Kerala: Un atípico sistema de Desarrollo

Rossi et al. (2014) extended the original work (Rossi et al., 2012) in two main directions: 1) instead of selecting only a single algorithm, combination of multiple regressors can be selected, when the average of the predictions perform better than the individual; and 2) more comprehensive experimental evaluation is performed by adding another real-world problem -

Electricity Demand Prediction (EDP) (see Table 2.1). Furthermore the list of MFs extracted from the data is also enhanced in this work, as listed in Table 2.7. The characteristics are extracted separately from training and evaluation windows because the training window has target information available from where supervised characteristics can be extracted, i.e., the information about the relationship between predictive and target variables. The pool of Base- and Meta-level algorithms with their configurations are listed in Table 2.3 and Table 2.6 respectively. The experimental results show that for TTP dataset the pair of regressors, regardless of the presence of tie resolution strategy, outperformed Default and Ensemble approaches. However, in case of EDP, MetaStream clearly outperformed default but was worse than Ensemble which can lead to a conclusion that the observations made for pairs of regressors are also valid for multi-regressors. Moreover, the slightly higher error rate is recorded for RF Meta-learner of the MetaStream than the Default but was lower than Ensemble approach for the TTP dataset, whereas for EDP dataset MetaStream outperformed Default but was worse than Ensemble. These results show that MetaStream is able to select the best algorithm more accurately than baseline trial-and-error and ensemble- based approaches in a time-changing environment.

Table 2.7: Meta-features used in MetaStream to characterize the data

Meta-features Training window Selection window

Average, Variance, Minimum, Maximum and Median of continuous features

4 4

Average, Variance, Minimum, Maximum and Median of the target

42 Adaptive Mechanisms

Correlation between numeric features 4

Correlation of numeric attributes to the target 4

Possibility of existence of outliers in numeric fea- tures

4

Possibility of existence of outliers in the target 4

Dispersion gain 4

Skewness of numeric features 4

Kurtosis of numeric features 4

2.5.4

Discussion and Summary

This section covers the adaptability mechanisms of the system which lead to the thorough study of several existing studies. In these studies, the main focus was put on the appli- cability of MLL particularly in the context of non-stationary environments. MLL can be very beneficial for this environment in minimizing the processing-time that is consumed to periodically train the model, extracting recurring concepts, automatically detecting concept drift and estimating dynamic adaptive window size, which in-turn generate accurate predic- tions in dynamic environments. However, applying MLL to support adaptive mechanism is a quite recent and emerging area. As a result most of the research take into account the same MFs for time-varying environment which have been used to represent the algorithm recommendation problem in the context of stationary environments. Whereas if MLL is introduced in any system then the overall performance becomes dependent on appropriate representation of the problem at Meta-level in the form of MFs. The drawback of using a set of MFs which are usually used in stationary environment is that the entire target dataset should be available at-once when MLL is applied to find the learning algorithm that obtain optimal performance for that dataset; which is not the case when instances or batches of data keep coming because there are some useful MFs which cannot be computed in the absence of target variable of the incoming data.

Widmer (1997) work on applying MLL for non-stationary environment is considered to be the earliest effort. The author addressed two key areas in context of dynamic en- vironment: 1) dynamic tracking of changes and 2) extraction of recurring concepts. The problem representation of Widmer (1997) was quite general, in that, very few predictive and contextual MFs were extracted, therefore neither of the two proposed MLL approaches performed better then the Default for several domains. On the other hand, the adaptive parameters, such as, window size, were fixed in this work. Klinkenberg (2005) used different BLL algorithms and their parametrization which are automatically selected at Meta-level. Additionally, Meta-level approach for adaptive time window and recurring concept extrac- tion for the target concept were part of the research. The research is one of the initial efforts to represent adaptivity problem with the relevant MFs rather than using general features which are usually productive for stationary environment. Although these features (as listed in Table 2.8) are not enough to represent non-stationary environment at Meta-level, but they are still better than general features (used to represent stationary problems) supported by the experiments, which showed a significant improvement.

EXISTING RESEARCH Adaptive Mechanisms

Sikora (2008) proposed reinforcement learning approach to address the automatic algo- rithm recommendation problem using MLL in a non-stationary environment. The focus of

the research was to find the optimal value of the Softmax algorithm’s parameter τ where

it would recommend the best algorithm for target concept at Meta-level. The same de- ficiency is observed in this work that the non-stationary problem representation was not addressed in detail and focus was only on algorithm recommendation using MFs which were proposed for static data. Kadlec and Gabrys (2009) proposed life-long learning architecture that provided several adaptation mechanisms across a pool of candidate learning algorithms and their combinations. The dynamic behaviour of the entire architecture is analyzed at Meta-level where the global performances and information from both pools can be analyzed to estimate the influence of the changes at different levels of the model. The decrease in prediction ability of local model below a certain level is considered as a new concept which leads to building a new receptive field. The landmarking approach is quite simple and effec- tive to detect concept drift, and based on that, periodically train new local predictor. The effectiveness of MLL for the two mentioned areas is supported by improved results recorded from two case-studies.

Rossi et al. (2012) approach was quite similar to Klinkenberg (2005) where periodic al- gorithm selection for time-changing data was proposed. Likewise in various other studies, the authors computed the DSIT MFs. Although the Meta-level approach performed better than the Base-level, but there is no comparison shown with the other MLL system from where it could be concluded that even the general representation of the problem can work for the non-stationary environment. Problem representation using general MFs is the dis- crepancy of this effort which is being tried to overcome in Rossi et al. (2014). The authors computed separate MFs for historical and incoming data. As target variable has been ab- sent from the incoming data so unsupervised features were computed for the data available in the evaluation window. The performance of the proposed approach was better than BLL and worse than Ensemble but still it was considered to be a good effort towards repre- senting time-varying problem at Meta-level. In almost all the researches that are discussed in this section MLL outperformed the BLL methods. However, a common discrepancy is observed in problem representation at Meta-level for time-varying data. Most of the work used general MFs whereas some tried to focus on this area by proposing some features for non-stationary data.

Model-Agnostic Meta-Learning (MAML) is an optimal fast adaptation method which learns a model initialization in few shots such that it can be adapted to solve a new task (Finn et al., 2017). MAML first learns task-specific parameters by performing one gradient step at a time and then learns model parameters in a way to minimize the expected loss across multiple tasks. The objective is to learn a model initialization that can be generalized well to a new task in a few gradient updates. Nagabandi et al. (2018) proposed a method to learn incoming stream of data using DNN along with MLL and applied it to the model-based RL. The authors used MAML to learn the initial weights whereas Chinese restaurant process is used to learn task distribution.

44 Hyper-parameter Optimization

Table 2.8: Adaptive mechanisms used in previous studies

Research Work Adaptivity mech-

anisms addressed

Meta-features/Parameters

Widmer (1997) Recurring concept

extraction

ω=100 and significance level=0.01

Klinkenberg (2005)

Recurring concept

extraction, adap-

tive time window,

periodic algorithm

selection

No. of batches used for training at previous batch No. of non-interrupted most recent training batches Most successful learner on the previous batch Most successful learner overall on all batches have seen so far

Kadlec and

Gabrys (2009)

Concept drift detec- tion and Periodic al- gorithm selection Landmarking Rossi et al. (2012) Periodic algorithm selection ML:ω=1000,ς=1, η=0 MLL:ω=300, γ=25,ς=1, η= 0 Rossi et al. (2014) Periodic algorithm selection (with

more relevant rep-

resentation of the non-stationary problem) TTP dataset: ML:ω=1000,ς=1, η=2 MLL:ω=300,γ=24,ς=1, η=0 EDP dataset: ML:ω=672,ς=336,η=0 MLL:ω=300,γ=25,ς=1, η=0

Finn et al. (2017) Gradient based few

shot learning adap- tation method

Ti is time horizon (e.g., Ti = 1 for classification tasks)

qi is the transition distribution (qi(x1) is prior over

initial observations)

LTi is loss function (cross entropy for classification

tasks)

p(T_i) is distribution to draw a task

Nagabandi et al. (2018)

Adaptation of DNN using MLL and ap- plied it to multi-task RL

MAML