ML Quiz.log

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**ML*Quiz.tex
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[]\OT1/cmtt/m/n/10 This is not true, because depending on the initial condition
, gradient descent may end up at different local optima.[] 
 []


Overfull \hbox (174.74547pt too wide) in paragraph at lines 24--24
[]\OT1/cmtt/m/n/10 YES If the learning rate is too small, then gradient descent
 may take a very long time to converge.[] 
 []


Overfull \hbox (479.24281pt too wide) in paragraph at lines 24--24
[]    \OT1/cmtt/m/n/10 If the learning rate is small, gradient descent ends up 
taking an extremely small step on each iteration, and therefore can take a long
 time to converge.[] 
 []


Overfull \hbox (279.74455pt too wide) in paragraph at lines 30--30
[]\OT1/cmtt/m/n/10 YES If $\theta_0$ and $\theta_1$ are initialized at the glob
al minimum, the one iteration will not change their values.[] 
 []


Overfull \hbox (248.24483pt too wide) in paragraph at lines 30--30
[]    \OT1/cmtt/m/n/10 At the global minimum, the derivative (gradient) is zero
, so gradient descent will not change the parameters.[] 
 []


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[]\OT1/cmtt/m/n/10 NO Setting the learning rate $\alpha$ to be very small is no
t harmful, and can only speed up the convergence of gradient descent.[] 
 []


Overfull \hbox (694.49094pt too wide) in paragraph at lines 36--36
[]   \OT1/cmtt/m/n/10 If the learning rate is small, gradient descent ends up t
aking an extremely small step on each iteration, so this would actually slow do
wn (rather than speed up) the convergence of the algorithm.[] 
 []


Overfull \hbox (48.74657pt too wide) in paragraph at lines 43--43
[]\OT1/cmtt/m/n/10 If ?0 and ?1 are initialized at a local minimum, the one ite
ration will not[] 
 []


Overfull \hbox (43.49661pt too wide) in paragraph at lines 43--43
[]\OT1/cmtt/m/n/10 At a local minimum, the derivative (gradient) is zero, so gr
adient descent[] 
 []


Overfull \hbox (300.74437pt too wide) in paragraph at lines 49--49
[]\OT1/cmtt/m/n/10 If gradient descent instead increases the objective value, t
hat means alpha is too large (or you have a bug in your code!).[] 
 []


Overfull \hbox (195.74529pt too wide) in paragraph at lines 54--54
[]\OT1/cmtt/m/n/10 YES If ?0 and ?1 are initialized at the global minimum, the 
one iteration will not change their values.
 []


Overfull \hbox (295.49442pt too wide) in paragraph at lines 54--54
\OT1/cmtt/m/n/10 Correct 0.25 At the global minimum, the derivative (gradient) 
is zero, so gradient descent will not change the parameters.[] 
 []


Overfull \hbox (452.99304pt too wide) in paragraph at lines 54--54
[]\OT1/cmtt/m/n/10 YES No matter how ?0 and ?1 are initialized, so long as a is
 sufficiently small, we can safely expect gradient descent to converge to the s
ame solution.
 []


Overfull \hbox (332.2441pt too wide) in paragraph at lines 54--54
\OT1/cmtt/m/n/10 Correct 0.25 This is not true, because depending on the initia
l condition, gradient descent may end up at different local optima.[] 
 []


Overfull \hbox (274.4946pt too wide) in paragraph at lines 58--58
[]\OT1/cmtt/m/n/10 NO Even if the learning rate a is very large, every iteratio
n of gradient descent will decrease the value of f(?0,?1).
 []


Overfull \hbox (473.99286pt too wide) in paragraph at lines 58--58
\OT1/cmtt/m/n/10 Inorrect 0.00 If the learning rate a is too large, one step of
 gradient descent can actually vastly "overshoot", and actuall increase the val
ue of f(?0,?1).[] 
 []


Overfull \hbox (657.74126pt too wide) in paragraph at lines 62--62
[]\OT1/cmtt/m/n/10 YES If ?0 and ?1 are initialized so that ?0=?1, then by symm
etry (because we do simultaneous updates to the two parameters), after one iter
ation of gradient descent, we will still have ?0=?1.
 []


Overfull \hbox (720.7407pt too wide) in paragraph at lines 62--62
\OT1/cmtt/m/n/10 Inorrect 0.00 The updates to ?0 and ?1 are different (even tho
ugh we're doing simultaneous updates), so there's no particular reason to expec
t them to be the same after one iteration of gradient descent.[] 
 []


Overfull \hbox (463.49295pt too wide) in paragraph at lines 69--69
[]\OT1/cmtt/m/n/10 Suppose that for some linear regression problem (say, predic
ting housing prices as in the lecture), we have some training set, and for our 
training set we[] 
 []


Overfull \hbox (458.243pt too wide) in paragraph at lines 69--69
[]\OT1/cmtt/m/n/10 managed to find some $\theta_0$, $\theta_1$ such that $J(\th
eta_0, \theta_1)$=0. Which of the statements below must then be true? (Check al
l that apply.)[] 
 []


Overfull \hbox (584.2419pt too wide) in paragraph at lines 73--73
[]\OT1/cmtt/m/n/10 NO We can perfectly predict the value of y even for new exam
ples that we have not yet seen. (e.g., we can perfectly predict prices of even 
new houses that we have not yet seen.)
 []


Overfull \hbox (636.74144pt too wide) in paragraph at lines 73--73
\OT1/cmtt/m/n/10 Inorrect 0.00 Even though we can fit our training set perfectl
y, this does not mean that we'll always make perfect predictions on houses in t
he future/on houses that we have not yet seen.[] 
 []


Overfull \hbox (295.49442pt too wide) in paragraph at lines 76--76
[]\OT1/cmtt/m/n/10 NO This is not possible: By the definition of J(?0,?1), it i
s not possible for there to exist ?0 and ?1 so that J(?0,?1)=0
 []


Overfull \hbox (169.49551pt too wide) in paragraph at lines 76--76
\OT1/cmtt/m/n/10 Correct 0.25 If all of our training examples lie perfectly on 
a line, then J(?0,?1)=0 is possible.[] 
 []

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[]\OT1/cmtt/m/n/10 YES Our training set can be fit perfectly by a straight line
, i.e., all of our training examples lie perfectly on some straight line.
 []


Overfull \hbox (258.74474pt too wide) in paragraph at lines 82--82
\OT1/cmtt/m/n/10 Inorrect 0.00 If J(?0,?1)=0, that means the line defined by th
e equation "y=?0+?1x" perfectly fits all of our data.[] 
 []


Overfull \hbox (169.49551pt too wide) in paragraph at lines 82--82
[]\OT1/cmtt/m/n/10 NO Gradient descent is likely to get stuck at a local minimu
m and fail to find the global minimum.
 []


Overfull \hbox (589.49185pt too wide) in paragraph at lines 82--82
\OT1/cmtt/m/n/10 Inorrect 0.00 The cost function J(?0,?1) for linear regression
 has no local optima (other than the global minimum), so gradient descent will 
not get stuck at a bad local minimum.[] 
 []

Missing character: There is no â in font cmtt10!
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[]\OT1/cmtt/m/n/10 NO For this to be true, we must have y(i)=0 for every value 
of i=1,2,,m.
 []


Overfull \hbox (636.74144pt too wide) in paragraph at lines 87--87
\OT1/cmtt/m/n/10 Correct 0.25 So long as all of our training examples lie on a 
straight line, we will be able to find ?0 and ?1 so that J(?0,?1)=0. It is not 
necessary that y(i)=0 for all of our examples.[] 
 []


Overfull \hbox (127.49588pt too wide) in paragraph at lines 87--87
[]\OT1/cmtt/m/n/10 NO For this to be true, we must have $\theta_0$=0 and $\thet
a_1$=0 so that $h_\theta$(x)=0
 []


Overfull \hbox (174.74547pt too wide) in paragraph at lines 103--103
[]\OT1/cmtt/m/n/10 YES Gradient descent is likely to get stuck at a local minim
um and fail to find the global minimum.[] 
 []


Overfull \hbox (358.49387pt too wide) in paragraph at lines 103--103
[]   \OT1/cmtt/m/n/10 Incorrect 0.00 The cost function $J(\theta_0, \theta_1)$ 
for linear regression has no local optima (other than the global minimum),[] 
 []


Overfull \hbox (347.99396pt too wide) in paragraph at lines 112--112
[]\OT1/cmtt/m/n/10 NO Our training set can be fit perfectly by a straight line,
 i.e., all of our training examples lie perfectly on some straight line.[] 
 []


Overfull \hbox (295.49442pt too wide) in paragraph at lines 112--112
[]   \OT1/cmtt/m/n/10 If $J(\theta_0, \theta_1)$=0, that means the line defined
 by the equation "y=$\theta_0$+$\theta_1$x" perfectly fits all[] 
 []


Overfull \hbox (305.99432pt too wide) in paragraph at lines 112--112
[]\OT1/cmtt/m/n/10 YES For these values of ?0 and ?1 that satisfy J(?0,?1)=0, w
e have that h?(x(i))=y(i) for every training example (x(i),y(i))
 []


Overfull \hbox (242.99487pt too wide) in paragraph at lines 112--112
\OT1/cmtt/m/n/10 Inorrect 0.00 J(?0,?1)=0, that means the line defined by the e
quation "y=?0+?1x" perfectly fits all of our data.[] 
 []

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