Hints

The systematic use of hints in the learning-from-examples paradigm is the subject of this review. Hints are the properties of the target function that are known to us independently of the training examples. The use of hints is tantamount to combining rules and data in learning, and is compatible with different learning models, optimization techniques, and regularization techniques. The hints are represented to the learning process by virtual examples, and the training examples of the target function are treated on equal footing with the rest of the hints. A balance is achieved between the information provided by the different hints through the choice of objective functions and learning schedules. The Adaptive Minimization algorithm achieves this balance by relating the performance on each hint to the overall performance. The application of hints in forecasting the very noisy foreign-exchange markets is illustrated. On the theoretical side, the information value of hints is contrasted to the complexity value and related to the VC dimension

An algorithm for learning from hints

To take advantage of prior knowledge (hints) about the function one wants to learn, we introduce a method that generalizes learning from examples to learning from hints. A canonical representation of hints is defined and illustrated. All hints are represented to the learning process by examples, and examples of the function are treated on equal footing with the rest of the hints. During learning, examples from different hints are selected for processing according to a given schedule. We present two types of schedules; fixed schedules that specify the relative emphasis of each hint, and adaptive schedules that are based on how well each hint has been learned so far. Our learning method is compatible with any descent technique

Feedback on Academic Essay Writing through pre-Emptive Hints: Moving Towards "Advice for Action"

This paper adopts an “advice for action” approach to feedback in educational practice: addressing how provision of “hints” to participants before they write academic essays can support their understanding and performance in essay-writing tasks. We explored differences in performance by type of hint, and whether there was a transfer of better performance in subsequent essays. Fifty participants were recruited, consisting of eight men and 42 women aged 18-80. Participants were assigned in rotation to four groups, and asked to write two essays. Groups 1 and 3 received hints before Essay 1, whilst Groups 2 and 4 received hints before Essay 2. Groups 1 and 2 received essential hints; Groups 3 and 4 received helpful hints. Essays were marked against set criteria. The results showed that an “advice for action” approach to essay-writing, in the form of hints, can significantly improve writers’ marks. Specifically higher marks were gained for the introduction, conclusion and use of evidence: critical components of “good” academic essays. As the hints given were content-free, this approach has the potential to instantly benefit tutors and students across subject domains and institutions and is informing the development of a technical system that can offer formative feedback as students draft essays

Hints and the VC Dimension

Learning from hints is a generalization of learning from examples that allows for a variety of information about the unknown function to be used in the learning process. In this paper, we use the VC dimension, an established tool for analyzing learning from examples, to analyze learning from hints. In particular, we show how the VC dimension is affected by the introduction of a hint. We also derive a new quantity that defines a VC dimension for the hint itself. This quantity is used to estimate the number of examples needed to "absorb" the hint. We carry out the analysis for two types of hints, invariances and catalysts. We also describe how the same method can be applied to other types of hints

Discovery of the Ordovician Kinnekulle K-bentonite at the Põõsaspea cliff, NW Estonia

A previously unknown outcrop of the Kinnekulle K-bentonite (metabentonite) is reported from the Põõsaspea cliff, NW Estonia. The bed has a sharp lower and a gradational upper contact and comprises ca 28 cm of clay overlain by ca 10 cm of hard K-feldspar-rich variety. The latter contains a layer of breccia, which indicates early onset of recrystallization and hardening of volcanic material. The discovery shows that the Põõsaspea cliff section is younger than previously thought and includes rocks of both Haljala and Keila stages

New Hints from General Relativity

The search for a quantum theory of gravity has followed two parallel but different paths. One aims at arriving at the final theory starting from a priori assumptions as to its form and building it from the ground up. The other tries to infer as much as possible about the unknown theory from the existing ones and use our current knowledge to constrain the possibilities for the quantum theory of gravity. Probably the biggest success of the second path has been the results of black hole thermodynamics. The subject of this essay is a new, highly promising such result, the application of quasinormal modes in quantum gravity.Comment: This essay received an "honorable mention" in the 2003 Essay Competition of the Gravity Research Foundatio

Cosmological Hints of Modified Gravity ?

The recent measurements of Cosmic Microwave Background temperature and polarization anisotropies made by the Planck satellite have provided impressive confirmation of the $\Lambda$CDM cosmological model. However interesting hints of slight deviations from $\Lambda$CDM have been found, including a $95 \%$ c.l. preference for a "modified gravity" structure formation scenario. In this paper we confirm the preference for a modified gravity scenario from Planck 2015 data, find that modified gravity solves the so-called $A_{lens}$ anomaly in the CMB angular spectrum, and constrains the amplitude of matter density fluctuations to $\sigma_8=0.815_{-0.048}^{+0.032}$, in better agreement with weak lensing constraints. Moreover, we find a lower value for the reionization optical depth of $\tau=0.059\pm0.020$ (to be compared with the value of $\tau= 0.079 \pm 0.017$ obtained in the standard scenario), more consistent with recent optical and UV data. We check the stability of this result by considering possible degeneracies with other parameters, including the neutrino effective number, the running of the spectral index and the amount of primordial helium. The indication for modified gravity is still present at about $95\%$ c.l., and could become more significant if lower values of $\tau$ were to be further confirmed by future cosmological and astrophysical data.Comment: 10 pages, 5 figures. Minor revisions, accepted for publication on PR