Author name cluster

Eric Martin

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

11 papers

2 author rows

I&C Journal 2022 Journal Article

Learners based on transducers

Sanjay Jain
Shao Ning Kuek
Eric Martin
Frank Stephan

The learners considered here process data in cycles and maintain as a long term memory a string which provides all internal data the learner can use in the next cycle. Updating of these strings is usually done by either recursive or automatic learners. The present work looks at transduced learners, which sit in-between. The results include that transduced learners can learn all learnable automatic families with memory exponential in the size of the longest input seen so far. Furthermore, there is a hierarchy based on the memory-allowance: if n is the size of the largest datum seen so far, then for all k ≥ 1, memory n k + 1 allows one to learn more automatic families than memory n k. Further results shed light on when it can be imposed that transduced learners be consistent, conservative or iterative. The main result of this kind is that all learnable automatic families have a consistent and conservative transduced learner.

Details DOI

TCS Journal 2013 Journal Article

Learning and classifying

Sanjay Jain
Eric Martin
Frank Stephan

We define and study a learning paradigm that sits between identification in the limit and classification. More precisely, we expect a learner to determine in the limit which members of a finite set D of possible data belong to a target language L, where D is arbitrary. So as D becomes larger and larger, the task becomes closer and closer to identifying L. But as D is always finite and L can be infinite, it can still be expected that Ex- and BC-learning are often more difficult than performing this classification task. The paper supports this intuition and makes it precise, taking into account desirable constraints on how the learner behaves, such as bounding the number of mind changes and being conservative. Special attention is given to various forms of consistency. In particular, we might not only require consistency between the members of D to classify, the current data σ and a language L, but also consistency between larger sets of possible data to classify (supersets of D ) and the same σ and L: whereas in the classical paradigms of inductive inference or classification, only the available data can grow, here both the available data and the set of possible data to classify can grow. We provide a fairly comprehensive set of results, many of which are optimal, that demonstrate the fruitfulness of the approach and the richness of the paradigm.

Details DOI

TCS Journal 2008 Journal Article

Absolute versus probabilistic classification in a logical setting

Sanjay Jain
Eric Martin
Frank Stephan

Suppose we are given a set W of logical structures, or possible worlds, a set of logical formulas called possible data and a logical formula φ. We then consider the classification problem of determining in the limit and almost always correctly whether a possible world M satisfies φ, from a complete enumeration of the possible data that are true in M. One interpretation of almost always correctly is that the classification might be wrong on a set of possible worlds of measure 0, with respect to some natural probability distribution over the set of possible worlds. Another interpretation is that the classifier is only required to classify a set W ′ of possible worlds of measure 1, without having to produce any claim in the limit on the truth of φ for the members of the complement of W ′ in W. We compare these notions with absolute classification of W with respect to a formula that is almost always equivalent to φ in W, hence we investigate whether the set of possible worlds on which the classification is correct is definable. We mainly work with the probability distribution that corresponds to the standard measure on the Cantor space, but we also consider an alternative probability distribution proposed by Solomonoff and contrast it with the former. Finally, in the spirit of the kind of computations considered in Logic programming, we address the issue of computing almost correctly in the limit witnesses to leading existentially quantified variables in existential formulas.

Details DOI

TCS Journal 2007 Journal Article

On the data consumption benefits of accepting increased uncertainty

Eric Martin
Arun Sharma
Frank Stephan

In the context of learning paradigms of identification in the limit, we address the question: why is uncertainty sometimes desirable? We use mind change bounds on the output hypotheses as a measure of uncertainty and interpret ‘desirable’ as reduction in data memorization, also defined in terms of mind change bounds. The resulting model is closely related to iterative learning with bounded mind change complexity, but the dual use of mind change bounds — for hypotheses and for data — is a key distinctive feature of our approach. We show that situations exist where the more mind changes the learner is willing to accept, the less the amount of data it needs to remember in order to converge to the correct hypothesis. We also investigate relationships between our model and learning from good examples, set-driven, monotonic and strong-monotonic learners, as well as class-comprising versus class-preserving learnability.

Details DOI

ICRA Conference 2006 Conference Paper

Autonomous Capture of a Tumbling Satellite

Guy Rouleau
Ioannis M. Rekleitis
Régent L'Archevêque
Eric Martin
Kourosh Parsa
Erick Dupuis

In this paper, we describe a framework for the autonomous capture and servicing of satellites. The work is based on laboratory experiments that illustrate the autonomy and remote-operation aspects. The satellite-capture problem is representative of most on-orbit robotic manipulation tasks where the environment is known and structured, but it is dynamic since the satellite to be captured is in free flight. Bandwidth limitations and communication dropouts dominate the quality of the communication link. The satellite-servicing scenario is implemented on a robotic test-bed in laboratory settings

Details

TCS Journal 2006 Journal Article

On ordinal VC-dimension and some notions of complexity

Eric Martin
Arun Sharma
Frank Stephan

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Details DOI

TCS Journal 2003 Journal Article

Learning power and language expressiveness

Eric Martin
Arun Sharma
Frank Stephan

The topic of the present work is to study the relationship between the power of the learning algorithms on the one hand, and the expressive power of the logical language which is used to represent the problems to be learned on the other hand. The central question is whether enriching the language results in more learning power. In order to make the question relevant and nontrivial, it is required that both texts (sequences of data) and hypotheses (guesses) be translatable from the “rich” language into the “poor” one. The issue is considered for several logical languages suitable to describe structures whose domain is the set of natural numbers. It is shown that enriching the language does not give any advantage for those languages which define a monadic second-order language being decidable in the following sense: there is a fixed interpretation in the structure of natural numbers such that the set of sentences of this extended language true in that structure is decidable. But enriching the original language even by only one constant gives an advantage if this language contains a binary function symbol (which will be interpreted as addition). Furthermore, it is shown that behaviourally correct learning has exactly the same power as learning in the limit for those languages which define a monadic second-order language with the property given above, but has more power in case of languages containing a binary function symbol. Adding the natural requirement that the set of all structures to be learned is recursively enumerable, it is shown that it pays off to enrich the language of arithmetics for both finite learning and learning in the limit, but it does not pay off to enrich the language for behaviourally correct learning.

Details DOI

IROS Conference 2001 Conference Paper

Force/moment accommodation control for tele-operated manipulators performing contact tasks in stiff environment

Farhad Aghili
Erick Dupuis
Eric Martin
Jean-Claude Piedboeuf

Analyses the performance and stability of a force/moment accommodation (FMA) loop closed around a joint rate controller. A synthesis methodology is given to select the gains of the accommodation controller. The bandwidth and coupling limitations of the FMA control architecture are discussed. It is shown that the closed-loop FMA exhibits natural decoupling when FMA acts on the "transpose Jacobian rate" controller. The theoretical developments in the paper are supported by simulation and experimental results.

Details

I&C Journal 2001 Journal Article

Induction by Enumeration

Eric Martin
Daniel Osherson

Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i. e. , the one pioneered by E. M. Gold (1967, Inform. and Control 10, 447–474)). The concept is less easily interpreted within the first-order paradigm discussed by K. T. Kelly (1996, “The Logic of Reliable Inquiry, ” Oxford Univ. Press, New York) and E. Martin and D. Osherson (1998, “Elements of Scientific Inquiry, ” MIT Press, Cambridge, MA), in which the scientist's data amount to the basic diagram of a structure. We formulate two kinds of enumerative induction that are appropriate to the first-order paradigm and analyze their potential for discovery. Among other results, it is shown that one form of enumerative induction achieves maximum inductive competence.

Details DOI

IROS Conference 1998 Conference Paper

A control scheme for the reduction of thruster-manipulator interactions in space robotic systems

Eric Martin
Evangelos Papadopoulos
Jorge Angeles

Space manipulators mounted on an on-off thruster-controlled base are envisioned to assist in the assembly and maintenance of space structures. When handling large payloads, manipulator joint and link flexibility become important, for they can result in payload-attitude controller fuel-replenishing dynamic interactions. In this paper, the dynamics model of an N-flexible-joint space manipulator is developed. The model of a three-flexible-joint manipulator mounted on a six-degree-of-freedom spacecraft is used to compare three different on-off thruster attitude control systems. Two variations of a classical control scheme are suggested to minimize such undesirable dynamic interactions, as well as thruster fuel consumption.

Details

IROS Conference 1995 Conference Paper

On the interaction of flexible modes and on-off thrusters in space robotic systems

Eric Martin
Evangelos Papadopoulos
Jorge Angeles

Space manipulators mounted on an on-off thruster-controlled base are envisioned to assist in the assembly and maintenance of space structures. When handling large payloads, manipulator joint and link flexibility become important for it can result in payload-attitude controller fuel-replenishing dynamic interactions. In this paper, the dynamic behavior of a flexible-joint manipulator on a free-flying base is approximated by a single-mode mechanical system, while its parameters are matched with available space-manipulator data. Describing functions are used to predict the dynamic performance of three alternative controller/estimator schemes, and to conduct a parametric study on the influence of key system parameters. Design guidelines and a particular state-estimator are suggested that can minimize such undesirable dynamic interactions as well as thruster fuel consumption.

Details