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Chapter Six in R Book Chapter 5 in Mount

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Title: Chapter Six in R Book Chapter 5 in Mount


1
Chapter Six in R BookChapter 5 in Mount
M.M. Dalkilic
  • Lecture VI

2
Outline
  • Algorithm vs. Heuristic
  • Statistics
  • FASTA BLAST brief introduction

3
Algorithm
  • General, well-specified sequence of instructions
    capable of being run on a Turing-complete
    computing device or formalism.
  • Youve already used BU Dynamic programming to
    find the minimal path from s to t in a structure

w
x
s
t
y
z
4
Algorithm
  • Formal parameters (signature)
  • Input (list of weights)
  • Output (path score)
  • Did you make your program generic?
  • Error checking?
  • Two other solutions

w
x
s
t
y
z
5
Algorithm
  • Formal parameters (signature)
  • Input (list of weights)
  • Output (path score)
  • Solution (I) Enumerate (path scores)
  • (p1 s1), (p2 s2),
  • linearly search for minimal pi

6
Heuristic
  • Formal parameters (signature)
  • Input (list of weights, threshold t, fitness
    function f, error e)
  • Output (path score)
  • Solution (II) Genetic Program (Sketchso you can
    work out some of the details yourselves)
  • Encode solution into binary form sb
  • Randomly change bits in sb to create a family of
    solutions S sb, sb1, sb2, , sbk
  • Form S sbi f(sbi) gt t
  • Limit lt max(f(S))
  • If (Previous Limit Current Limit lt e) return
    sbi that is maximum
  • From S by randomly swapping bits BETWEEN
    solutions
  • From S change a few bits randomly in a few
    solutions
  • GOTO 3

7
Heuristic
  • Formal parameters (signature)
  • Input (list of weights, threshold t, fitness
    function f, error e)
  • Fitness function measures goodness of solution
  • Error is the degree to which youre willing to be
    different from the actual solution were it to
    exist (think about that)

8
Heuristic
  • Problems
  • Local optima (in this case convex areas)
  • Difficult to search entire space(kangaroos in
    the mist)so must sometimes make leaps of faith
  • Not guarantee to convergeso you need to keep
    track of iterations
  • Does not produce same output, given same input

9
Heuristic
  • Problems
  • Local optima (in this case convex areas)
  • Difficult to search entire space(kangaroos in
    the mist)so must sometimes make leaps of faith
  • Not guarantee to convergeso you need to keep
    track of iterations
  • Does not produce same output, given same input

10
More Statistics
  • Recall F test is ratio of estimation of
    population variance from sample means to estimate
    average of sample variances
  • A large F value indicates differencea small
    indicates no difference. Large can be
    associated with P valuethe uncertainty youre
    willing to accept in assuming the F value is
    truly reflective of the population.

11
  • Handout showing (Matlab and P values)
  • For comparing two variances

12
t Test
  • Most often used test
  • Most often incorrectly used test
  • Cannot do sum of jointwise groups without taking
    into all parameters that affect P value
  • t ratio of difference of sample means to
    standard error of difference of sample means
  • When there are two samples Ft2

13
t Test
14
t Test
  • What if samples differ?

15
To Dos Due Next Friday
  • Pick a disease of unknown etiology and begin
    accumulating papers on itminimal (10)
  • Rewrite solutions to BU DP problem using Sol (I)
    and Sol (II).
  • Create a 2D plot in R of the solutions you
    generate from the above. The abscissa is a
    number created by prefixing the nodes on the
    leftmost side of the graph 1,2,3,4,5 from top to
    bottom to the base 10 value of the sequence of
    1s and 0s for up and down respective. The
    bottom most path would be 5(1010)_2 510. This
    is paired with the value of the path 17. You
    would then have a point at (510,17). Plot Sol
    (I) in RED and Sol (II) in BLUE. Interpret the
    graph with respect to the search space and
    solution.
  • Problem 1 page 222 in Mount
  • What does TFIIIA bind to? Using BLASTA what
    orthologues do you find. What is its function?
  • You have three groups, Control, Group A, Group B.
    What do you conclude from the data given next
    about the groups

16
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