Concept Drift Detection Using Online Histogram-Based Bayesian Classifiers

In this paper, we present a novel algorithm that performs online histogram-based classification, i.e., specifically designed for the case when the data is dynamic and its distribution is non-stationary. Our method, called the Online Histogram-based Naïve Bayes Classifier (OHNBC) involves a statistical classifier based on the well-established Bayesian theory, but which makes some assumptions with respect to the independence of the attributes. Moreover, this classifier generates a prediction model using uni-dimensional histograms, whose segments or buckets are fixed in terms of their cardinalities but dynamic in terms of their widths. Additionally, our algorithm invokes the principles of information theory to automatically identify changes in the performance of the classifier, and consequently, forces the reconstruction of the classification model in run-time as and when it is needed. These properties have been confirmed experimentally over numerous data sets (In the interest of space and brevity, we present here only a subset of the available results. More detailed results are found in [2].) from different domains. As far as we know, our histogram-based Naïve Bayes classification paradigm for time-varying datasets is both novel and of a pioneering sort

On the online classification of data streams using weak estimators

In this paper, we propose a novel online classifier for complex data streams which are generated from non-stationary stochastic properties. Instead of using a single training model and counters to keep important data statistics, the introduced online classifier scheme provides a real-time self-adjusting learning model. The learning model utilizes the multiplication-based update algorithm of the Stochastic Learning Weak Estimator (SLWE) at each time instant as a new labeled instance arrives. In this way, the data statistics are updated every time a new element is inserted, without requiring that we have to rebuild its model when changes occur in the data distributions. Finally, and most importantly, the model operates with the understanding that the correct classes of previously-classified patterns become available at a later juncture subsequent to some time instances, thus requiring us to update the training set and the training model. The results obtained from rigorous empirical analysis on multinomial distributions, is remarkable. Indeed, it demonstrates the applicability of our method on synthetic datasets, and proves the advantages of the introduced scheme

Identifying unreliable sensors without a knowledge of the ground truth in deceptive environments

This paper deals with the extremely fascinating area of “fusing” the outputs of sensors without any knowledge of the ground truth. In an earlier paper, the present authors had recently pioneered a solution, by mapping it onto the fascinating paradox of trying to identify stochastic liars without any additional information about the truth. Even though that work was significant, it was constrained by the model in which we are living in a world where “the truth prevails over lying”. Couched in the terminology of Learning Automata (LA), this corresponds to the Environment (Since the Environment is treated as an entity in its own right, we choose to capitalize it, rather than refer to it as an “environment”, i.e., as an abstract concept.) being “Stochastically Informative”. However, as explained in the paper, solving the problem under the condition that the Environment is “Stochastically Decepti”, as opposed to informative, is far from trivial. In this paper, we provide a solution to the problem where the Environment is deceptive (We are not aware of any other solution to this problem (within this setting), and so we believe that our solution is both pioneering and novel.), i.e., when we are living in a world where “lying prevails over the truth”

A Learning Automaton-based Scheme for Scheduling Domestic Shiftable Loads in Smart Grids

In this paper, we consider the problem of scheduling shiftable loads, over multiple users, in smart electrical grids. We approach the problem, which is becoming increasingly pertinent in our present energy-thirsty society, using a novel distributed game-theoretic framework. In our specific instantiation, we consider the scenario when the power system has a local-area Smart Grid (SG) subnet comprising of a single power source and multiple customers. The objective of the exercise is to tacitly control the total power consumption of the customers’ shiftable loads so to approach the rigid power budget determined by the power source, but to simultaneously not exceed this threshold. As opposed to the “traditional” paradigm that utilizes a central controller to achieve the load scheduling, we seek to achieve this by pursuing a distributed approach that allows the users¹ to make individual decisions by invoking negotiations with other customers. The decisions are essentially of the sort where the individual users can choose whether they want to be supplied or not. From a modeling perspective, the distributed scheduling problem is formulated as a game, and in particular, a so-called “Potential” game. This game has at least one pure strategy Nash Equilibrium (NE), and we demonstrate that the NE point is a global optimal point. The solution that we propose, which utilize

Concept drift detection using online histogram-based bayesian classifiers

In this paper, we present a novel algorithm that performs online histogram-based classification, i.e., specifically designed for the case when the data is dynamic and its distribution is non-stationary. Our method, called the Online Histogram-based Naïve Bayes Classifier (OHNBC) involves a statistical classifier based on the well-established Bayesian theory, but which makes some assumptions with respect to the independence of the attributes. Moreover, this classifier generates a prediction model using uni-dimensional histograms, whose segments or buckets are fixed in terms of their cardinalities but dynamic in terms of their widths. Additionally, our algorithm invokes the principles of information theory to automatically identify changes in the performance of the classifier, and consequently, forces the reconstruction of the classification model in run-time as and when it is needed. These properties have been confirmed experimentally over numerous data sets (In the interest of space and brevity, we present here only a subset of the available results. More detailed results are found in [2].) from different domains. As far as we know, our histogram-based Naïve Bayes classification paradigm for time-varying datasets is both novel and of a pioneering sort

Learning automaton based on-line discovery and tracking of spatio-temporal event patterns

Discovering and tracking of spatio-temporal patterns in noisy sequences of events is a difficult task that has become increasingly pertinent due to recent advances in ubiquitous computing, such as community-based social networking applications. The core activities for applications of this class include the sharing and notification of events, and the importance and usefulness of these functionalites increases as event-sharing expands into larger areas of one's life. Ironical

Novel results on random walk-jump chains that possess Tree-based transitions

The most difficult task in analyzing and appraising algorithms in Artificial Intelligence (AI) involves their formal mathematical analysis. In general, such an analysis is intractable because of the size of the search space and the fact that the transitions between the states within this space can be very intricate. That is why AI algorithms are, for the most part, evaluated empirically and experimentally, i.e., by simulations. However, whenever such an analysis is undertaken, it usually involves an analysis of the underlying stochastic process. In this connection, the most common tools used involve Random Walks (RWs), which is a field that has been extensively studied for more than a century [6]. These walks have traditionally been on a line, and the generalizations for two and three dimensions, have been by extending the random steps to the corresponding neighboring positions in one or many of the dimensions. The analysis of RWs on a tree have received little attention, even though it is an important topic since a tree is a counter-part space representation of a line whenever there is some ordering on the nodes on the line. Nevertheless, RWs on a tree entail moving to non-neighbor states in the space, which makes the analysis involved, and in many cases, impossible. This is precisely what we achieve in this rather pioneering paper. The applications of this paper are numerous. Indeed, the RW on the tree that this paper models, is a type of generalization of dichotomous search with faulty feedback about the direction of the search, rendering the real-life application of the model to be pertinent. To resolve this, we advocate the concept of “backtracking” transitions in order to efficiently explore the search space. Interestingly, it is precisely these “backtracking” transitions that naturally render the chain to be “time reversible”. By doing this, we are able to bridge the gap between deterministic dichotomous search and its faulty version, explained, in detail, in [21]

On the analysis of a random walk-jump chain with tree-based transitions and its applications to faulty dichotomous search

Random walks (RWs) have been extensively studied for more than a century (Feller, 1968). These walks have traditionally been on a line, and the generalizations for two and three dimensions have been by extending the random steps to the corresponding neighboring positions in one or many of the dimensions. Among the most popular RWs on a line are the various models for birth and death processes, renewal processes, and the gambler’s ruin problem. All of these RWs operate on a discretized line, and the walk is achieved by performing small steps to the current state’s neighbor states. Indeed, it is this neighbor-step motion that renders their analyses tractable. When some of the transitions are to non-neighbour states, a formal analysis is typically impossible because the difference equations of the steady-state probabilities are not solvable. One endeavor on such an analysis is found in Yazidi et al. (2011). The problem is far more complex when the transitions of the walk follow an underlying tree-like structure. The analysis of RWs on a treehave received little attention, even though it is an important topic since a tree is a counterpart space representation of a line whenever there is some ordering on the nodes on the line. Nevertheless, RWs on a tree entail moving to non-neighborstates in the space, which makes the analysis involved and, in many cases, impossible. In this article, we consider the analysis of one such fascinating RW. We demonstrate that an analysis of the chain is feasible because we can invoke the phenomenon time reversibility. Apart from the analysis being interesting in itself from an analytical perspective, the RW on the tree that this article models is a type of generalization of dichotomous search with faulty feedback about the direction of the search, rendering the real-life application of the model to be pertinent. To resolve this, we advocate the concept of “backtracking” transitions in order to efficiently explore the search space. Interestingly, it is precisely these backtracking transitions that naturally render the chain to be time reversible. By doing this, we are able to bridge the gap between deterministic dichotomous search and its faulty version. The article contains the analysis of the chain, reports some fascinating limiting properties, and also includes simulations that justify the analytic steady-state results