9 research outputs found
Editors’ Introduction to [Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, October 1-4, 2007. Proceedings]
Learning theory is an active research area that incorporates ideas,
problems, and techniques from a wide range of disciplines including
statistics, artificial intelligence, information theory, pattern
recognition, and theoretical computer science. The research reported
at the 18th International Conference on Algorithmic Learning Theory
(ALT 2007) ranges over areas such as unsupervised learning,
inductive inference, complexity and learning, boosting and
reinforcement learning, query learning models, grammatical
inference, online learning and defensive forecasting, and kernel
methods. In this introduction we give an overview of the five
invited talks and the regular contributions of ALT 2007
Non-adaptive Group Testing on Graphs
Grebinski and Kucherov (1998) and Alon et al. (2004-2005) study the problem
of learning a hidden graph for some especial cases, such as hamiltonian cycle,
cliques, stars, and matchings. This problem is motivated by problems in
chemical reactions, molecular biology and genome sequencing.
In this paper, we present a generalization of this problem. Precisely, we
consider a graph G and a subgraph H of G and we assume that G contains exactly
one defective subgraph isomorphic to H. The goal is to find the defective
subgraph by testing whether an induced subgraph contains an edge of the
defective subgraph, with the minimum number of tests. We present an upper bound
for the number of tests to find the defective subgraph by using the symmetric
and high probability variation of Lov\'asz Local Lemma
Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, October 1-4, 2007. Proceedings
The LNAI series reports state-of-the-art results in artificial intelligence research, development, and education. This volume (LNAI 4754) contains research papers presented at the 18th International Conference on Algorithmic Learning Theory (ALT 2007), which was held in Sendai (Japan) during October 1-4, 2007. The main objective of the conference was to provide an interdisciplinary forum for high-quality talks with a strong theoretical background and scientific interchange in areas such as query models, online learning, inductive inference, boosting, kernel methods, complexity and learning, reinforcement learning, unsupervised learning, grammatical inference, and algorithmic forecasting. The conference was co-located with the 10th International Conference on Discovery Science (DS 2007). The volume includes 25 technical contributions that were selected from 50 submissions, and five invited talks presented to the audience of ALT and DS. Longer versions of the DS invited papers are available in the proceedings of DS 2007
On the Parameterized Complexity of Learning Monadic Second-Order Formulas
Within the model-theoretic framework for supervised learning introduced by
Grohe and Tur\'an (TOCS 2004), we study the parameterized complexity of
learning concepts definable in monadic second-order logic (MSO). We show that
the problem of learning a consistent MSO-formula is fixed-parameter tractable
on structures of bounded tree-width and on graphs of bounded clique-width in
the 1-dimensional case, that is, if the instances are single vertices (and not
tuples of vertices). This generalizes previous results on strings and on trees.
Moreover, in the agnostic PAC-learning setting, we show that the result also
holds in higher dimensions. Finally, via a reduction to the MSO-model-checking
problem, we show that learning a consistent MSO-formula is para-NP-hard on
general structures
Causal Modeling with Stationary Diffusions
We develop a novel approach towards causal inference. Rather than structural
equations over a causal graph, we learn stochastic differential equations
(SDEs) whose stationary densities model a system's behavior under
interventions. These stationary diffusion models do not require the formalism
of causal graphs, let alone the common assumption of acyclicity. We show that
in several cases, they generalize to unseen interventions on their variables,
often better than classical approaches. Our inference method is based on a new
theoretical result that expresses a stationarity condition on the diffusion's
generator in a reproducing kernel Hilbert space. The resulting kernel deviation
from stationarity (KDS) is an objective function of independent interest
Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling
In this work we consider the problem of numerical integration, i.e.,
approximating integrals with respect to a target probability measure using only
pointwise evaluations of the integrand. We focus on the setting in which the
target distribution is only accessible through a set of i.i.d.
observations, and the integrand belongs to a reproducing kernel Hilbert space.
We propose an efficient procedure which exploits a small i.i.d. random subset
of samples drawn either uniformly or using approximate leverage scores
from the initial observations. Our main result is an upper bound on the
approximation error of this procedure for both sampling strategies. It yields
sufficient conditions on the subsample size to recover the standard (optimal)
rate while reducing drastically the number of functions evaluations,
and thus the overall computational cost. Moreover, we obtain rates with respect
to the number of evaluations of the integrand which adapt to its
smoothness, and match known optimal rates for instance for Sobolev spaces. We
illustrate our theoretical findings with numerical experiments on real
datasets, which highlight the attractive efficiency-accuracy tradeoff of our
method compared to existing randomized and greedy quadrature methods. We note
that, the problem of numerical integration in RKHS amounts to designing a
discrete approximation of the kernel mean embedding of the target distribution.
As a consequence, direct applications of our results also include the efficient
computation of maximum mean discrepancies between distributions and the design
of efficient kernel-based tests.Comment: 46 pages, 5 figures. Submitted to JML
State-similarity metrics for continuous Markov decision processes
In recent years, various metrics have been developed for measuring the similarity of states in probabilistic transition systems (Desharnais et al., 1999; van Breugel & Worrell, 2001a). In the context of Markov decision processes, we have devised metrics providing a robust quantitative analogue of bisimulation. Most importantly, the metric distances can be used to bound the differences in the optimal value function that is integral to reinforcement learning (Ferns et al. 2004; 2005). More recently, we have discovered an efficient algorithm to calculate distances in the case of finite systems (Ferns et al., 2006). In this thesis, we seek to properly extend state-similarity metrics to Markov decision processes with continuous state spaces both in theory and in practice. In particular, we provide the first distance-estimation scheme for metrics based on bisimulation for continuous probabilistic transition systems. Our work, based on statistical sampling and infinite dimensional linear programming, is a crucial first step in real-world planning; many practical problems are continuous in nature, e.g. robot navigation, and often a parametric model or crude finite approximation does not suffice. State-similarity metrics allow us to reason about the quality of replacing one model with another. In practice, they can be used directly to aggregate states