Determining Principal Component Cardinality through the Principle of Minimum Description Length

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.Comment: LOD 201

PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control the risk of the latter. These results allow to bound the risk of very general estimation procedures, as well as to perform model selection

Language Model Co-occurrence Linking for Interleaved Activity Discovery

As ubiquitous computer and sensor systems become abundant, the potential for automatic identification and tracking of human behaviours becomes all the more evident. Annotating complex human behaviour datasets to achieve ground truth for supervised training can however be extremely labour-intensive, and error prone. One possible solution to this problem is activity discovery: the identification of activities in an unlabelled dataset by means of an unsupervised algorithm. This paper presents a novel approach to activity discovery that utilises deep learning based language production models to construct a hierarchical, tree-like structure over a sequential vector of sensor events. Our approach differs from previous work in that it explicitly aims to deal with interleaving (switching back and forth between between activities) in a principled manner, by utilising the long-term memory capabilities of a recurrent neural network cell. We present our approach and test it on a realistic dataset to evaluate its performance. Our results show the viability of the approach and that it shows promise for further investigation. We believe this is a useful direction to consider in accounting for the continually changing nature of behaviours

Handwritten digit recognition by bio-inspired hierarchical networks

The human brain processes information showing learning and prediction abilities but the underlying neuronal mechanisms still remain unknown. Recently, many studies prove that neuronal networks are able of both generalizations and associations of sensory inputs. In this paper, following a set of neurophysiological evidences, we propose a learning framework with a strong biological plausibility that mimics prominent functions of cortical circuitries. We developed the Inductive Conceptual Network (ICN), that is a hierarchical bio-inspired network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes. The outputs of the top-most node of ICN hierarchy, representing the highest input generalization, allow for automatic classification of inputs. We found that the ICN clusterized MNIST images with an error of 5.73% and USPS images with an error of 12.56%

Selective deuteration as a tool for resolving autoxidation mechanisms in <i>α</i>-pinene ozonolysis

Highly oxygenated organic molecules (HOMs) from α-pinene ozonolysis have been shown to be significant contributors to secondary organic aerosol (SOA), yet our mechanistic understanding of how the peroxy-radical-driven autoxidation leads to their formation in this system is still limited. The involved isomerisation reactions such as H-atom abstractions followed by O2 additions can take place on sub-second timescales in short-lived intermediates, making the process challenging to study. Similarly, while the end-products and sometimes radical intermediates can be observed using mass spectrometry, their structures remain elusive. Therefore, we propose a method utilising selective deuterations for unveiling the mechanisms of autoxidation, where the HOM products can be used to infer which C atoms have taken part in the isomerisation reactions. This relies on the fact that if a C−D bond is broken due to an abstraction by a peroxy group forming a −OOD hydroperoxide, the D atom will become labile and able to be exchanged with a hydrogen atom in water vapour (H2O), effectively leading to loss of the D atom from the molecule. In this study, we test the applicability of this method using three differently deuterated versions of α-pinene with the newly developed chemical ionisation Orbitrap (CI-Orbitrap) mass spectrometer to inspect the oxidation products. The high mass-resolving power of the Orbitrap is critical, as it allows the unambiguous separation of molecules with a D atom (mD=2.0141) from those with two H atoms (mH2=2.0157). We found that the method worked well, and we could deduce that two of the three tested compounds had lost D atoms during oxidation, suggesting that those deuterated positions were actively involved in the autoxidation process. Surprisingly, the deuterations were not observed to decrease HOM molar yields, as would have been expected due to kinetic isotope effects. This may be an indication that the relevant H (or D) abstractions were fast enough that no competing pathways were of relevance despite slower abstraction rates of the D atom. We show that selective deuteration can be a very useful method for studying autoxidation on a molecular level and likely is not limited to the system of α-pinene ozonolysis tested here.</p

Triplet energy differences and the low lying structure of Ga 62

Background: Triplet energy differences (TED) can be studied to yield information on isospin-non-conserving interactions in nuclei. Purpose: The systematic behavior of triplet energy differences (TED) of T=1, J\u3c0=2+ states is examined. The A=62 isobar is identified as having a TED value that deviates significantly from an otherwise very consistent trend. This deviation can be attributed to the tentative assignments of the pertinent states in Ga62 and Ge62. Methods: An in-beam \u3b3-ray spectroscopy experiment was performed to identify excited states in Ga62 using Gamma-Ray Energy Tracking In-Beam Nuclear Array with the S800 spectrometer at NSCL using a two-nucleon knockout approach. Cross-section calculations for the knockout process and shell-model calculations have been performed to interpret the population and decay properties observed. Results: Using the systematics as a guide, a candidate for the transition from the T=1, 2+ state is identified. However, previous work has identified similar states with different J\u3c0 assignments. Cross-section calculations indicate that the relevant T=1, 2+ state should be one of the states directly populated in this reaction. Conclusions: As spins and parities were not measurable, it is concluded that an unambiguous identification of the first T=1, 2+ state is required to reconcile our understanding of TED systematics

On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.Comment: accepted for publications, Journal of Computational Neuroscienc

Encountering religious diversity : multilevel governance of Islamic education in Finland and Ireland

Recent decades have witnessed a change in European governments’ policies from benign neglect to active management of religious diversity, where Islam is often seen as the most challenging for the European social order. However, the ways that this “management” is justified and undertaken varies from country to country and depends on the issues at hand. This paper will take up the issue of Islamic education in Finland and Ireland where it is incorporated into the public school system and where the state has taken an active role in order to control Islam in the field of education. The main argument of this article is that the “management” of Islamic education in both of the above-mentioned countries is ridden with contradictions arising from the difficulty to balance between an emphasis on particular national traditions, on the one hand, and public policies concerning religious diversity, on the other hand. Theoretically, the article will employ the perspective of multilevel governance which helps to widen the perspective from the state as a primary explanatory to different agents of the civil society in encountering religious diversity.Peer reviewe