Configuration
Once the behavior model is built, the steps that lead to automatic parameter configu- ration are as follows (See Fig. 4.1 for details):
• A data mining model is needed for a specific data set,
• Current circumstance (C′) is observed and the quality requirements (Q′) are ac-
quired,
• Configuration (P′) of the data mining algorithm is determined autonomously by
Categories of domain variables Evaluate current circumstance, required quality Bayesian network of circumstances, parameters and quality measurements Inference from Bayes network Circumstance, quality criteria ARM Request Configurate and run the algorithm Configuration • Circumstantial Information • Configuration Parameters • Quality Measurements Create execution record Execution record Group circumstantial, configuration, quality measures as nodes of the network Discretize Execution records Discretized records
Determine the level of each group Domain variables & groups CONSTRUCT BAYESIAN NETWORK Search relationship between nodes in all adjacent levels
The most likely configuration is inferred from the behavior model by estimating the probabilities of possible parameter settings from previous runs of the algorithm in ex- ecution circumstances similar to current in order to obtain quality levels similar to the required. In particular, p(x|F) which is the conditional probability of x (an instantiation of parameter variable) given F (instantiations of circumstance and quality variables), is evaluated. Formal definition of inferring a value of a parameter from a Bayesian network structure is as follows:
Definition 5 Consider CI and QI defined in Definition 2 and Definition 3 respectively.
Let ctuple be any single tuple from CI and qtuple be the associated quality tuple from QI.
Consider the relation schema P (p1 : D1, ..., pn : Dn) that defines data mining algo-
rithm’s parameters(Definition 1). Let domi ={x1, x2, ...} be the domain set of pi. The
most likely setting of pi by a value from domi under the circumstance ctuple in order to
attain the data mining quality qtuple is the maximum of the φ calculated by: φk = P robability(pi = xk| ctuple, qtuple) ∀k 6 |domi|
Chapter 5
SELF-CONFIGURATION USING DECISION
TREES
5.1
Modeling the Behavior of a Data Mining Algo-
rithm with Classifiers
Predictive data mining is discovering from training data, patterns that can be gener- alized to forecast explicit values. Since, our approach for predicting future parameter settings is learning a model from past executions of the algorithm, we have chosen predictive data mining as the appropriate technique for discovering configurations.
Classification is a predictive data mining technique where a training set is used for discovering patterns to predict categorical values. We propose to use classification of execution data, E given in Definition 4 to create the behavior model of the data mining algorithm with the aim to use the model for predictive analysis of the algorithm’s behavior. Thus past execution data of the algorithm is used as the training data required for supervised learning of classification methods.
Efficiency of the data mining process and/or efficacy of data mining model, which will be referred as data mining quality thereafter, are the objectives of parameter set- tings for a particular execution of a data mining algorithm. For that reason, we analyze
under different circumstances the effect of parameter settings on the data mining quality and thereupon we determine data mining quality as the class label to be predicted.
We will first elaborate on the properties of the class label chosen while discussing the necessary transformations and later explain in detail behavior model construction by using a specific classifier, decision tree. We have chosen decision trees classifiers due to the following reasons: i) Behavior model is constructed on a ubiquitous computing device where lowest resource consumption is essential. Existence of several computa- tionally inexpensive and fast decision tree construction algorithms makes decision tree classifier a suitable choice. ii) Data mining to be configured may have any kind of parameters. Decision trees can deal with continuous data as well as categorical data so that every kind of data mining parameters can be configured. iii) In general, accuracy of decision trees is comparable to other classification techniques. iv) It is possible to extract classification rules from decision trees which provide a convenient way to infer configurations.
5.1.1
Data Mining Quality as the Class Label
Since we have determined to use classifiers for solving automatic parameter setting problem, data mining quality attributes (each qi in Definition 3) are converted to cate-
gorical attributes. Formal definition of discretized data mining quality Q is as follows:
Definition 6 Let QD(q1 : D1, ..., qn : Dn) be a relation schema defining quality fea-
tures, qi, where 1≤ i ≤ n. Let domi be the set of pairs (l, u) associated with the domain
named Di such that each pair corresponds to the lower and upper boundaries of a bin
interval after discretization.
An instance of QD that satisfies the domain constraints is a set of tuples with n fields:
In order to use data mining quality as the class label of the classifier, Q given in Definition 6 is converted to a unary relation having a single attribute (say qA). Next, we
define the aggregation function to derive aggregated data mining quality. The aggrega- tion function, fA that will be used for this purpose may consist of arbitrary operations
given that a single value, qA is obtained by making use of all other quality attributes
q1, , qn and fA should be an invertible function so that q1, , qn could be re-generated
given qA:
Definition 7 Let Qtuple be a set containing any single tuple from Q
DI. Let Q
tuple A be
a singleton set containing a unary tuple. Aggregation function for data mining quality, fA is an invertible function that defines the mapping from Qtuple to QtupleA given as:
fA : Qtuple −→ Q tuple A
Finally, formal definition of aggregated data mining quality is as follows:
Definition 8 Let QA(qA : DA) define a relation schema for aggregated data mining
quality and domA= RfA is the set of values associated with the domain named DA.
An instance of aggregated data mining quality, QAthat satisfies the domain constraints
is a set of tuples with 1 field: QAI ={< qA : dA>|dA∈ domA}