Overview

1
Overview

• A Quantum Computation Simulation Language
• Anomaly Detection in the Windows Registry
• Detecting Splice Sites in Genes
• Rotationally Invariant Face Detection

2
-HSK

• A Quantum Programming Language and Compiler

Katherine Heller, Krysta Svore, Maryam Kamvar (Al
Aho)
3
What is -HSK?

• Quantum Computation Simulation Language
• Quantum Compiler
• Q-HSK enables simplified programming of quantum
  algorithms with built-in graphics

4
Many Worlds Interpretation

• One formulation of quantum theory
• Each universe has a corresponding amplitude
  (i.e. complex number)
• amplitude2 probability of existence

u3
u1
x
u2
u4
5
Qubits

• Quantum analogue of a classical bit
• Takes on values 0, 1, or superposition of
  states
• ? a 0 ß 1 where a2 ß2
  1
• ? cos(? / 2) 0 eif sin(? / 2) 1

6
Quantum Gates

• Reversible all unitary operators (U UI)
• Universal quantum gates U2,XOR, Toffoli
• Some common gates Hadamard, QFT, CNOT

H
H
1
0
1/v2 ( 0 1)
7
Key Features of the Q-HSK Compiler

• Familiar C-style syntax
• Matrix operations via CBLAS
• Complex and real data types
• A quantum type qreg
• A graphical view of quantum algorithms
• Lucid representation of quantum qubits,
  registers, and gates
• Interactive user options (start, stop, pause,
  change animation rate)
• Detailed text output to trace algorithm

8
A Simple Example

• int main( )
• int a, i
• qreg q
• qcreate(5)
• i 0
• while (i lt 5)
• qi (0.0, 0.0)
• i i 1
• q computeHadamard(q)
• a Measure(q)
• printf(This is the measure d, a)
• return 0

H
M
0
0
0
q
0
0
9
Shors Algorithm

• Factors large numbers
• n - number to factorize
• x random number
• a ranges from 0 to q-1
• n2ltqlt2n2
• r period of xa (mod n) exp. classically
• one factor of n is gcd(xr/2-1,n) fast
  classically

10
Graphical Interface
11
Architecture of Q-HSK Compiler
lex.yy.c
y.tab.c
translate.c
Program.q
Lexical Analyzer
Syntax Analyzer
Semantic Analyzer
Translator
Program.cpp
g
Executable
Java
javac
Graphics
12
One Class Support Vector Machines for Detecting
Anomalous Windows Registry Accesses
Collaborators Krysta Svore, Angelos Keromytis,
Sal Stolfo
13
Host Based Intrusion Detection Systems

• Microsoft Windows most often attacked
• Current method to combat attacks
• Virus Scanners and Security Patches
• Problem These do not combat unknown attacks so
  frequent updates are needed
• Host based IDS
• Monitor system accesses to detect intrusions
• Application of data mining techniques

14
The Windows Registry and RAD

• Windows Registry
• Stores configuration settings for system
  parameters security information, programs, etc.
• Programs query the registry for information
• Registry Anomaly Detection
• audit sensor
• model generator
• anomaly detector

Process EXPLORER.EXE Query OpenKey Key
HKCR\CKSUD\B41DB860-8EE4-11D2-9906-EA9FADC173CA\
shellex\MayChangeDefaultMenu Response
SUCCESS ResultValue NOTFOUND
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Probabilistic Anomaly Detection Algorithm

• Computes 25 consistency checks
• P(Xi) and P(XiXj)
• Multinomial with Hierarchical Prior
• For observed elements i
• P(X i) C(Ni a)/(k0aN)
• where N - total number of observations
• Ni - number of observations of symbol I
• a pseudo count for each observed symbol
• k0 number of observed symbols
• L number of possible symbols
• For unobserved elements i
• P(X i) (1-C)1/(L-k0)
• C N/(NL-k0 )

16
One Class SVMs

• Analogous to two class SVM where all data lies
  in the first class and the origin is sole member
  of second class
• Solve optimization problem to find rule f with
  maximal margin
• f(x)w,xb
• Equivalent to solving the dual quadratic
  programming problem
• mina (1/2) ?I,j aiajK(xi,xj) s.t.
  0ai1/(?l) , ?i ai 0
• Kernel function projects input vectors into a
  feature space allowing for non-linear decision
  boundaries
• F X ? RN K(xi,xj) F(xi), F(xj)

17
Experiments

• Kernels
• Linear K(x,y) (xy)
• Polynomial K(x,y) (xy1)d
• Gaussian K(x,y) e -x-y2/(2s2)
• Feature Vectors
• Binary
• Frequency-based

18
Results
19
Sequence Information for the Splicing of Human
Pre-mRNA Identified by Support Vector Machine
Classification
Collaborators Xiang Zhang, Ilana Hefter,
Christina Leslie, Larry Chasin
20
What Is Splicing?
DNA
mRNA
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Pseudo Exons

• Consensus Sequences
• Donor Site MAGgtragt (MA/C, ra/g)
• Acceptor Site (y)10ncagG (yc/t, na/c/g/t)
• Donor and acceptor sites scored based on
  closeness to consensus
• Identifying Pseudo Exons
• Intronic segments
• Have high scoring donor and acceptor sites
• We look for discriminative signals in intronic
  regions near real and pseudo exons

22
String Kernels

• Feature map number of times each k-length
  (contiguous) string occurs in sequence
• Dimension of feature space is Nk

Example
k2
Sequence ACCTGGTG
1
AC
23
Splice Kernels

• Hypothesis False splice sites are intrinsically
  defective due to bad internal nt combinations
• All possible size k internal nt combinations are
  features
• Example (k2) If the internal combination
  (3g,5a) occurs, that feature value is 1,
  otherwise it is 0

24
Recursive Feature Selection

• Normal vector to the hyperplane
• w?i1..m yiaixi
• If wj large in absolute value, the jth feature
  is important for SVM discrimination
• Approximation due to degree 2 polynomial kernel
  calculate wup and wdown separately, then
  eliminate bottom 50 of features for each
• Stop when ROC score drops below 90 of original
  value on untouched test set

25
Results
26
Rotationally Invariant Face Detection Using
Multi-Resolution Histograms
Collaborators Shikher Bisaria, Tony Jebara
27
Face Detection

• Given a picture with faces, how do we determine
  where the faces are in the image? Which pixels
  are face pixels?
• We would like to determine this with a system
  that
• Runs in real time
• Recognizes rotations of faces
• (e.g. when someone tilts their head to one side)

28
Gaussian Blurring

• Face images are greyscale (.pgms)
• Successive levels of blur are obtained by
  reconvolving previous level of blur images with a
  2 dimensional gaussian function
• Mathematically equivalent to two passes of a one
  dimensional gaussian function
• g(i,j) 1/(2ps2) ?m?n e -(m2n2)/(2s2)
  f(i-m,j-n)
• 1/(2ps2) ?m e -m2/(2s2) ?n e
  -n2/(2s2) f(i-m,j-n)

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Multi-Resolution Histograms

• Histogram equalize the image
• Concatenate histograms of image together after
  successive levels of gaussian blurring

30
Average Histograms

• Compute average face and non-face
  multi-resolution histograms from training set
• Average Non-Face Histogram Average
  Face Histogram

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Optimization Problem

• C(a) mina HFAVG hF2 HNFAVG hNF2
• Where hF (1/?i ai) ?i aihi
• hNF (1/?i (1- ai)) ?i (1-ai)hi
• such that 0 ai 1 , ?i ai 1
• Let ßi (1- ai)
• Q hi,hj
• ca hi,HFAVG constant
• cß hi,HNFAVG constant
• mina,ß aTQa 1/(N-1)2 ßTQß 2caTa
  2/(N-1)cßTß

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Solve Using SMO

• aiNEW 1/(N-1)2 Qii - 1/(N-1)2 ?k?i,jak Qjj
  (1- ?k?i,jak ) Qjj
• - (1- ?k?i,jak ) Qij 1/(N-1)2 ?k?i,jak Qij -
  1/(N-1)2 Qij - cai
• cßi caj - cßj ?k?i,j(ak Qik) - ?k?i,j(ak
  Qjk)
• - 1/(N-1)2 ?k?i,j(ak Qik) 1/(N-1)2 ?k?i,j(ak
  Qjk) / Qii Qjj
• - 2Qij 1/(N-1)2 Qii 1/(N-1)2 Qjj -
  2/(N-1)2 Qij
• Bounds for aiNEW
• L 0
• H 1 - ?k?i,jak
• ajNEW (1 - ?k?i,jak ) - aiNEW

33
Results