, n.d. Web. 03 Oct. 2014. .

“RSV in Babies: Symptoms, Causes, Treatment, and Vaccine.” WebMD. WebMD, n.d. Web. 01 Oct. 2014. .

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