An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
13th Edition
ISBN: 9781461471370
Author: Gareth James
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Chapter 4, Problem 2E
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Baye’s classifier
- To find the Baye’s classifier, as the log function is increasing it is equivalent for finding k that is
- As the last term is independen
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It is said all algorithms have an inductive bias -- a set of assumptions about the nature of the target function.
Please match the algorithms to the inductive biases below and provide a reason in one or two sentences.
1. There is a linear relationship between the inputs and the output.
2. Most cases that are near each other belong to the same class.
3. Given a class label, the probability of a feature is independent of each other.
4. The best classifier is one that maximizes the width of the boundary between classes.
5. Features that have high discriminative power should be used first to minimize the number of rules.
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Algorithm: ____________
Reason: ______________
Construct a graphical representation of DFA that accepts L={w∈(a+b)*: na(w) is even, nb(w)>1}no need to include explanations, just the graphical DFA.Please note that “a”s don't need to be consecutive.
. Draw the ERD for the following scenario.
In a university, a Lecturer can teach many different courses and even the same course numerous times. Courses can also be taught by many lecturers. A student is enrolled in only one program but a program can contain many students. Students can be rolled in many courses at the same time and the courses have many students enrolled.
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An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
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- Suppose a biking environment consists of n ≥ 3 landmarks,which are linked by bike route in a cyclical manner. That is, thereis a bike route between landmark 1 and 2, between landmark 2 and 3,and so on until we link landmark n back to landmark 1. In the centerof these is a mountain which has a bike route to every single landmark.Besides these, there are no other bike routes in the biking environment.You can think of the landmarks and the single mountain as nodes, andthe bike routes as edges, which altogether form a graph G. A path is asequence of bike routes.What is the number of paths of length 2 in the graph in termsof n?What is the number of cycles of length 3 in the graph in termsof n?What is the number of cycles in the graph in terms of n?arrow_forwardmake Membership Testing AlgorithmInput: a group G operating on f = 1,2,.....n; a permutation g of f = 1,2,.....n; a base and strong enerating set for G; Schreier vectors v I 1 I k, for the stabiliser chainOutput: a boolean result showing if g G is in the group; function is in group(p: permutation; I 1..k+l): boolean; (* return true if the permutation p is in the group G I *)arrow_forwardIn a binary classification problem, assume we have a classifier R that guesses randomly (50/50 positive/negative). For data that has 70% positive and 30% negative instances, show that R gets 50% error.arrow_forward
- Please answer the following question in depth with full detail. Consider the 8-puzzle that we discussed in class. Suppose we define a new heuristic function h3 which is the average of h1 and h2, and another heuristic function h4 which is the sum of h1 and h2. That is, for every state s ∈ S: h3(s) =h1(s) + h2(s) 2 h4(s) =h1(s) + h2(s) where h1 and h2 are defined as “the number of misplaced tiles”, and “the sum of the distances of the tiles from their goal positions”, respectively. Are h3 and h4 admissible? If admissible, compare their dominance with respect to h1 and h2, if not, provide a counterexample, i.e. a puzzle configuration where dominance does not hold.arrow_forwardA-By using the perceptron rule learning, find the weights required to perform the following classification: vectors [1 -1 -1 1], [-1 -1 1 1] and [1 1 -1 1] are members of class with target value (-1); vector [ 1 1 1 -1] not a member of class with target value (1). Initially the weights and (e) are taken as zero Y= F(yin)= { 1 if yin > e 0 if yin ≤ e -1 if yin <-e B- By using Genetic algorithm, find the value of (y1, y2, y3, y4, y5) to the following equation. F(x)=(7*X1+ 2.4*X2 + 5.5 *X3 + 0.8 *X4 + 6.4*X5) F(x)=14 Error =1 f(x) new - f(x) /arrow_forwardAppendix A 10-Fold Cross Validation for Parameter Selection Cross Validation is the standard method for evaluation in empirical machine learning. It can also be used for parameter selection if we make sure to use the training set only. To select parameter A of algorithm A(X) over an enumerated range d E [A1,..., A] using dataset D, we do the following: 1. Split the data D into 10 disjoint folds. 2. For each value of A e (A1,..., Ar]: (a) For i = 1 to 10 Train A(A) on all folds but ith fold Test on ith fold and record the error on fold i (b) Compute the average performance of A on the 10 folds. 3. Pick the value of A with the best average performance Now, in the above, D only includes the training data and the parameter A is chosen without the knowledge of the test data. We then re-train on the entire train set D using the chosen A and evaluate the result on the test set.arrow_forward
- 6. In many pattern classification problems one has the option either to assign the pat- tern to one of Ne classes, or to reject it as being unrecognizable. Let o,, i = 1,..., Ne be the action of deciding that the true state of nature is wi, and let o Net1 be the action of rejecting the pattern as unrecognizable. Let the loss function be 0, i = j A, i = Ne +1 d., otherwise where A, and A, are non-negative constants; A, is the loss associated with rejection, and A, is the loss associated with a wrong classification. Show that the minimum risk decision rule is to decide w, if P(w, x) > P(w,x) for all j and if P(w; x) >1-A/A., and reject otherwise. What happens in A, = 0? What happens if A, > 1,?arrow_forwardThe PDDL is put to use in order to provide a description of a made-up setting known as the JUNGLE. This universe has a total of five constants and three predicates, each of which may take a maximum of four arguments. There should be a limit placed on the total number of states on this JUNGLE planet. Do we need to offer justification for this?arrow_forwardQuestion 47.Random forests are one of the most famous machine learning methods. They are easy to understand,easy to implement and reach good prediction performances even without a hyper-parameter tuning. Which of thefollowing statements on random forest are correct?a) The prediction of a classification forest is made by a majority vote of the trees’ predictions.b) The prediction of a regression forest is the median of the tree predictions.c) Each single tree in the forest uses only a part of the data available.d) The training time of a random forest scales linear with the number of trees used.arrow_forward
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