We establish the convergence of the min-sum message passing algorithm for minimization of a broad class of quadratic objective functions: those that admit a convex decomposition. Our results also apply to the equivalent problem of the convergence of Gaussian belief propagation.

The advent of the Semantic Web necessitates paradigm shifts away from centralized client/server architectures towards decentralization and peer-to-peer computation, making the existence of central authorities superfluous and even impossible. At the same time, recommender systems are gaining considerable impact in e-commerce, providing people with recommendations that are personalized and tailored to their very needs. These recommender systems have traditionally been deployed with stark centralized scenarios in mind, operating in closed communities detached from their host network's outer perimeter. We aim at marrying these two worlds, i.e., decentralized peer-to-peer computing and recommender systems, in one agent-based framework. Our architecture features an epidemic-style protocol maintaining neighborhoods of like-minded peers in a robust, selforganizing fashion. In order to demonstrate our architecture's ability to retain scalability, robustness and to allow for convergence towards high-quality recommendations, we conduct offline experiments on top of the popular MovieLens dataset.

Many AI researchers and cognitive scientists have argued that analogy is the core of cognition. The most influential work on computational modeling of analogy-making is Structure Mapping Theory (SMT) and its implementation in the Structure Mapping Engine (SME). A limitation of SME is the requirement for complex hand-coded representations. We introduce the Latent Relation Mapping Engine (LRME), which combines ideas from SME and Latent Relational Analysis (LRA) in order to remove the requirement for hand-coded representations. LRME builds analogical mappings between lists of words, using a large corpus of raw text to automatically discover the semantic relations among the words. We evaluate LRME on a set of twenty analogical mapping problems, ten based on scientific analogies and ten based on common metaphors. LRME achieves human-level performance on the twenty problems. We compare LRME with a variety of alternative approaches and find that they are not able to reach the same level of performance.

Many AI researchers and cognitive scientists have argued that analogy is the core of cognition. The most influential work on computational modeling of analogy-making is Structure Mapping Theory (SMT) and its implementation in the Structure Mapping Engine (SME). A limitation of SME is the requirement for complex hand-coded representations. We introduce the Latent Relation Mapping Engine (LRME), which combines ideas from SME and Latent Relational Analysis (LRA) in order to remove the requirement for hand-coded representations. LRME builds analogical mappings between lists of words, using a large corpus of raw text to automatically discover the semantic relations among the words. We evaluate LRME on a set of twenty analogical mapping problems, ten based on scientific analogies and ten based on common metaphors. LRME achieves human-level performance on the twenty problems. We compare LRME with a variety of alternative approaches and find that they are not able to reach the same level of performance.

The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway's game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the constraint-programming community. Bucket elimination (BE) is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply BE is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques unpractical for large size problems. In response to this situation, we present a memetic algorithm for the MDSLP in which BE is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multi-level model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. Extensive experimental results analyze the performance of these models and multi-parent recombination. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances.

It is well-known that acting in an individually rational manner, according to the principles of classical game theory, may lead to sub-optimal solutions in a class of problems named social dilemmas. In contrast, humans generally do not have much difficulty with social dilemmas, as they are able to balance personal benefit and group benefit. As agents in multi-agent systems are regularly confronted with social dilemmas, for instance in tasks such as resource allocation, these agents may benefit from the inclusion of mechanisms thought to facilitate human fairness. Although many of such mechanisms have already been implemented in a multi-agent systems context, their application is usually limited to rather abstract social dilemmas with a discrete set of available strategies (usually two). Given that many real-world examples of social dilemmas are actually continuous in nature, we extend this previous work to more general dilemmas, in which agents operate in a continuous strategy space. The social dilemma under study here is the well-known Ultimatum Game, in which an optimal solution is achieved if agents agree on a common strategy. We investigate whether a scale-free interaction network facilitates agents to reach agreement, especially in the presence of fixed-strategy agents that represent a desired (e.g. human) outcome. Moreover, we study the influence of rewiring in the interaction network. The agents are equipped with continuous-action learning automata and play a large number of random pairwise games in order to establish a common strategy. From our experiments, we may conclude that results obtained in discrete-strategy games can be generalized to continuous-strategy games to a certain extent: a scale-free interaction network structure allows agents to achieve agreement on a common strategy, and rewiring in the interaction network greatly enhances the agents' ability to reach agreement. However, it also becomes clear that some alternative mechanisms, such as reputation and volunteering, have many subtleties involved and do not have convincing beneficial effects in the continuous case.

Several multiagent reinforcement learning (MARL) algorithms have been proposed to optimize agents' decisions. Due to the complexity of the problem, the majority of the previously developed MARL algorithms assumed agents either had some knowledge of the underlying game (such as Nash equilibria) and/or observed other agents actions and the rewards they received. We introduce a new MARL algorithm called the Weighted Policy Learner (WPL), which allows agents to reach a Nash Equilibrium (NE) in benchmark 2-player-2-action games with minimum knowledge. Using WPL, the only feedback an agent needs is its own local reward (the agent does not observe other agents actions or rewards). Furthermore, WPL does not assume that agents know the underlying game or the corresponding Nash Equilibrium a priori. We experimentally show that our algorithm converges in benchmark two-player-two-action games. We also show that our algorithm converges in the challenging Shapley's game where previous MARL algorithms failed to converge without knowing the underlying game or the NE. Furthermore, we show that WPL outperforms the state-of-the-art algorithms in a more realistic setting of 100 agents interacting and learning concurrently. An important aspect of understanding the behavior of a MARL algorithm is analyzing the dynamics of the algorithm: how the policies of multiple learning agents evolve over time as agents interact with one another. Such an analysis not only verifies whether agents using a given MARL algorithm will eventually converge, but also reveals the behavior of the MARL algorithm prior to convergence. We analyze our algorithm in two-player-two-action games and show that symbolically proving WPL's convergence is difficult, because of the non-linear nature of WPL's dynamics, unlike previous MARL algorithms that had either linear or piece-wise-linear dynamics. Instead, we numerically solve WPL's dynamics differential equations and compare the solution to the dynamics of previous MARL algorithms.

Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment Multi-Valued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR Multi-Valued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is search-based, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inference-based and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.

Motivation: Profile hidden Markov Models (pHMMs) are a popular and very useful tool in the detection of the remote homologue protein families. Unfortunately, their performance is not always satisfactory when proteins are in the 'twilight zone'. We present HMMER-STRUCT, a model construction algorithm and tool that tries to improve pHMM performance by using structural information while training pHMMs. As a first step, HMMER-STRUCT constructs a set of pHMMs. Each pHMM is constructed by weighting each residue in an aligned protein according to a specific structural property of the residue. Properties used were primary, secondary and tertiary structures, accessibility and packing. HMMER-STRUCT then prioritizes the results by voting. Results: We used the SCOP database to perform our experiments. Throughout, we apply leave-one-family-out cross-validation over protein superfamilies. First, we used the MAMMOTH-mult structural aligner to align the training set proteins. Then, we performed two sets of experiments. In a first experiment, we compared structure weighted models against standard pHMMs and against each other. In a second experiment, we compared the voting model against individual pHMMs. We compare method performance through ROC curves and through Precision/Recall curves, and assess significance through the paired two tailed t-test. Our results show significant performance improvements of all structurally weighted models over default HMMER, and a significant improvement in sensitivity of the combined models over both the original model and the structurally weighted models.

We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state automata with a specified number, m, of states to the set of all binary sequences. We detail optimal algorithms to predict sequences generated in this way. We explore a finite setting for the problem of prediction.