1 Mining Decision Trees from Data Streams Tong Suk Man Ivy CSIS DB Seminar February 12, 2003.

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Mining Decision Trees fromData Streams

Tong Suk Man Ivy

CSIS DB SeminarFebruary 12, 2003

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Contents

Introduction: problems in mining data streams Classification of stream data

VFDT algorithm

Window approach CVFDT algorithm

Experimental results Conclusions Future work

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Data Streams

Characteristics Large volume of ordered data points, possibly infinite Arrive continuously Fast changing

Appropriate model for many applications: Phone call records Network and security monitoring Financial applications (stock exchange) Sensor networks

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Problems in Mining Data Streams

Traditional data mining techniques usually require Entire data set to be present Random access (or multiple passes) to the data Much time per data item

Challenges of stream mining Impractical to store the whole data Random access is expensive Simple calculation per data due to time and space

constraints

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Classification of Stream Data

VFDT algorithm “Mining High-Speed Data Streams”, KDD 2000.

Pedro Domingos, Geoff Hulten

CVFDT algorithm (window approach) “Mining Time-Changing Data Streams”, KDD 2001.

Geoff Hulten, Laurie Spencer, Pedro Domingos

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Hoeffding Trees

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Definitions

A classification problem is defined as: N is a set of training examples of the form (x, y) x is a vector of d attributes y is a discrete class label

Goal: To produce from the examples a model y=f(x) that predict the classes y for future examples x with high accuracy

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Decision Tree Learning One of the most effective and

widely-used classification methods

Induce models in the form of decision trees Each node contains a test on the

attribute Each branch from a node

corresponds to a possible outcome of the test

Each leaf contains a class prediction A decision tree is learned by

recursively replacing leaves by test nodes, starting at the root

Age<30?

Car Type=Sports Car?

No

Yes

Yes

Yes No

No

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Challenges

Classic decision tree learners assume all training data can be simultaneously stored in main memory

Disk-based decision tree learners repeatedly read training data from disk sequentially Prohibitively expensive when learning complex trees

Goal: design decision tree learners that read each example at most once, and use a small constant time to process it

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Key Observation

In order to find the best attribute at a node, it may be sufficient to consider only a small subset of the training examples that pass through that node. Given a stream of examples, use the first ones to choose the

root attribute. Once the root attribute is chosen, the successive examples

are passed down to the corresponding leaves, and used to choose the attribute there, and so on recursively.

Use Hoeffding bound to decide how many examples are enough at each node

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Hoeffding Bound

Consider a random variable a whose range is R Suppose we have n observations of a Mean: Hoeffding bound states:

With probability 1- , the true mean of a is at least

, where

n

R

2

)/1ln(2

_

a

_

a

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How many examples are enough? Let G(Xi) be the heuristic measure used to choose test

attributes (e.g. Information Gain, Gini Index) Xa : the attribute with the highest attribute evaluation

value after seeing n examples. Xb : the attribute with the second highest split

evaluation function value after seeing n examples. Given a desired , if after

seeing n examples at a node, Hoeffding bound guarantees the true , with

probability 1-. This node can be split using Xa, the succeeding examples will

be passed to the new leaves.

0 GG

n

R

2

)/1ln(2

)()( ba XGXGG

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Algorithm

Calculate the information gain for the attributes and determines the best two attributes Pre-pruning: consider a “null” attribute that consists of not

splitting the node At each node, check for the condition

)()( ba XGXGG

If condition satisfied, create child nodes based on the test at the node

If not, stream in more examples and perform calculations till condition satisfied

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Data Stream

Data Stream

(Gender)-Type) (Car_

GG_

Age<30?

Yes

Yes No

Age<30?


No

Yes

Yes

Yes No

No

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Performance Analysis

p: probability that an example passed through DT

to level i will fall into a leaf at that point The expected disagreement between the tree

produced by Hoeffding tree algorithm and that produced using infinite examples at each node is no greater than /p.

Required memory: O(leaves * attributes * values * classes)

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VFDT

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VFDT (Very Fast Decision Tree)

A decision-tree learning system based on the Hoeffding tree algorithm

Split on the current best attribute, if the difference is less than a user-specified threshold Wasteful to decide between identical attributes

Compute G and check for split periodically Memory management

Memory dominated by sufficient statistics Deactivate or drop less promising leaves when needed

Bootstrap with traditional learner Rescan old data when time available

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VFDT(2)

Scales better than pure memory-based or pure disk-based learners Access data sequentially Use subsampling to potentially require much less than

one scan

VFDT is incremental and anytime New examples can be quickly incorporated as they

arrive A usable model is available after the first few examples

and then progressively defined

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Experiment Results (VFDT vs. C4.5)

Compared VFDT and C4.5 (Quinlan, 1993) Same memory limit for both (40 MB)

100k examples for C4.5

VFDT settings: δ= 10-7, τ= 5%, nmin=200

Domains: 2 classes, 100 binary attributes Fifteen synthetic trees 2.2k – 500k leaves Noise from 0% to 30%

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Experiment Results

Accuracy as a function of the number of training examples

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Experiment Results

Tree size as a function of number of training examples

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Mining Time-Changing Data Stream

Most KDD systems, include VFDT, assume training data is a sample drawn from stationary distribution

Most large databases or data streams violate this assumption Concept Drift: data is generated by a time-changing

concept function, e.g. Seasonal effects Economic cycles

Goal: Mining continuously changing data streams Scale well

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Window Approach

Common Approach: when a new example arrives, reapply a traditional learner to a sliding window of w most recent examples Sensitive to window size

If w is small relative to the concept shift rate, assure the availability of a model reflecting the current concept

Too small w may lead to insufficient examples to learn the concept

If examples arrive at a rapid rate or the concept changes quickly, the computational cost of reapplying a learner may be prohibitively high.

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CVFDT

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CVFDT

CVFDT (Concept-adapting Very Fast Decision Tree learner) Extend VFDT Maintain VFDT’s speed and accuracy Detect and respond to changes in the example-

generating process

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Observations

With a time-changing concept, the current splitting attribute of some nodes may not be the best any more.

An outdated subtree may still be better than the best single leaf, particularly if it is near the root. Grow an alternative subtree with the new best attribute

at its root, when the old attribute seems out-of-date. Periodically use a bunch of samples to evaluate

qualities of trees. Replace the old subtree when the alternate one

becomes more accurate.

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CVFDT algorithm

Alternate trees for each node in HT start as empty. Process examples from the stream indefinitely. For

each example (x, y), Pass (x, y) down to a set of leaves using HT and all

alternate trees of the nodes (x, y) passes through. Add (x, y) to the sliding window of examples. Remove and forget the effect of the oldest examples, if the

sliding window overflows. CVFDTGrow CheckSplitValidity if f examples seen since last checking of

alternate trees. Return HT.

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CVFDT algorithm: process each example

Pass example down to leaves

add example to sliding window

Window overflow? Forget oldest example

CVFDTGrow

CheckSplitValidty

f examples since last checking?

Yes No

No

Yes

Read new example

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CVFDTGrow

CheckSplitValidty


Yes No

No

Yes

Read new example

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CVFDTGrow

For each node reached by the example in HT, Increment the corresponding statistics at the node. For each alternate tree Talt of the node,

CVFDTGrow

If enough examples seen at the leaf in HT which the example reaches, Choose the attribute that has the highest average

value of the attribute evaluation measure (information gain or gini index).

If the best attribute is not the “null” attribute, create a node for each possible value of this attribute

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CVFDTGrow

CheckSplitValidty


Yes No

No

Yes

Read new example

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Forget old example

Maintain the sufficient statistics at every node in HT to monitor the validity of its previous decisions. VFDT only maintain such statistics at leaves.

HT might have grown or changed since the example was initially incorporated. Assigned each node a unique, monotonically increasing ID

as they are created. forgetExample (HT, example, maxID)

For each node reached by the old example with node ID no larger than the max leave ID the example reaches,

Decrement the corresponding statistics at the node. For each alternate tree Talt of the node, forget(Talt, example, maxID).

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Read new example




CVFDTGrow

CheckSplitValidty


Yes No

No

Yes

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CheckSplitValidtiy

Periodically scans the internal nodes of HT. Start a new alternate tree when a new winning

attribute is found. Tighter criteria to avoid excessive alternate tree

creation. Limit the total number of alternate trees.

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Smoothly adjust to concept drift

Alternate trees are grown the same way HT is.

Periodically each node with non-empty alternate trees enter a testing mode. M training examples to

compare accuracy. Prune alternate trees

with non-increasing accuracy over time.

Replace if an alternate tree is more accurate.

No

Age<30?


No

Yes

Yes

Yes

No

Married?

Yes No

Yes No

Experience<1 year?

No Yes

Yes No

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Adjust to concept drift(2)

Dynamically change the window size Shrink the window when many nodes gets

questionable or data rate changes rapidly. Increase the window size when few nodes are

questionable.

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Performance

Require memory O(nodes * attributes * attribute values * classes). Independent of the total number of examples.

Running time O(Lc * attributes * attribute values * number of classes). Lc : the longest length an example passes through * number

of alternate trees. Model learned by CVFDT vs. the one learned by

VFDT-Window: Similar in accuracy O(1) vs. O(window size) per new example.

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Experiment Results

Compare CVFDT, VFDT, VFDT-Window 5 million training examples Concept changed at every 50k examples Drift Level: average percentage of the test points that

changes label at each concept change. About 8% of test points change label each drift

100,000 examples in window 5% noise Test the model every 10k examples throughout the run,

averaged these results.

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Experiment Results (CVFDT vs. VFDT)

Error rate as a function of number of attributes

drift level

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Tree size as a function of number of attributes

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Error rates of learners as a function of the numberof examples seen

Portion of data setthat is labelled -ve

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Error rates as a function of the amount of concept drift

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Experiment Results

CVFDT’s drift characteristics

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Experiment Results (CVFDT vs. VFDT vs. VFDT-window)

Error rates over time of CVFDT, VFDT, and VFDT-window

Stimulated by running VFDT on W for every 100K examples instead of every example

Error Rate: VFDT: 19.4%CVFDT: 16.3%VFDT-Window: 15.3%

Running Time:VFDT: 10 minutesCVFDT: 46 minutesVFDT-Window: expect 548 days

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Experiment Results

CVFDT not use too much RAM D=50, CVFDT never uses more than 70MB

Use as little as half the RAM of VFDT VFDT often had twice as many leaves as the

number of nodes in CVFDT’s HT and alternate subtrees combined

Reason: VFDT considers many more outdated examples and is forced to grow larger trees to make up for its earlier wrong decisions due to concept drift

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Conclusions

CVFDT – a decision-tree induction system capable of learning accurate models from high speed, concept-drifting data streams

Grow an alternative subtree whenever an old one becomes questionable

Replace the old subtree when the new more accurate

Similar in accuracy to applying VFDT to a moving window of examples

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Future Work

Concepts changed periodically and removed subtrees may become useful again

Comparisons with related systems Continuous attributes Weighting examples

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Reference List

P. Domingos and G. Hulten. Mining high-speed data streams. In Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2000.

G. Hulten, L. Spencer, and P. Domingos. Mining time-changing data streams. In Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2001

V. Ganti, J. Gehrke, and R. Ramakrishnan. DEMON: Mining and monitoring evolving data. In Proceedings of the Sixteenth International Conference on Data Engineering, 2000.

J. Gehrke, V. Ganti, R. Ramakrishnan, and W.L. Loh. BOAT: optimistic decision tree construction. In Proceedings of the 1999 ACM SIGMOD International Conference on Management of Data, 1999.

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The end

Q & A

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Thank You!

1 Mining Decision Trees from Data Streams Tong Suk Man Ivy CSIS DB Seminar February 12, 2003.

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