1,654 research outputs found
Tight Bounds for the Cover Times of Random Walks with Heterogeneous Step Lengths
Search patterns of randomly oriented steps of different lengths have been observed on all scales of the biological world, ranging from the microscopic to the ecological, including in protein motors, bacteria, T-cells, honeybees, marine predators, and more. Through different models, it has been demonstrated that adopting a variety in the magnitude of the step lengths can greatly improve the search efficiency. However, the precise connection between the search efficiency and the number of step lengths in the repertoire of the searcher has not been identified. Motivated by biological examples in one-dimensional terrains, a recent paper studied the best cover time on an n-node cycle that can be achieved by a random walk process that uses k step lengths. By tuning the lengths and corresponding probabilities the authors therein showed that the best cover time is roughly n 1+Θ(1/k). While this bound is useful for large values of k, it is hardly informative for small k values, which are of interest in biology. In this paper, we provide a tight bound for the cover time of such a walk, for every integer k > 1. Specifically, up to lower order polylogarithmic factors, the upper bound on the cover time is a polynomial in n of exponent 1+ 1/(2k−1). For k = 2, 3, 4 and 5 the exponent is thus 4/3 , 6/5 , 8/7 , and 10/9 , respectively. Informally, our result implies that, as long as the number of step lengths k is not too large, incorporating an additional step length to the repertoire of the process enables to improve the cover time by a polynomial factor, but the extent of the improvement gradually decreases with k
Dissimilarity Clustering by Hierarchical Multi-Level Refinement
We introduce in this paper a new way of optimizing the natural extension of
the quantization error using in k-means clustering to dissimilarity data. The
proposed method is based on hierarchical clustering analysis combined with
multi-level heuristic refinement. The method is computationally efficient and
achieves better quantization errors than theComment: 20-th European Symposium on Artificial Neural Networks, Computational
Intelligence and Machine Learning (ESANN 2012), Bruges : Belgium (2012
Підготовка майбутнього вчителя початкових класів до білінгвального навчання молодших школярів як методична проблема
(uk) В статті здійснено загальний аналіз проблеми професійної підготовки майбутнього вчителя початкових класів до білінгвального навчання. Визначено основи білінгвальної освіти та умови їхньої реалізації майбутніми фахівцями.(en) In the article the problem of training future elementary school teachers for bilingual teaching is analyzed. The bases of bilingual education and terms of their implementation by future specialists are determined
A Predictive Approach to Bayesian Nonparametric Survival Analysis
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is conjugate with respect to right-censored data. Eliciting these priors, particularly in the presence of covariates, can be challenging and inference typically relies on computationally intensive Markov chain Monte Carlo schemes. In this paper, we build on recent work that recasts Bayesian inference as assigning a predictive distribution on the unseen values of a population conditional on the observed samples, thus avoiding the need to specify a complex prior. We describe a copula-based predictive update which admits a scalable sequential importance sampling algorithm to perform inference that properly accounts for right-censoring. We provide theoretical justification through an extension of Doob’s consistency theorem and illustrate the method on a number of simulated and real data sets, including an example with covariates. Our approach enables analysts to perform Bayesian nonparametric inference through only the specification of a predictive distribution
Manifestations of Local Supersolidity of He around a Charged Molecular Impurity
A frozen, solid helium core, dubbed snowball, is typically observed around
cations in liquid helium. Here we discover, using path integral simulations,
that around a cationic molecular impurity, protonated methane, the He atoms
are indeed strongly localized akin to snowballs but still participate in vivid
bosonic exchange induced by the ro-vibrational motion of the impurity. Such
combination of solid-like order with pronounced superfluid response in the
first helium shell indicates that manifestations of local supersolid behavior
of He can be induced -- and probed experimentally -- by charged molecules
PAC-learning gains of Turing machines over circuits and neural networks
A caveat to many applications of the current Deep Learning approach is the
need for large-scale data. One improvement suggested by Kolmogorov Complexity
results is to apply the minimum description length principle with
computationally universal models. We study the potential gains in sample
efficiency that this approach can bring in principle. We use polynomial-time
Turing machines to represent computationally universal models and Boolean
circuits to represent Artificial Neural Networks (ANNs) acting on
finite-precision digits.
Our analysis unravels direct links between our question and Computational
Complexity results. We provide lower and upper bounds on the potential gains in
sample efficiency between the MDL applied with Turing machines instead of ANNs.
Our bounds depend on the bit-size of the input of the Boolean function to be
learned. Furthermore, we highlight close relationships between classical open
problems in Circuit Complexity and the tightness of these
Efficiency Separation between RL Methods: Model-Free, Model-Based and Goal-Conditioned
We prove a fundamental limitation on the efficiency of a wide class of
Reinforcement Learning (RL) algorithms. This limitation applies to model-free
RL methods as well as a broad range of model-based methods, such as planning
with tree search.
Under an abstract definition of this class, we provide a family of RL
problems for which these methods suffer a lower bound exponential in the
horizon for their interactions with the environment to find an optimal
behavior. However, there exists a method, not tailored to this specific family
of problems, which can efficiently solve the problems in the family.
In contrast, our limitation does not apply to several types of methods
proposed in the literature, for instance, goal-conditioned methods or other
algorithms that construct an inverse dynamics model
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