Transcript 8392_S2a - Lyle School of Engineering

CSE 8392 SPRING 1999
DATA MINING: CORE TOPICS
Overview / Statistical Foundation
Professor Margaret H. Dunham
Department of Computer Science and Engineering
Southern Methodist University
Dallas, Texas 75275
(214) 768-3087
fax: (214) 768-3085
email: [email protected]
www: http://www.seas.smu.edu/~mhd
January 1999
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DATA MINING APPLICATION:
MARKETING
• Building, Using, and Managing the Data
Warehouse, Edited by Ramon Barquin and Herb
Edelstein, Prentice Hall PTR, 1997, Ch 8.
• Fig 8-1, p139
• Ex p 138
• Modeling goal
– Pick all (and only) buyers (Precision/recall)
– Lift: Ratio of percent of accurate responders
– Cumulative Lift- Fig 8-6, p 146 (Deciles sorted based
on most likely to buy as predicted by model.)
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DEVELOPING A MODEL
• DM requires fitting a model (pattern) to the data
• Solving Data Mining Problems Through Pattern
Recognition, by Ruby L. Kennedy, Yuchun Lee,
Benjamin Van Roy, Christopher D. Reed, and
Richard D. Lippmann, Prentice Hall PTR, 19951997, Section 1.7 (pp 1-10 - 1-20).
• Fig 1-7, p 1-19
• May preprocess data to reduce overhead.
However, must be careful to avoid introducing a
bias.
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PREDICTIVE DATA MINING
• Predictive Data Mining, by Sholom M. Weiss and
Nitin Indurkhya, Morgan Kaufmann, 1998.
• Table 1.1 p8
• Data Reduction
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DM Human Participation
• Determine how to transform/reduce data
• Identify important features to model
• Correctly interpret results
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FIXED MODELS
• Fixed formula describing how output is derived
from input. Applications fully understood - no
need to look at data.
• Ex: Fixed threshold for loans
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PARAMETRIC MODELS
• Good idea of how the model should be described,
but not exact. Needs some data
• “Explicit mathematical equations characterize the
structure of the relationship between inputs and
outputs, but a few parameters are unspecified.”
(p 1-14,Kennedy)
• Training Sets - Pick parameters by looking at
data.
n
c
• Ex: Linear Regression ̂ j  
ij y i
i 1
• Fig 8-2, p140 (Barquin)
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NONPARAMETRIC MODELS
• Rely on data examination to understand the model.
(A.k.a. Data-Driven Models)
• Large amounts of data.
• Premise - Observations found in current data will
be true in future.
• May preprocess data based on knowledge which
you have.
• Methods rather than models
• Ex: Nearest Neighbor,Neural Nets, Decision-Trees
• Fig 8-3, p142 (Barquin) (More accurately reflects
training sets than linear
model)
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ERROR?
• Bias - “Difference in error between the best
solution and the proposed solution” (p 47, Weiss)
• Variance - “Expected difference in error between a
solution found for a single sample and the average
solution obtained over many random samples” (p
48, Weiss)
• Causes
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Data Warehouse/Reduction/Transformation
Survey Data/Sampling
Medical Studies with volunteers
Erroneous assumptions about the data
Problem Simplification also introduces errors
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STATISTICAL PERSPECTIVES ON DATA
MINING (Elder and Pregibon)
• Development of Statistical Methods
– Common theme: increases in memory and processor
capabilities influence statistical methods
• 1960s (Robust/Resistant)
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–
–
–
–
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Estimators sensitive to contamination
Develop new estimators
Identify and study causes of errors
Reflects realism - data does not obey mathematics
Robustness removes limitations of narrow models
No work on how to use these new/improved estimators
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• Early 1970s
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EDA: Exploratory Data Analysis
Insights and modeling data driven
Look at the data first??? (p 85, Fayyad)
Data = Fit + Residual (Fayyad formula 4.1.1, p. 85)
• Structure and noise; Iterative
– Graphical methods assist in visualization
– Data transformation: Reexpression/Splitting (p86)
• Late 1970s
– Generalized linear models (nonlinear, not normal dist)
– EM algorithm
• Solves estimation problem with incomplete data
• Treat as incomplete for “computational purposes”
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• Early 1980s
– Resampling methods
• Replace n observations with estimates
(pseudovalues pi )
ˆ  (n  k )
ˆ
p  n
i
all
i
p   pi n
• Jackknife estimate:
– Bias reduction tool
– Estimate of error in estimate
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• Late 1980s
– Globally linear  locally linear
– Scatterpoint smoothing
• Early 1990s
– Projection pursuit and squashing
– Focus shifts from model estimation to model selection
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Statistical Perspective
• Interpretability
• Characterization of uncertainty
• Borrowing strength
– Artificial stability
• Examine model for
– residuals,
– diagnostics,
– parameter covariances
• Regularization
– Ockham’s razor
– Simpler model yields best generalization
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• Common Statistical Methods
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–
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n
Linear models
Nonparametric methods
Projection pursuit
Neural networks
Polynomial networks
Decision trees
• Classification
• Estimation
– Splines
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• Summary
– Statistical Approach Strengths
• Uncertainty controlled
• Explicit assumptions
• Stability
• Interpretability
• Quantification of Variance
– Statistical methods are essential knowledge discovery
tools
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