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 Problem Solving


Problem Solving and Computational Thinking in a Learning Environment

arXiv.org Artificial Intelligence

Computational thinking is a new problem solving method named for its extensive use of computer science techniques. It synthesizes critical thinking and existing knowledge and applies them to solve complex technological problems. The term was coined by J. Wing [1], but the relationship between computational and critical thinking, the two modes of thinking in solving problems, has not been yet clearly established. This paper aims in shedding some light into this relationship. We also present two classroom experiments performed recently at the Graduate Technological Educational Institute (TEI) of Patras, Greece. The result of these experiment give a strong indication that the use of computers as a tool for problem solving enhances the students‟ abilities in solving real world problems involving mathematical modelling. This is crossed by earlier findings of other researchers for the problem solving process in general (not only for mathematical problems).


Shadows and Headless Shadows: an Autobiographical Approach to Narrative Reasoning

arXiv.org Artificial Intelligence

The Xapagy cognitive architecture has been designed with the explicit goal of narrative reasoning: to model and mimic the activities performed by humans when witnessing, reading, recalling, narrating and talking about stories. Xapagy has been developed from scratch, which required us to revisit many of the problems identified in the classic literature of the story understanding. In particular, the Xapagy architecture takes an unusual approach to knowledge representation: the autobiographical narrative is the only source of knowledge, the autobiographical memory is the only memory model and there is no retrieval from long term into working memory. The claim made by this paper is that these design decisions, supported by the shadowing / headless shadows based reasoning mechanism, can yield a system which can successfully perform narrative reasoning. We support the claim by a detailed description of the representation and reasoning model.


Learning and Detecting Patterns in Multi-Attributed Network Data

AAAI Conferences

Network analysis is a growing field across many domains, including computer vision, social media marketing, transportation networks, and intelligence analysis. The growing use of digital communication devices and platforms, as well as persistent surveillance sensors, has resulted in explosion of the quantity of data and stretched the abilities of current technologies to process this data and draw meaningful conclusions. Current tools either require significant levels of manual intervention (e.g., to prepare the data, to define patterns, or to draw conclusions from data) or are unable to generalize to new data sources and analysis needs. In this paper, we present automated solutions to two major problems in network analysis: (a) finding patterns in the network data that contains high levels of noise and irrelevant information; and (b) learning repetitive patterns and dependencies between entities and attributes. Our modeling framework represents network data using multi-attributed graphs that can encode various discrete and continuous features and relationships between network entities. The pattern search and learning model is based on probabilistic multi-attributed graph matching, and implemented using distributed message passing algorithms. Our algorithms achieved high accuracy rates in learning and finding patterns in the data, are flexible to new domains and data types, and scale to large datasets using the Map-Reduce framework.


POWERPLAY: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem

arXiv.org Artificial Intelligence

Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. The novel algorithmic framework POWERPLAY (2011) continually searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Wow-effects are achieved by continually making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. POWERPLAY's search orders candidate pairs of tasks and solver modifications by their conditional computational (time & space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. The computational costs of validating new tasks need not grow with task repertoire size. POWERPLAY's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Goedel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. POWERPLAY may be viewed as a greedy but practical implementation of basic principles of creativity. A first experimental analysis can be found in separate papers [53,54].


Fast Exact Inference for Recursive Cardinality Models

arXiv.org Machine Learning

Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalization and sampling have not been addressed as thoroughly in the machine learning community. We show that there exists a simple algorithm for computing marginal probabilities and drawing exact joint samples that runs in O(Dlog2 D) time, and we show how to frame the algorithm as efficient belief propagation in a low order tree-structured model that includes additional auxiliary variables. We then develop a new, more general class of models, termed Recursive Cardinality models, which take advantage of this efficiency. Finally, we show how to do efficient exact inference in models composed of a tree structure and a cardinality potential. We explore the expressive power of Recursive Cardinality models and empirically demonstrate their utility.


Distributed Problem Solving

AI Magazine

Distributed problem solving is a subfield within multiagent systems, where agents are assumed to be part of a team and collaborate with each other to reach a common goal. In this article, we illustrate the motivations for distributed problem solving and provide an overview of two distributed problem solving models, namely distributed constraint satisfaction problems (DCSPs) and distributed constraint optimization problems (DCOPs), and some of their algorithms.


AI@NICTA

AI Magazine

NICTA is Australia's Information and Communications Technology (ICT) Centre of Excellence. It is the largest organization in Australia dedicated to ICT research. While it has close links with local universities, it is in fact an independent but not-for-profit company in the business of doing research, commercializing that research and training PhD students to do that research. Much of the work taking place at NICTA involves various topics in artificial intelligence. In this article, we survey some of the AI work being undertaken at NICTA.


Fast Heuristic Search for RTS Game Combat Scenarios

AAAI Conferences

Heuristic search has been very successful in abstract game domains such as Chess and Go. In video games, however, adoption has been slow due to the fact that state and move spaces are much larger, real-time constraints are harsher, and constraints on computational resources are tighter. In this paper we present a fast search method — Alpha-Beta search for durative moves— that can defeat commonly used AI scripts in RTS game combat scenarios of up to 8 vs. 8 units running on a single core in under 5ms per search episode. This performance is achieved by using standard search enhancements such as transposition tables and iterative deepening, and novel usage of combat AI scripts for sorting moves and state evaluation via playouts. We also present evidence that commonly used combat scripts are highly exploitable — opening the door for a promising line of research on opponent combat modelling.


Unfolding Latent Tree Structures using 4th Order Tensors

arXiv.org Machine Learning

Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper, we propose a quartet based approach which is \emph{agnostic} to this number. The key contribution is a novel rank characterization of the tensor associated with the marginal distribution of a quartet. This characterization allows us to design a \emph{nuclear norm} based test for resolving quartet relations. We then use the quartet test as a subroutine in a divide-and-conquer algorithm for recovering the latent tree structure. Under mild conditions, the algorithm is consistent and its error probability decays exponentially with increasing sample size. We demonstrate that the proposed approach compares favorably to alternatives. In a real world stock dataset, it also discovers meaningful groupings of variables, and produces a model that fits the data better.


Cognitive Bias for Universal Algorithmic Intelligence

arXiv.org Artificial Intelligence

Existing theoretical universal algorithmic intelligence models are not practically realizable. More pragmatic approach to artificial general intelligence is based on cognitive architectures, which are, however, non-universal in sense that they can construct and use models of the environment only from Turing-incomplete model spaces. We believe that the way to the real AGI consists in bridging the gap between these two approaches. This is possible if one considers cognitive functions as a "cognitive bias" (priors and search heuristics) that should be incorporated into the models of universal algorithmic intelligence without violating their universality. Earlier reported results suiting this approach and its overall feasibility are discussed on the example of perception, planning, knowledge representation, attention, theory of mind, language, and some others.