Algorithmic Learning Theory 

About: Algorithmic Learning Theory is an academic conference. The conference publishes majorly in the area(s): Learnability & Upper and lower bounds. Over the lifetime, 1210 publications have been published by the conference receiving 19851 citations.

Measuring statistical dependence with hilbert-schmidt norms

Abstract: We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC) This approach has several advantages, compared with previous kernel-based independence criteria First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods

A Hilbert space embedding for distributions

Abstract: We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert space. Applications of this technique can be found in two-sample tests, which are used for determining whether two sets of observations arise from the same distribution, covariate shift correction, local learning, measures of independence, and density estimation.

Efficient Induction of Logic Programs

Abstract: Recently there has been increasing interest in systems which induce rst order logic programs from examples. However, many diiculties need to be overcome. Well-known algorithms fail to discover correct logical descriptions for large classes of interesting predicates , due either to the intractability of search or overly strong limitations applied to the hypothesis space. In contrast, search is avoided within Plotkin's framework of relative least general generalisation (rlgg). It is replaced by the process of constructing a unique clause which covers a set of examples relative to given background knowledge. However, such a clause can in the worst case contain innnitely many literals, or at best grow exponentially with the number of examples involved. In this paper we introduce the concept of h-easy rlgg clauses and show that they have nite length. We also prove that the length of a certain class of \determinate" rlgg is bounded by a polynomial function of certain features of the background knowledge. This function is independent of the number of examples used to construct them. An existing implementation called GOLEM is shown to be capable of inducing many interesting logic programs which have not been demonstrated to be learnable using other algorithms.

Thompson sampling: an asymptotically optimal finite-time analysis

Abstract: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.

Pure exploration in multi-armed bandits problems

Abstract: We consider the framework of stochastic multi-armed bandit problems and study the possibilities and limitations of strategies that perform an online exploration of the arms. The strategies are assessed in terms of their simple regret, a regret notion that captures the fact that exploration is only constrained by the number of available rounds (not necessarily known in advance), in contrast to the case when the cumulative regret is considered and when exploitation needs to be performed at the same time.We believe that this performance criterion is suited to situations when the cost of pulling an arm is expressed in terms of resources rather than rewards. We discuss the links between the simple and the cumulative regret. The main result is that the required exploration-exploitation trade-offs are qualitatively different, in view of a general lower bound on the simple regret in terms of the cumulative regret.