16978245
Learning with the Knowledge of an Upper Bound on Program Size
Abstract Two learning situations are considered: machine identification of programs from graphs of recursive functions (modeling inductive hypothesis formation) and machine identification of grammars from texts of recursively enumerable languages (modeling first language acquisition). Both these learning models are extended to account for situations in which a learning machine is provided additional information in the form of knowledge about an upper bound on the minimal size program (grammar) for the function (language) being identified. For a number of such extensions, it is shown that larger classes of functions (languages) can be algorithmically identified in the presence of upper bound information. Numerous interesting relationships are shown between different models of learning, number of anomalies allowed in the inferred program (grammar), and number of anomalies allowed in the upper bound information.
39847140
Team Learning of Recursive Languages
A team of learning machines is a multiset of learning machines. A team is said to successfully learn a concept just in case each member of some nonempty subset, of predetermined size, of the team learns the concept. Team learning of languages turns out to be a suitable theoretical model for studying computational limits on multi-agent machine learning. Team learning of recursively enumerable languages has been extensively studied. However, it may be argued that from a practical point of view all languages of interest are recursive. 
 
This paper gives theoretical results about team learnability of recursive languages. These results are mainly about two issues: redundancy and aggregation. The issue of redundancy deals with the impact of increasing the size of a team and increasing the number of machines required to be successful. The issue of aggregation deals with conditions under which a team may be replaced by a single machine without any loss in learning ability. The learning scenarios considered are: (a) Identification in the limit of accepting grammars for recursive languages. (b) Identification in the limit of decision procedures for recursive languages. (c) Identification in the limit of accepting grammars for indexed families of recursive languages. (d) Identification in the limit of accepting grammars for indexed families with enumerable class of grammars for the family as the hypothesis space. Scenarios which can be modeled by team learning are also presented.
145211
Computational Limits on Team Identification of Languages
A team of learning machines is a multiset of learning machines. A team is said to successfully identify a concept just in case each member of some nonempty subset, of predetermined size, of the team identifies the concept. Team identification of programs for computable functions from their graphs has been investigated by Smith. Pitt showed that this notion is essentially equivalent to function identification by a single probabilistic machine. The present paper introduces, motivates, and studies the more difficult subject of team identification of grammars for languages from positive data. It is shown that an analog of Pitt's result about equivalence of team function identification and probabilistic function identification does not hold for language identification, and the results in the present paper reveal a very complex structure for team language identification. It is also shown that for certain cases probabilistic language identification is strictly more powerful than team language identification. Proofs of many results in the present paper involve very sophisticated diagonalization arguments. Two very general tools are presented that yield proofs of new results from simple arithmetic manipulation of the parameters of known ones.
122230605
On the intrinsic complexity of learning recursive functions
The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy. Some self-describing classes turn out to be complete. Furthermore, the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity, though in general, intrinsic complexity and mind change complexity can behave "orthogonally".
5851955
Vacillatory Learning of Nearly Minimal Size Grammars
In Gold's influential language learning paradigm a learning machine converges in the limit to one correct grammar. In an attempt to generalize Gold's paradigm, Case considered the question whether people might converge to vacillating between up to (some integer) n > 1 distinct, but equivalent, correct grammars. He showed that larger classes of languages can be algorithmically learned (in the limit) by converging to up to n + 1 rather than up to n correct grammars. He also argued that, for ''small'' n>1, it is plausible that people might sometimes converge to vacillating between up to n grammars. The insistence on small n was motivated by the consideration that, for ''large'' n, at least one of n grammars would be too large to fit in people's heads. Of course, even for Gold's n = 1 case, the single grammar converged to in the limit may be infeasibly large. An interesting complexity restriction to make, then, on the final grammar(s) converged to in the limit is that they all have small size. In this paper we study some of the trade-offs in learning power involved in making a well-defined version of this restriction. We show and exploit as a tool the desirable property that the learning power under our size-restricted criteria (for successful learning) is independent of the underlying acceptable programming systems. We characterize the power of our size-restricted criteria and use this characterization to prove that some classes of languages, which can be learned by converging in the limit to up to n + 1 nearly minimal size correct grammars, cannot be learned by converging to up to n unrestricted grammars even if these latter grammars are allowed to have a finite number of anomalies (i.e., mistakes) per grammar. We also show that there is no loss of learning power in demanding that the final grammars be nearly minimal size iff one is willing to tolerate an unbounded, finite number of anomalies in the final grammars and there is a constant bound on the number of different grammars converged to in the limit. Hence, if we allow an unbounded, finite number of anomalies in the final grammars and the number of different grammars converged to in the limit is unbounded but finite (or if there is a constant bound on the number of anomalies allowed in the final grammars), then there is a loss of learning power in requiring that the final grammars be nearly minimal size. These results do not always match what might be expected from the cases, previously examined by Freivalds, Kinber, and Chen, of learning nearly minimal size programs for functions.
30890449
Prudence in Vacillatory Language Identification (Extended Abstract)
The present paper settles an open question about ‘prudent’ vacillatory identification of grammars from positive data only.
47220301
Expert simulation for on-line scheduling
The state-of-the-art in manufacturing has moved toward flexibility, automation and integration. The efforts spent on bringing computer-integrated manufacturing (CIM) to plant floors have been motivated by the overall thrust to increase the speed of new products to market. One of the links in CIM is plant floor scheduling, which is concerned with efficiently orchestrating the plant floor to meet the customer demand and responding quickly to changes on the plant floor and changes in customer demand. The Expert System Scheduler (ESS) has been developed to address this link in CIM. The scheduler utilizes real-time plant information to generate plant floor schedules which honor the factory resource constraints while taking advantage of the flexibility of its components.
The scheduler uses heuristics developed by an experienced human factory scheduler for most of the decisions involved in scheduling. The expertise of the human scheduler has been built into the computerized version using the expert system approach of the discipline of artificial intelligence (AI). Deterministic simulation concepts have been used to develop the schedule and determine the decision points. As such, simulation modeling and AI techniques share many concepts, and the two disciplines can be used synergistically. Examples of some common concepts are the ability of entities to carry attributes and change dynamically (simulation—entities/attributes or transaction/parameters versus AI—frames/slots); the ability to control the flow of entities through a model of the system (simulation—conditional probabilities versus AI—production rules); and the ability to change the model based upon state variables (simulation—language constructs based on variables versus AI—pattern-invoked programs). Shannon [6] highlights similarities and differences between conventional simulation and an AI approach. Kusiak and Chen [3] report increasing use of simulation in development of expert systems.
ESS uses the synergy between AI techniques and simulation modeling to generate schedules for plant floors. Advanced concepts from each of the two areas are used in this endeavor. The expert system has been developed using frames and object-oriented coding which provides knowledge representation flexibility. The concept of “backward” simulation, similar to the AI concept of backward chaining, is used to construct the events in the schedule. Some portions of the schedule are constructed using forward or conventional simulation.
The implementation of expert systems and simulation concepts is intertwined in ESS. However, the application of the concepts from these two areas will be treated separately for ease of presentation. We will first discuss the expert system approach and provide a flavor of the heuristics. The concept of backward simulation and the motive behind it will then be explored along with some details of the implementation and the plant floor where the scheduler is currently being used. We will then highlight some advantages and disadvantages of using the expert simulation approach for scheduling, and, finally, the synergetic relationship between expert systems and simulation.
6467955
Low degree metabolites explain essential reactions and enhance modularity in biological networks
BackgroundRecently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints.ResultsIn the metabolic networks of Escherichia coli, Saccharomyces cerevisiae and Staphylococcus aureus, we identified metabolites with a low degree of connectivity, particularly those that are produced and/or consumed in just a single reaction. Using flux balance analysis (FBA) we also determined reactions essential for growth in these metabolic networks. We find that most reactions identified as essential in these networks turn out to be those involving the production or consumption of low degree metabolites. Applying graph theoretic methods to these metabolic networks, we identified connected clusters of these low degree metabolites. The genes involved in several operons in E. coli are correctly predicted as those of enzymes catalyzing the reactions of these clusters. Furthermore, we find that larger sized clusters are over-represented in the real network and are analogous to a 'network motif. Using FBA for the above mentioned three organisms we independently identified clusters of reactions whose fluxes are perfectly correlated. We find that the composition of the latter 'functional clusters' is also largely explained in terms of clusters of low degree metabolites in each of these organisms.ConclusionOur findings mean that most metabolic reactions that are essential can be tagged by one or more low degree metabolites. Those reactions are essential because they are the only ways of producing or consuming their respective tagged metabolites. Furthermore, reactions whose fluxes are strongly correlated can be thought of as 'glued together' by these low degree metabolites. The methods developed here could be used in predicting essential reactions and metabolic modules in other organisms from the list of metabolic reactions.
3133166
Tradeoffs in building a generic supply chain simulation capability
Building a simulation model for any large complex system requires high expertise and effort. These requirements can be reduced through building generic simulation capability that includes artifacts for facilitating the development of the simulation model. The artifacts can have a range of capabilities depending on the design goals for the simulation. This paper focuses on issues to be considered in building a generic simulation capability for supply chains. A number of approaches used in recent years for building generic supply chain simulation capability are discussed. Such approaches include data-driven simulators, interactive simulators, and sub-models for supply chain components. Tradeoffs are identified that should be considered in selecting an approach for building a generic supply chain simulation capability.
11952430
David vs. Goliath: An Analysis of Asymmetric Mixed-Strategy Games and Experimental Evidence
Mixed strategies are widely used to model strategic situations in diverse fields such as economics, marketing, political science, and biology. However, some of the implications of asymmetric mixed-strategy solutions are counterintuitive. We develop a stylized model of patent race to examine some of these implications. In our model two firms compete to develop a product and obtain a patent. However, one firm values the patent more because of its market advantages, such as brand reputation and distribution network. Contrary to some intuition, we find that the firm that values the patent less is likely to invest more aggressively in developing the product and will also win the patent more often. We argue that the reason for these counterintuitive results is inherent in the very concept of mixed strategy solution. In a laboratory test, we examine whether subjects' behavior conforms to the equilibrium predictions. We find that the aggregate behavior of our subjects is consistent with the game-theoretic predictions. With the help of the experience-weighted attraction (EWA) learning model proposed by Camerer and Ho (1999), we show that adaptive learning can account for the investment behavior of our subjects.We find that the EWA learning model tracks the investment decisions of our subjects well, whether we hold out trials or an entire group of subjects.
120386960
Evolutionary games with two timescales
We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.