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- Billing, Erik, 1981-
(author)
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Cognition reversed : Robot learning from demonstration
- 2009
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Licentiate thesis (other academic/artistic)abstract
- The work presented in this thesis investigates techniques for learning from demonstration (LFD). LFD is a well established approach to robot learning, where a teacher demonstrates a behavior to a robot pupil. This thesis focuses on LFD where a human teacher demonstrates a behavior by controlling the robot via teleoperation. The robot should after demonstration be able to execute the demonstrated behavior under varying conditions. Several views on representation, recognition and learning of robot behavior are presented and discussed from a cognitive and computational perspective. LFD-related concepts such as behavior, goal, demonstration, and repetition are defined and analyzed, with focus on how bias is introduced by the use of behavior primitives. This analysis results in a formalism where LFD is described as transitions between information spaces. Assuming that the behavior recognition problem is partly solved, ways to deal with remaining ambiguities in the interpretation of a demonstration are proposed. A total of five algorithms for behavior recognition are proposed and evaluated, including the dynamic temporal difference algorithm Predictive Sequence Learning (PSL). PSL is model-free in the sense that it makes few assumptions of what is to be learned. One strength of PSL is that it can be used for both robot control and recognition of behavior. While many methods for behavior recognition are concerned with identifying invariants within a set of demonstrations, PSL takes a different approach by using purely predictive measures. This may be one way to reduce the need for bias in learning. PSL is, in its current form, subjected to combinatorial explosion as the input space grows, which makes it necessary to introduce some higher level coordination for learning of complex behaviors in real-world robots. The thesis also gives a broad introduction to computational models of the human brain, where a tight coupling between perception and action plays a central role. With the focus on generation of bias, typical features of existing attempts to explain humans' and other animals' ability to learn are presented and analyzed, from both a neurological and an information theoretic perspective. Based on this analysis, four requirements for implementing general learning ability in robots are proposed. These requirements provide guidance to how a coordinating structure around PSL and similar algorithms should be implemented in a model-free way.
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- Dmytryshyn, Andrii, 1986-, et al.
(author)
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Codimension computations of congruence orbits of matrices, symmetric and skew-symmetric matrix pencils using Matlab
- 2013
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Reports (other academic/artistic)abstract
- Matlab functions to work with the canonical structures for congru-ence and *congruence of matrices, and for congruence of symmetricand skew-symmetric matrix pencils are presented. A user can providethe canonical structure objects or create (random) matrix examplesetups with a desired canonical information, and compute the codi-mensions of the corresponding orbits: if the structural information(the canonical form) of a matrix or a matrix pencil is known it isused for the codimension computations, otherwise they are computednumerically. Some auxiliary functions are provided too. All thesefunctions extend the Matrix Canonical Structure Toolbox.
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- Dmytryshyn, Andrii, 1986-, et al.
(author)
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Orbit closure hierarchies of skew-symmetric matrix pencils
- 2014
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In: SIAM Journal on Matrix Analysis and Applications. - Umeå : Society for Industrial and Applied Mathematics. - 0895-4798 .- 1095-7162. ; 35:4, s. 1429-1443
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Journal article (peer-reviewed)abstract
- We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. The developed theory relies on our main theorem stating that a skew-symmetric matrix pencil A - lambda B can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C - lambda D if and only if A - lambda B can be approximated by pencils congruent to C - lambda D.
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| 7. |
- Dmytryshyn, Andrii
(author)
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Skew-symmetric matrix pencils : stratification theory and tools
- 2014
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Licentiate thesis (other academic/artistic)abstract
- Investigating the properties, explaining, and predicting the behaviour of a physical system described by a system (matrix) pencil often require the understanding of how canonical structure information of the system pencil may change, e.g., how eigenvalues coalesce or split apart, due to perturbations in the matrix pencil elements. Often these system pencils have different block-partitioning and / or symmetries. We study changes of the congruence canonical form of a complex skew-symmetric matrix pencil under small perturbations. The problem of computing the congruence canonical form is known to be ill-posed: both the canonical form and the reduction transformation depend discontinuously on the entries of a pencil. Thus it is important to know the canonical forms of all such pencils that are close to the investigated pencil. One way to investigate this problem is to construct the stratification of orbits and bundles of the pencils. To be precise, for any problem dimension we construct the closure hierarchy graph for congruence orbits or bundles. Each node (vertex) of the graph represents an orbit (or a bundle) and each edge represents the cover/closure relation. Such a relation means that there is a path from one node to another node if and only if a skew-symmetric matrix pencil corresponding to the first node can be transformed by an arbitrarily small perturbation to a skew-symmetric matrix pencil corresponding to the second node. From the graph it is straightforward to identify more degenerate and more generic nearby canonical structures. A necessary (but not sufficient) condition for one orbit being in the closure of another is that the first orbit has larger codimension than the second one. Therefore we compute the codimensions of the congruence orbits (or bundles). It is done via the solutions of an associated homogeneous system of matrix equations. The complete stratification is done by proving the relation between equivalence and congruence for the skew-symmetric matrix pencils. This relation allows us to use the known result about the stratifications of general matrix pencils (under strict equivalence) in order to stratify skew-symmetric matrix pencils under congruence. Matlab functions to work with skew-symmetric matrix pencils and a number of other types of symmetries for matrices and matrix pencils are developed and included in the Matrix Canonical Structure (MCS) Toolbox.
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| 8. |
- Drewes, Frank, et al.
(author)
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The Generative Power of Delegation Networks
- 2012
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Reports (other academic/artistic)abstract
- A device that generates trees over a ranked alphabet ∑, together with an interpretation of the symbols in ∑ as functions or relations on a domain A, generates subsets of A. This concept of tree-based generators is well known and essentially already present in the seminal paper by Mezei and Wright from 1967. A delegation network is a system consisting of a finite set of such generators that can "delegate" parts of the generation process to each other. It can be viewed as consisting of an (extended) IO context-free tree grammar and an interpretation. We investigate the language-theoretic properties of these systems and establish several characterizations of the generated languages. In particular, we obtain results in the style of Mezei and Wright. We also study the hierarchy of tree language classes obtained by iterating the concept of delegation, and show that this hierarchy is properly contained in the closure of the regular tree languages under nondeterministic macro tree transductions, but not in the IO-hierarchy.
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