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Added by
Vanja Dosko\\v{c}
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning task which can be found in many areas, for example learning of (subsets of) regular languages or learning of natural languages. We are interested in various restrictions on learning, such as consistency, conservativeness or set-drivenness, exemplifying various natural learning restrictions. Building on previous results from the literature, we provide several maps (depictions of all pairwise relations) of various groups of learning criteria, including a map for monotonicity restrictions and similar criteria and a map for restrictions on data presentation. Furthermore, we consider, for various learning criteria, whether learners can be assumed consistent.
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This paper studies the problem of learning with augmented classes (LAC), where augmented classes unobserved in the training data might emerge in the testing phase. Previous studies generally attempt to discover augmented classes by exploiting geometric properties, achieving inspiring empirical performance yet lacking theoretical understandings particularly on the generalization ability. In this paper we show that, by using unlabeled training data to approximate the potential distribution of augmented classes, an unbiased risk estimator of the testing distribution can be established for the LAC problem under mild assumptions, which paves a way to develop a sound approach with theoretical guarantees. Moreover, the proposed approach can adapt to complex changing environments where augmented classes may appear and the prior of known classes may change simultaneously. Extensive experiments confirm the effectiveness of our proposed approach.
Maximum Variance Unfolding (MVU) and its variants have been very successful in embedding data-manifolds in lower dimensional spaces, often revealing the true intrinsic dimension. In this paper we show how to also incorporate supervised class information into an MVU-like method without breaking its convexity. We call this method the Isometric Separation Map and we show that the resulting kernel matrix can be used as a binary/multiclass Support Vector Machine-like method in a semi-supervised (transductive) framework. We also show that the method always finds a kernel matrix that linearly separates the training data exactly without projecting them in infinite dimensional spaces. In traditional SVMs we choose a kernel and hope that the data become linearly separable in the kernel space. In this paper we show how the hyperplane can be chosen ad-hoc and the kernel is trained so that data are always linearly separable. Comparisons with Large Margin SVMs show comparable performance.
The success of reinforcement learning in typical settings is, in part, predicated on underlying Markovian assumptions on the reward signal by which an agent learns optimal policies. In recent years, the use of reward machines has relaxed this assumption by enabling a structured representation of non-Markovian rewards. In particular, such representations can be used to augment the state space of the underlying decision process, thereby facilitating non-Markovian reinforcement learning. However, these reward machines cannot capture the semantics of stochastic reward signals. In this paper, we make progress on this front by introducing probabilistic reward machines (PRMs) as a representation of non-Markovian stochastic rewards. We present an algorithm to learn PRMs from the underlying decision process as well as to learn the PRM representation of a given decision-making policy.
Feature selection plays a pivotal role in learning, particularly in areas were parsimonious features can provide insight into the underlying process, such as biology. Recent approaches for non-linear feature selection employing greedy optimisation of Centred Kernel Target Alignment(KTA), while exhibiting strong results in terms of generalisation accuracy and sparsity, can become computationally prohibitive for high-dimensional datasets. We propose randSel, a randomised feature selection algorithm, with attractive scaling properties. Our theoretical analysis of randSel provides strong probabilistic guarantees for the correct identification of relevant features. Experimental results on real and artificial data, show that the method successfully identifies effective features, performing better than a number of competitive approaches.
In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks which encompasses a set of optimization techniques for high-order tensors used in quantum physics and numerical analysis. We first present an intrinsic relation between WFA and the tensor train decomposition, a particular form of tensor network. This relation allows us to exhibit a novel low rank structure of the Hankel matrix of a function computed by a WFA and to design an efficient spectral learning algorithm leveraging this structure to scale the algorithm up to very large Hankel matrices. We then unravel a fundamental connection between WFA and second-order recurrent neural networks~(2-RNN): in the case of sequences of discrete symbols, WFA and 2-RNN with linear activation functions are expressively equivalent. Furthermore, we introduce the first provable learning algorithm for linear 2-RNN defined over sequences of continuous input vectors. This algorithm relies on estimating low rank sub-blocks of the Hankel tensor, from which the parameters of a linear 2-RNN can be provably recovered. The performances of the proposed learning algorithm are assessed in a simulation study on both synthetic and real-world data.
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