3,801 research outputs found
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 -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 . Hopefully, in upcoming work, this will be
proved for any value of .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
- …