机器学习错题集
1. Some of the problems below are best addressed using a supervised learning algorithm, and the others with an unsupervised learning algorithm. Which of the following would you apply supervised learning to? (Select all that apply.) In each case,
assume some appropriate dataset is available for your algorithm to learn from. 【A,C】
A. Given historical data of childrens' ages and heights, predict children's height as a function of their age.
【解析】This is a supervised learning, regression problem, where we can learn from a training set to predict height.
B. Examine a large collection of emails that are known to be spam email, to discover if there are sub-types of spam mail.
【解析】This can addressed using a clustering (unsupervised learning) algorithm, to cluster spam mail into sub-types.
C. Examine the statistics of two football teams, and predicting which team will win tomorrow's match (given historical data of teams' wins/losses to learn from).
【解析】This can be addressed using supervised learning, in which we learn from historical records to make win/loss predictions.
D. Given a large dataset of medical records from patients suffering from heart disease, try to learn whether there might be different clusters of such patients for which we might tailor separate treatements.
【解析】This can be addressed using an unsupervised learning, clustering, algorithm, in which we group patients into different clusters.
2. Suppose that for some linear regression problem (say, predicting housing prices as in the lecture), we have some training set, and for our training set we managed to find some θ0, θ1 such that J(θ0,θ1)=0. Which of the statements below must then
be true? 【A】
A. For these values of θ0 and θ1 that satisfy J(θ0,θ1)=0, we have that hθ(x(i))=y(i) for every training example (x(i),y(i))
【解析】J(θ0,θ1)=0, that means the line defined by the equation "y=θ0+θ1x" perfectly fits all of our data.
B. For this to be true, we must have y(i)=0 for every value of i=1,2,…,m.
【解析】So long as all of our training examples lie on a straight line, we will be able to find θ0 and θ1 so that J(θ0,θ1)=0. It is not necessary that y(i)=0 for all of our examples.
C. Gradient descent is likely to get stuck at a local minimum and fail to find the global minimum.
【解析】The cost function J(θ0,θ1) for linear regression has no local optima (other than the global minimum), so gradient descent will not get stuck at a bad local minimum.
D.We can perfectly predict the value of y even for new examples that we have not yet seen. (e.g., we can perfectly predict prices of even new houses that we have not yet seen.)
【解析】Even though we can fit our training set perfectly, this does not mean that we'll always make perfect predictions on houses in the future/on houses that we have not yet seen.
3. Which of the following are reasons for using feature scaling?
It speeds up gradient descent by making it require fewer iterations to get to a good solution.
【解析】Feature scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features take on much larger values than the rest.
The cost function J(θ) for linear regression has no local optima.
The magnitude of the feature values are insignificant in terms of computational cost.
4.You run gradient descent for 15 iterations with α=0.3 and compute J(θ) aftereach iteration. You find that the value of J(θ) decreases quickly
then levels off. Based on this, which of the following conclusions seems most plausible?
A smaller learning rate will only decrease the rate of convergence to the cost function's minimum, thus increasing the number of iterations needed.
5. You are training a classification model with logistic regression. Which of the following statements are true? Check all that apply.【D】
A. Introducing regularization to the model always results in equal or better performance on the training set.
Introducing regularization to the model always results in equal or better performance on the training set.
【解析】If we introduce too much regularization, we can underfit the training set and have worse performance on the training set.
B.Adding many new features to the model helps prevent overfitting on the training set.
【解析】Adding many new features gives us more expressive models which are able to better fit our training set. If too many new features are added, this can lead to overfitting of the training set.
C. Adding a new feature to the model always results in equal or better performance on examples not in
the training set.
【解析】Adding more features might result in a model that overfits the training set, and thus can lead to worse performs for examples which are not in the training set.
D.Adding a new feature to the model always results in equal or better performance on the training set.
【解析】By adding a new feature, our model must be more (or just as) expressive, thus allowing it learn more complex hypotheses to fit the training set.
6. Which
of the following statements about regularization are true? Check all that apply.【D】
A.Because regularization causes J(θ) to no longer be convex, gradient descent may not always converge to the global minimum (when λ>0, and when using an appropriate learning rate α).
【解析】Regularized logistic regression and regularized linear regression are both convex, and thus gradient descent will still converge to the global minimum.
B.Using too large a value of λ can cause your hypothesis to overfit the data; this can be avoided by reducing λ.
【解析】Using a very large value of λ can lead to underfitting of the training set.
C.Because logistic regression outputs values 0≤hθ(x)≤1, it's range of output values can only be "shrunk" slightly by regularization anyway, so regularization is generally not helpful for it.
【解析】Regularization affects the parameters θ and is also helpful for logistic regression.
D.Consider a classification problem. Adding regularization may cause your classifier to incorrectly classify some training examples (which it had correctly classified when not using regularization, i.e. when λ=0).
【解析】Regularization penalizes complex models (with large values of θ).They can lead to a simpler models, which misclassifies more training examples.
7. Which of the following statements about regularization are true? Check all that apply.【A,B,C,D】
A.For computational efficiency, after we have performed gradient checking to verify that our backpropagation code is correct, we usually disable gradient checking before using backpropagation to train the network.
【解析】Checking the gradient numerically is a debugging tool: it helps ensure a corre ct implementation,
but it is too slow to use as a method for actually computing gradients.
B.If our neural network overfits the training set, one reasonable step to take is to increase the regularization
parameter λ.
【解析】Just as with logistic regression, a large value of λ will penalize large parameter values, thereby reducing the changes of overfitting the training set.
C.Suppose you are training a neural network using gradient descent. Depending on your random initialization, your algorithm may converge to different local optima (i.e., if you run the algorithm twice with different random initializations, gradient descent may converge
to two different solutions).
【解析】The
cost function for a neural network is non-convex, so it may have multiple minima. Which minimum you find with gradient descent depends on the initialization.
D.Suppose we have a correct implementation of backpropagation, and are training a neural network using gradient descent. Suppose we plot J(Θ) as a function of the number of iterations, and find that it isincreasing rather than decreasing. One possible cause of this is that the learning rate α is too large.
【解析】If the learning rate is too large, the cost function can diverge during gradient descent. Thus, you should select a smaller value of α.
E.Suppose that the parameter Θ(1) is a square matrix (meaning the number of rows equals the number of columns). If we replace Θ(1) with its transpose (Θ(1))T, then we have not changed the function that the network is computing.
【解析】Θ(1) can be an arbitrary matrix, so when you compute a(2)=g(Θ(1)a(1)), replacing Θ(1) with its transpose will compute a different value.
F.Suppose we are using gradient descent with learning rate α. For logistic regression and linear regression, J(θ) was a convex optimization problem and thus we did not want to choose a learning rate α that is too large. For a neural network however, J(Θ) may not be convex, and thus choosing a very large value of α can only speed up convergence.
【解析】Even when J(Θ) is not convex, a learning rate that is too large can prevent gradient descent from converging.
G.Using a large value of λ cannot hurt the performance of your neural network; the only reason we do not set λ to be too large is to avoid numerical problems.
【解析】A large value of λ can be quite detrimental. If you set it too high, then the network will be underfit to the training data and give poor predictions on both training data and new, unseen test data.
H.Gradient checking is useful if we are using gradient descent as our optimization algorithm. However, it serves little purpose if we are using one of the advanced optimization methods (such as in fminunc).
【解析】Gradient checking will still be useful with advanced optimization methods, as they depend on computing the gradient at given parameter settings. The difference is they use the gradient values in more sophisticated ways than gradient descent.