Natural Language Processing 10 Probabilistic CFGs

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Natural Language Processing(10) Probabilistic
CFGs

• Dr. Xuan Wang(? ?)
• Intelligence Computing Research Center
• Harbin Institute of Technology Shenzhen Graduate
  School
• Slides from Slides from Dr. Mary P. Harper ECE,
  Purdue University

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Motivation

• N-gram models and HMM Tagging only allow us to
  process sentences linearly however, the
  structural analysis of simple sentences require a
  nonlinear model that reflects the hierarchical
  structure of sentences rather than the linear
  order of words.
• Context-free grammars can be generalized to
  include probabilistic information by adding rule
  use statistics.
• Probabilistic Context Free Grammars (PCFGs) are
  the simplest and most natural probabilistic model
  for tree structures and the algorithms for them
  are closely related to those for HMMs.
• Note, however, that there are other ways of
  building probabilistic models of syntactic
  structure (see Chapter 12).

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CFG Parse Example
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Dependency Parse Example
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PCFG Notation
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Formal Definition of a PCFG
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Probability of a Derivation Tree anda String
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Assumptions of the PCFG Model
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Probability of a Rule
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Estimating Probability of a Rule
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Computing Inside Probability
Caculate(2,5)
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Worlds Superstar1996 Turing Award Winners

• Amir Pnueli
• For seminal work introducing temporal logic into
  computing science and for outstanding
  contributions to program and systems
  verification.

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Biographical Data

• Amir Pnueli was born in Nahalal, Israel, on Apr.
  22, 1941. He finished his B.Sc. degree in
  Mathematics at the Technion, Haifa, and received
  his Ph.D. degree in Applied Mathematics at the
  Weizmann Institute of Science, Rehovot, Israel,
  submitting a thesis on "Calculation of Tides in
  the Ocean" in 1967.
• He switched into Computer Science while being a
  post-doctoral fellow at Stanford University, and
  at Watson Research Center, Yorktown.
• He then returned to Israel to a position of a
  Senior Researcher in the Department of Applied
  Mathematics of the Weizmann Institute.
• In 1973, Prof. Pnueli moved to Tel-Aviv
  University, where he founded the Department of
  Computer Science and was its first chairman.
• In 1981, Pnueli returned to the Weizmann
  Institute, as a Professor of Computer Science.

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Main Research Interests

• Semantics and Verification of Concurrent
  Programs, Temporal Logic, Logics of Programs,
  Specification and Non Procedural languages,
  Automatic Proof Methods for Correctness,
  Verification and Synthesis of Programs, Theory of
  Computation, Schemata Theory and its relations to
  Formal Languages Theory, Specification,
  Verification and Systematic development of
  Real-Time and Hybrid Systems. Refinement, using
  Temporal Logic. Compositional verification of
  reactive, real-time, and hybrid systems.
  Synthesis of such systems.

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Worlds Superstar1995 Turing Award Winners

• Manuel Blum
• In recognition of his contributions to the
  foundations of computational complexity theory
  and its application to cryptography and program
  checking.

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• B.S. in Electrical Engineering, Massachusetts
  Intitute of Technology, 1959M.S. in Electrical
  Engineering, Massachusetts Intitute of
  Technology, 1961Ph.D. in Mathematics,
  Massachusetts Institute of Technology, 1964

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• Thanks!