Abstract
Learning from data streams is a research area of increasing importance. Nowadays, several stream learning algorithms have been developed. Most of them learn decision models that continuously evolve over time, run in resource-aware environments, detect and react to changes in the environment generating data. One important issue, not yet conveniently addressed, is the design of experimental work to evaluate and compare decision models that evolve over time. There are no golden standards for assessing performance in non-stationary environments. This paper proposes a general framework for assessing predictive stream learning algorithms. We defend the use of Predictive Sequential methods for error estimate - the prequential error. The prequential error allows us to monitor the evolution of the performance of models that evolve over time. Nevertheless, it is known to be a pessimistic estimator in comparison to holdout estimates. To obtain more reliable estimators we need some forgetting mechanism. Two viable alternatives are: sliding windows and fading factors. We observe that the prequential error converges to an holdout estimator when estimated over a sliding window or using fading factors. We present illustrative examples of the use of prequential error estimators, using fading factors, for the tasks of: i) assessing performance of a learning algorithm; ii) comparing learning algorithms; iii) hypothesis testing using McNemar test; and iv) change detection using Page-Hinkley test. In these tasks, the prequential error estimated using fading factors provide reliable estimators. In comparison to sliding windows, fading factors are faster and memory-less, a requirement for streaming applications. This paper is a contribution to a discussion in the good-practices on performance assessment when learning dynamic models that evolve over time.

Abstract
The problem of extracting meaningful patterns from time changing data streams is of increasing importance for the machine learning and data mining communities. We present an algorithm which is able to learn regression trees from fast and unbounded data streams in the presence of concept drifts. To our best knowledge there is no other algorithm for incremental learning regression trees equipped with change detection abilities. The FIRT-DD algorithm has mechanisms for drift detection and model adaptation, which enable to maintain accurate and updated regression models at any time. The drift detection mechanism is based on sequential statistical tests that track the evolution of the local error, at each node of the tree, and inform the learning process for the detected changes. As a response to a local drift, the algorithm is able to adapt the model only locally, avoiding the necessity of a global model adaptation. The adaptation strategy consists of building a new tree whenever a change is suspected in the region and replacing the old ones when the new trees become more accurate. This enables smooth and granular adaptation of the global model. The results from the empirical evaluation performed over several different types of drift show that the algorithm has good capability of consistent detection and proper adaptation to concept drifts.

Abstract
The aim of this PhD program is the study of algorithms for learning histograms, with the capacity of representing continuous high-speed flows of data and dealing with the current problem of change detection on data streams. In many modern applications, information is no longer gathered as finite stored data sets, but assuming the form of infinite data streams. As a large volume of information is produced at a high-speed rate it is no longer possible to use memory algorithms which require the full historic data stored in the main memory, so new ones are needed to process data online at the rate it is available. Moreover, the process generating data is not strictly stationary and evolves over time; so algorithms should, while extracting some sort of knowledge from this incessantly growing data, be able to adapt themselves to changes, maintaining a representation consistent with the most recent status of nature. In this work, we presented a feasible approach, using incremental histograms and monitoring data distributions, to detect concept drift in data stream context.