Convex recovery of tensors using nuclear norm penalization

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining much interest due to its potential applications to signal processing, statistics and engineering. The goal of this paper is to present an applications to the problem of low rank tensor recovery based on linear random measurement by extending the results of Tropp to the tensors setting.Comment: To appear in proceedings LVA/ICA 2015 at Czech Republi

ForestHash: Semantic Hashing With Shallow Random Forests and Tiny Convolutional Networks

Hash codes are efficient data representations for coping with the ever growing amounts of data. In this paper, we introduce a random forest semantic hashing scheme that embeds tiny convolutional neural networks (CNN) into shallow random forests, with near-optimal information-theoretic code aggregation among trees. We start with a simple hashing scheme, where random trees in a forest act as hashing functions by setting `1' for the visited tree leaf, and `0' for the rest. We show that traditional random forests fail to generate hashes that preserve the underlying similarity between the trees, rendering the random forests approach to hashing challenging. To address this, we propose to first randomly group arriving classes at each tree split node into two groups, obtaining a significantly simplified two-class classification problem, which can be handled using a light-weight CNN weak learner. Such random class grouping scheme enables code uniqueness by enforcing each class to share its code with different classes in different trees. A non-conventional low-rank loss is further adopted for the CNN weak learners to encourage code consistency by minimizing intra-class variations and maximizing inter-class distance for the two random class groups. Finally, we introduce an information-theoretic approach for aggregating codes of individual trees into a single hash code, producing a near-optimal unique hash for each class. The proposed approach significantly outperforms state-of-the-art hashing methods for image retrieval tasks on large-scale public datasets, while performing at the level of other state-of-the-art image classification techniques while utilizing a more compact and efficient scalable representation. This work proposes a principled and robust procedure to train and deploy in parallel an ensemble of light-weight CNNs, instead of simply going deeper.Comment: Accepted to ECCV 201

The early life microbiota protects neonatal mice from pathological small intestinal epithelial cell shedding

The early life gut microbiota plays a crucial role in regulating and maintaining the intestinal barrier, with disturbances in these communities linked to dysregulated renewal and replenishment of intestinal epithelial cells. Here we sought to determine pathological cell shedding outcomes throughout the postnatal developmental period, and which host and microbial factors mediate these responses. Surprisingly, neonatal mice (Day 14 and 21) were highly refractory to induction of cell shedding after intraperitoneal administration of liposaccharide (LPS), with Day 29 mice showing strong pathological responses, more similar to those observed in adult mice. These differential responses were not linked to defects in the cellular mechanisms and pathways known to regulate cell shedding responses. When we profiled microbiota and metabolites, we observed significant alterations. Neonatal mice had high relative abundances of Streptococcus, Escherichia, and Enterococcus and increased primary bile acids. In contrast, older mice were dominated by Candidatus Arthromitus, Alistipes, and Lachnoclostridium, and had increased concentrations of SCFAs and methyamines. Antibiotic treatment of neonates restored LPS-induced small intestinal cell shedding, whereas adult fecal microbiota transplant alone had no effect. Our findings further support the importance of the early life window for microbiota-epithelial interactions in the presence of inflammatory stimuli and highlights areas for further investigation

Harnack inequality for fractional sub-Laplacians in Carnot groups

In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups

lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p<=1, then for any fraction of outliers the most significant subspace can be recovered by lp minimization with overwhelming probability (which depends on the generating distribution and its parameters). We show that when adding small noise around the underlying subspaces the most significant subspace can be nearly recovered by lp minimization for any 0<p<=1 with an error proportional to the noise level. On the other hand, if p>1 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.Comment: This is a revised version of the part of 1002.1994 that deals with single subspace recovery. V3: Improved estimates (in particular for Lemma 3.1 and for estimates relying on it), asymptotic dependence of probabilities and constants on D and d and further clarifications; for simplicity it assumes uniform distributions on spheres. V4: minor revision for the published versio

Tuning of Human Modulation Filters Is Carrier-Frequency Dependent

Licensed under the Creative Commons Attribution License

Carbon stock growth in a forest stand: the power of age

BACKGROUND: Understanding the relationship between the age of a forest stand and its biomass is essential for managing the forest component of the global carbon cycle. Since biomass increases with stand age, postponing harvesting to the age of biological maturity may result in the formation of a large carbon sink. This article quantifies the carbon sequestration capacity of forests by suggesting a default rule to link carbon stock and stand age. RESULTS: The age dependence of forest biomass is shown to be a power-law monomial where the power of age is theoretically estimated to be 4/5. This theoretical estimate is close to the known empirical estimate; therefore, it provides a scientific basis for a quick and transparent assessment of the benefits of postponing the harvest, suggesting that the annual magnitude of the sink induced by delayed harvest lies in the range of 1–2% of the baseline carbon stock. CONCLUSION: The results of this study imply that forest age could be used as an easily understood and scientifically sound measure of the progress in complying with national targets on the protection and enhancement of forest carbon sinks

Austerity, ageing and the financialisation of pensions policy in the UK

This article offers a detailed analysis of the recent history of pensions policy in the United Kingdom, culminating in two apparent ‘revolutions’ in policy now underway: the introduction of ‘automatic enrolment’ into private pensions, and proposals for a new ‘single-tier’ state pension. These reforms are considered exemplary of the ‘financialisation’ of UK welfare provision – typified in pensions policy by the notion that individuals must take personal responsibility for their own long-term financial security, and engage intimately with the financial services industry to do so. As such, the reforms represent the continuation of pensions policy between the Labour and coalition governments, despite the coalition government’s novel rhetorical commitment to austerity. In fact, the pensions revolutions will actually cost the state significantly more than current arrangements, yet the importance of fears about population ageing means that the government is both able to marshal the imagery of austerity to justify financialisation, but is also required to partly conceal the increased expenditure this requires. The article shows therefore how the financialisation agenda in pensions policy was evident before the financial crisis, but has evolved to both take advantage, and mitigate the constraints, of a post-crisis political climate

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

The impact of emotional well-being on long-term recovery and survival in physical illness: a meta-analysis

This meta-analysis synthesized studies on emotional well-being as predictor of the prognosis of physical illness, while in addition evaluating the impact of putative moderators, namely constructs of well-being, health-related outcome, year of publication, follow-up time and methodological quality of the included studies. The search in reference lists and electronic databases (Medline and PsycInfo) identified 17 eligible studies examining the impact of general well-being, positive affect and life satisfaction on recovery and survival in physically ill patients. Meta-analytically combining these studies revealed a Likelihood Ratio of 1.14, indicating a small but significant effect. Higher levels of emotional well-being are beneficial for recovery and survival in physically ill patients. The findings show that emotional well-being predicts long-term prognosis of physical illness. This suggests that enhancement of emotional well-being may improve the prognosis of physical illness, which should be investigated by future research