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Exact fit of simple finite mixture models

arXiv.org Machine Learning

How to forecast next year's portfolio-wide credit default rate based on last year's default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year's portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fix. From this observation we can conclude that the standard default rate forecast based on last year's conditional default rates will always be located between last year's portfolio-wide default rate and the ML forecast for next year. As an application example, then cost quantification is discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.


False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time

Journal of Artificial Intelligence Research

False-name manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Relatedly, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. For the problems of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley--Shubik and the normalized Banzhaf index, merely NP-hardness lower bounds are known, leaving the question about their exact complexity open. For the Shapley--Shubik and the probabilistic Banzhaf index, we raise these lower bounds to hardness for PP, "probabilistic polynomial time," a class considered to be by far a larger class than NP. For both power indices, we provide matching upper bounds for beneficial merging and, whenever the new players' weights are given, also for beneficial splitting, thus resolving previous conjectures in the affirmative. Relatedly, we consider the beneficial annexation problem, asking whether a single player can increase her power by taking over other players' weights. It is known that annexation is never disadvantageous for the Shapley--Shubik index, and that beneficial annexation is NP-hard for the normalized Banzhaf index. We show that annexation is never disadvantageous for the probabilistic Banzhaf index either, and for both the Shapley--Shubik index and the probabilistic Banzhaf index we show that it is NP-complete to decide whether annexing another player is advantageous. Moreover, we propose a general framework for merging and splitting that can be applied to different classes and representations of games.


Integrating Queueing Theory and Scheduling for Dynamic Scheduling Problems

Journal of Artificial Intelligence Research

Dynamic scheduling problems consist of both challenging combinatorics, as found in classical scheduling problems, and stochastics due to uncertainty about the arrival times, resource requirements, and processing times of jobs. To address these two challenges, we investigate the integration of queueing theory and scheduling. The former reasons about long-run stochastic system characteristics, whereas the latter typically deals with short-term combinatorics. We investigate two simple problems to isolate the core differences and potential synergies between the two approaches: a two-machine dynamic flowshop and a flexible queueing network. We show for the first time that stability, a fundamental characteristic in queueing theory, can be applied to approaches that periodically solve combinatorial scheduling problems. We empirically demonstrate that for a dynamic flowshop, the use of combinatorial reasoning has little impact on schedule quality beyond queueing approaches. In contrast, for the more complicated flexible queueing network, a novel algorithm that combines long-term guidance from queueing theory with short-term combinatorial decision making outperforms all other tested approaches. To our knowledge, this is the first time that such a hybrid of queueing theory and scheduling techniques has been proposed and evaluated.


Feature Reinforcement Learning: State of the Art

AAAI Conferences

Feature reinforcement learning was introduced five years ago as a principled and practical approach to history-based learning. This paper examines the progress since its inception. We now have both model-based and model-free cost functions, most recently extended to the function approximation setting. Our current work is geared towards playing ATARI games using imitation learning, where we use Feature RL as a feature selection method for high-dimensional domains.


Preface

AAAI Conferences

This workshop aims to bring together a wide range of computer scientists, biomedical and health informaticians, researchers, students, industry professionals, national and international public health agencies, and NGOs interested in the theory and practice of computational models of web-based public health intelligence to highlight the latest achievements in epidemiological surveillance based on monitoring online communications and interactions on the World Wide Web. The workshop includes contributions on theory, methods, systems, and applications of data mining, machine learning, databases, natural language processing, knowledge representation, artificial intelligence, semantic web, and big data analytics in web-based health-care applications, with focus on public health.


Spectral Bandits for Smooth Graph Functions with Applications in Recommender Systems

AAAI Conferences

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each recommended item is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens nodes evaluations.


Exploiting Incremental Reasoning in Healthcare Based on Hadoop and Amazon Cloud

AAAI Conferences

With a large volume of semantic data and their fast growth in semantic cities, significant challenges in performing efficient and scalable reasoning has emerged in diverse domains. When dealing with large-scale ontologies, the performance of traditional centralized reasoning methods is not sufficient, distributed reasoning methods have thus emerged to improve the scalability and efficiency of inferences. In this paper, an incremental and distributed reasoning method for large-scale ontologies is proposed to realize high-performance reasoning and online query. A novel representation method, transfer reasoning tree and underived assertional triples, is presented to store the incremental ontologies more efficiently, based on which the reasoning process is accelerated and ontology inconsistency is recovered. Finally, a system is implemented on Hadoop and Amazon Cloud, and its application in healthcare validates the effectiveness of the proposed approach.


Human and Computer Preferences at Chess

AAAI Conferences

Distributional analysis of large data-sets of chess games played by humans and those played by computers shows the following differences in preferences and performance:   (1) The average error per move scales uniformly higher the more advantage is enjoyed by either side, with the effect much sharper for humans than computers;   (2) For almost any degree of advantage or disadvantage, a human player has a significant 2--3\% lower scoring expectation if it is his/her turn to move, than when the opponent is to move; the effect is nearly absent for computers.   (3) Humans prefer to drive games into positions with fewer reasonable options and earlier resolutions, even when playing as human-computer {\em freestyle\/} tandems.   The question of whether the phenomenon (1) owes more to human perception of relative value, akin to phenomena documented by Kahneman and Tversky, or to rational risk-taking in unbalanced situations, is also addressed. Other regularities of human and computer performances are described with implications for decision-agent domains outside chess.


An Application of Multiagent Learning in Highly Dynamic Environments

AAAI Conferences

We explore the emergent behavior of game theoretic algorithms in a highly dynamic applied setting in which the optimal goal for the agents is constantly changing. Our focus is on a variant of the traditional predator-prey problem entitled Defender. Consisting of multiple predators and multiple prey, Defender shares similarities with rugby, soccer, and football, in addition to current problems in the field of Multiagent Systems (MAS). Observations, communications, and knowledge about the world-state are designed to be information-sparse, modeling real-world uncertainty. We propose a solution to Defender by means of the well-known multiagent learning algorithm fictitious play, and compare it with rational learning, regret matching, minimax regret, and a simple greedy strategy. We provide the modifications required to build these agents and state the implications of their application of them to our problem. We show fictitious play's performance to be superior at evenly assigning predators to prey in spite of it being an incomplete and imperfect information game that is continually changing its dimension and payoff. Interestingly, its performance is attributed to a synthesis of fictitious play, partial observability, and an anti-coordination game which reinforces the payoff of actions that were previously taken.


Communication-Restricted Exploration for Robot Teams

AAAI Conferences

In the event of an earthquake or fire, search and rescue efforts may be delayed until it is safe for the human rescue team to enter the area.  A team of robots could enter in advance to  provide maps, images and locations of interest to the human team, allowing them to prepare their approach when they can enter.  In a disaster area, communication may be limited, either due to infrastructure being down, or because of environmental interference. We propose an algorithm that makes use of a small number of robots, which spread as far as their communication allows, but which otherwise stay together while they explore the unknown environment.  We show that the algorithm will allow the team of robots to fully explore the environment and maintain communication in order to return the information to the waiting search and rescue team.  We also show that this can be achieved with multiple methods of communication.