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Structure and Complexity in Planning with Unary Operators
Unary operator domains -- i.e., domains in which operators have a single effect -- arise naturally in many control problems. In its most general form, the problem of STRIPS planning in unary operator domains is known to be as hard as the general STRIPS planning problem -- both are PSPACE-complete. However, unary operator domains induce a natural structure, called the domain's causal graph. This graph relates between the preconditions and effect of each domain operator. Causal graphs were exploited by Williams and Nayak in order to analyze plan generation for one of the controllers in NASA's Deep-Space One spacecraft. There, they utilized the fact that when this graph is acyclic, a serialization ordering over any subgoal can be obtained quickly. In this paper we conduct a comprehensive study of the relationship between the structure of a domain's causal graph and the complexity of planning in this domain. On the positive side, we show that a non-trivial polynomial time plan generation algorithm exists for domains whose causal graph induces a polytree with a constant bound on its node indegree. On the negative side, we show that even plan existence is hard when the graph is a directed-path singly connected DAG. More generally, we show that the number of paths in the causal graph is closely related to the complexity of planning in the associated domain. Finally we relate our results to the question of complexity of planning with serializable subgoals.
Algorithmic Luckiness
Herbrich, Ralf, Williamson, Robert C.
In contrast to standard statistical learning theory which studies uniform bounds on the expected error we present a framework that exploits the specific learning algorithm used. Motivated by the luckiness framework [8] we are also able to exploit the serendipity of the training sample. The main difference to previous approaches lies in the complexity measure; rather than covering all hypotheses in a given hypothesis space it is only necessary to cover the functions which could have been learned using the fixed learning algorithm. We show how the resulting framework relates to the VC, luckiness and compression frameworks. Finally, we present an application of this framework to the maximum margin algorithm for linear classifiers which results in a bound that exploits both the margin and the distribution of the data in feature space. 1 Introduction Statistical learning theory is mainly concerned with the study of uniform bounds on the expected error of hypotheses from a given hypothesis space [9, 1].
Analog Soft-Pattern-Matching Classifier using Floating-Gate MOS Technology
Yamasaki, Toshihiko, Shibata, Tadashi
A flexible pattern-matching analog classifier is presented in conjunction with a robust image representation algorithm called Principal Axes Projection (PAP). In the circuit, the functional form of matching is configurable in terms of the peak position, the peak height and the sharpness of the similarity evaluation. The test chip was fabricated in a 0.6-µm CMOS technology and successfully applied to handwritten pattern recognition and medical radiograph analysis using PAP as a feature extraction pre-processing step for robust image coding. The separation and classification of overlapping patterns is also experimentally demonstrated.
On Spectral Clustering: Analysis and an algorithm
Ng, Andrew Y., Jordan, Michael I., Weiss, Yair
For clustering points in Rna main application focus of this paper-one standard approach is based on generative models, in which algorithms such as EM are used to learn a mixture density. These approaches suffer from several drawbacks. First, to use parametric density estimators, harsh simplifying assumptions usually need to be made (e.g., that the density of each cluster is Gaussian). Second, the log likelihood can have many local minima and therefore multiple restarts are required to find a good solution using iterative algorithms. Algorithms such as K-means have similar problems.
Online Learning with Kernels
Kivinen, Jyrki, Smola, Alex J., Williamson, Robert C.
We consider online learning in a Reproducing Kernel Hilbert Space. Our method is computationally efficient and leads to simple algorithms. In particular we derive update equations for classification, regression, and novelty detection. The inclusion of the -trick allows us to give a robust parameterization.
A Parallel Mixture of SVMs for Very Large Scale Problems
Collobert, Ronan, Bengio, Samy, Bengio, Yoshua
However, SVMs require to solve a quadratic optimization problem which needs resources that are at least quadratic in the number of training examples, and it is thus hopeless to try solving problems having millions of examples using classical SVMs. In order to overcome this drawback, we propose in this paper to use a mixture of several SVMs, each of them trained only on a part of the dataset. The idea of an SVM mixture is not new, although previous attempts such as Kwok's paper on Support Vector Mixtures [5] did not train the SVMs on part of the dataset but on the whole dataset and hence could not overcome the'Part of this work has been done while Ronan Collobert was at IDIAP, CP 592, rue du Simplon 4, 1920 Martigny, Switzerland.
Rao-Blackwellised Particle Filtering via Data Augmentation
Andrieu, Christophe, Freitas, Nando D., Doucet, Arnaud
SMC is often referred to as particle filtering (PF) in the context of computing filtering distributions for statistical inference and learning. It is known that the performance of PF often deteriorates in high-dimensional state spaces. In the past, we have shown that if a model admits partial analytical tractability, it is possible to combine PF with exact algorithms (Kalman filters, HMM filters, junction tree algorithm) to obtain efficient high dimensional filters (Doucet, de Freitas, Murphy and Russell 2000, Doucet, Godsill and Andrieu 2000). In particular, we exploited a marginalisation technique known as Rao-Blackwellisation (RB). Here, we attack a more complex model that does not admit immediate analytical tractability.
Kernel Machines and Boolean Functions
Kowalczyk, Adam, Smola, Alex J., Williamson, Robert C.
We give results about the learnability and required complexity of logical formulae to solve classification problems. These results are obtained by linking propositional logic with kernel machines. In particular we show that decision trees and disjunctive normal forms (DNF) can be represented by the help of a special kernel, linking regularized risk to separation margin. Subsequently we derive a number of lower bounds on the required complexity of logic formulae using properties of algorithms for generation of linear estimators, such as perceptron and maximal perceptron learning.
Active Learning in the Drug Discovery Process
Warmuth, Manfred K. K., Rätsch, Gunnar, Mathieson, Michael, Liao, Jun, Lemmen, Christian
We investigate the following data mining problem from Computational Chemistry: From a large data set of compounds, find those that bind to a target molecule in as few iterations of biological testing as possible. In each iteration a comparatively small batch of compounds is screened for binding to the target. We apply active learning techniques for selecting the successive batches. One selection strategy picks unlabeled examples closest to the maximum margin hyperplane. Another produces many weight vectors by running perceptrons over multiple permutations of the data.