Write an classifier algorithm for ∏M i=1 p(yi|X,α)
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Write an classifier
i=1 p(yi|X,α)
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- import numpy as np # Define the differential equation functiondef func(t, y): return t - y**2# Define the initial conditions and parameterst0 = 0y0 = 1t_max = 2n = 10h = (t_max - t0) / n# Implement Euler's methodt = t0y = y0for i in range(n): y += h * func(t, y) t += hprint(y)print("\n")Construct a DFA A so that L(A) = L(N) where N is the following NFA:Given the following recursively defined set S: Basis: 0 € S and 7 € S Recursive rule: if x ES and y = S, then: • x+yЄS x-yes Prove that every element in S is divisible by 7.
- Describe each of the following sets.a. {x ∈ R|−5 < x < 1}b. {x ∈ Z|−5 < x < 1}c. {x ∈ Z−|−5 < x < 1}NORMALIZATION PROBLEM: Normalization is one of the most basic preprocessing techniques in data analytics. This involves centering and scaling process. Centering means subtracting the data from the mean and scaling means dividing with its standard deviation. Mathematically, normalization can be expressed as: Z = X-x σ In Python, element-wise mean and element-wise standard deviation can be obtained by using .mean() and .std() calls. In this problem, create a random 5 x 5 ndarray and store it to variable X. Normalize X.1: |R|←|P| Reserve space for |P| = 13 values.2: x ← n3: for i ← 0 ...(|P| − 1) do4: c ← x div Pi Number of multiplicands Pi in x.5: Ri ← c6: x ← x − c · Pi7: end for8: return RA Java programmer could implement Algorithm by first modelling the primitivenumbers with the enumeration type RomanNumeral. Each enum constant (I, IV, ..., M) is declared with its decimal value, which can be accessed with the function getValue().
- L₁ = {abman: n ≥ 0, m>0} Use the rule of contradiction, prove that following language is regular or not.Input: A set of n movies. A positive integer k. A positive integer q. A function f that takes two movies X, Y, and gives a positive similarity score f(X,Y) in constant time. Task: Design an efficient algorithm that partitions the movies into exactly k disjoint sets such that movies from different sets have a similarity score at most q. If such groups cannot be made, then print 'Unsatisfiable'. Give an efficient algorithm (to the best of your knowledge) and a formal proof of correctness for your algorithm. An answer without any formal proof will be considered incomplete. Analyze the running time of the algorithm. You must write down your algorithm as pseudocode or describe it as a set of steps (as we do in the class). Do not provide code that is written in a code editor using C/C++/Python/Java, etc.Python Lee has discovered what he thinks is a clever recursive strategy for printing the elements in a sequence (string, tuple, or list). He reasons that he can get at the first element in a sequence using the 0 index, and he can obtain a sequence of the rest of the elements by slicing from index 1. This strategy is realized in a function that expects just the sequence as an argument. If the sequence is not empty, the first element in the sequence is printed and then a recursive call is executed. On each recursive call, the sequence argument is sliced using the range 1:. Here is Lee’s function definition: def printAll(seq): if seq: print(seq[0]) printAll(seq[1:]) Write a program that tests this function and add code to trace the argument on each call. Does this function work as expected? If so, are there any hidden costs in running it? how ???
- Python Lee has discovered what he thinks is a clever recursive strategy for printing the elements in a sequence (string, tuple, or list). He reasons that he can get at the first element in a sequence using the 0 index, and he can obtain a sequence of the rest of the elements by slicing from index 1. This strategy is realized in a function that expects just the sequence as an argument. If the sequence is not empty, the first element in the sequence is printed and then a recursive call is executed. On each recursive call, the sequence argument is sliced using the range 1:. Here is Lee’s function definition: def printAll(seq): if seq: print(seq[0]) printAll(seq[1:]) Write a program that tests this function and add code to trace the argument on each call. Does this function work as expected? If so, are there any hidden costs in running it? its supposed to print something like thisThe following recursive definition of a set S over {a, b, c, d}. Basis: "", a, b, c E S. Recursive Step: If ax E S, then bax ES and cax E S. If bx € S, then cbx € S. If cx = S, then bax ES and bcx = S. If dx E S, then ddx E S. Closure: SE S only if it is a, b or c or it can be obtained from a, b or c using finitely many operations of the Recursive Step. a) What recursive step can be removed from the above definition and why? b) Derive from the definition of S that bcbc S. c) Explain why baa & S.S is a set of strings over the alphabet {a, b}* recursively defined as: Base case: λ ∈ S, a ∈ S, b ∈ S Recursive rules: If x ∈ S, then Rule 1: axb ∈ S Rule 2: bxa ∈ S List all the strings in S of length 3.