Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Compressive Classification

This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry of the source, the geometry of the measurement system and their interplay. The measurement gain, which represents the counterpart of the coding gain, is also shown to depend on geometrical quantities. It is argued that the diversity order and the measurement gain also offer an optimization criterion to perform dictionary learning for compressive classification applications.Comment: 5 pages, 3 figures, submitted to the 2013 IEEE International Symposium on Information Theory (ISIT 2013

On the design of linear projections for compressive sensing with side information

In this paper, we study the problem of projection kernel design for the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information, assuming that the signal of interest and the side information signal are described by a joint Gaussian mixture model (GMM). In particular, we consider the case where the projection kernel for the signal of interest is random, whereas the projection kernel associated to the side information is designed. We then derive sufficient conditions on the number of measurements needed to guarantee that the minimum meansquared error (MMSE) tends to zero in the low-noise regime. Our results demonstrate that the use of a designed kernel to capture side information can lead to substantial gains in relation to a random one, in terms of the number of linear projections required for reliable reconstruction

Innovation activities and Italian SMEs' exports decisions: a multi-treatment analysis

Abstract: This study aims at estimating the effect of innovation on export growth for a sample of Italian small and medium size manufacturing firms. We define two classes of innovation, namely technological and non-technological. For each class of innovation, we use a propensity score matching strategy to assess if innovating in period t – 1 led to an increase in firms’ probability of seeking for new exporting markets in period t + 1. Moreover, we assess the combined effect of both classes of innovation upon the probability of seeking for new markets. We found that both technological and non-technological innovations increases the probability that a firm will plan to look for new markets abroad, the former type of innovation being, on average, twice as relevant as the latter. Moreover, we found evidence that these are complementary activities, which are more effective on future exports decisions when combined

Signal reconstruction in the presence of side information: The impact of projection kernel design

This paper investigates the impact of projection design on the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information. In particular, we assume that both the signal of interest and the side information are described by a joint Gaussian mixture model (GMM) distribution. Sharp necessary and sufficient conditions on the number of measurements needed to guarantee that the average reconstruction error approaches zero in the low-noise regime are derived, for both cases when the side information is available at the decoder or at the decoder and encoder. Numerical results are also presented to showcase the impact of projection design on applications with real imaging data in the presence of side information

Low-power Secret-key Agreement over OFDM

Information-theoretic secret-key agreement is perhaps the most practically feasible mechanism that provides unconditional security at the physical layer to date. In this paper, we consider the problem of secret-key agreement by sharing randomness at low power over an orthogonal frequency division multiplexing (OFDM) link, in the presence of an eavesdropper. The low power assumption greatly simplifies the design of the randomness sharing scheme, even in a fading channel scenario. We assess the performance of the proposed system in terms of secrecy key rate and show that a practical approach to key sharing is obtained by using low-density parity check (LDPC) codes for information reconciliation. Numerical results confirm the merits of the proposed approach as a feasible and practical solution. Moreover, the outage formulation allows to implement secret-key agreement even when only statistical knowledge of the eavesdropper channel is available.Comment: 9 pages, 4 figures; this is the authors prepared version of the paper with the same name accepted for HotWiSec 2013, the Second ACM Workshop on Hot Topics on Wireless Network Security and Privacy, Budapest, Hungary 17-19 April 201

Green bean biofortification for Si through soilless cultivation: Plant response and Si bioaccessibility in pods

Food plants biofortification for micronutrients is a tool for the nutritional value improvement of food. Soilless cultivation systems, with the optimal control of plant nutrition, represent a potential effective technique to increase the beneficial element content in plant tissues. Silicon (Si), which proper intake is recently recommended for its beneficial effects on bone health, presents good absorption in intestinal tract from green bean, a high-value vegetable crop. In this study we aimed to obtain Si biofortified green bean pods by using a Si-enriched nutrient solution in soilless system conditions, and to assess the influence of boiling and steaming cooking methods on Si content, color parameters and Si bioaccessibility (by using an in vitro digestion process) of pods. The Si concentration of pods was almost tripled as a result of the biofortification process, while the overall crop performance was not negatively influenced. The Si content of biofortified pods was higher than unbiofortified also after cooking, despite the cooking method used. Silicon bioaccessibility in cooked pods was more than tripled as a result of biofortification, while the process did not affect the visual quality of the product. Our results demonstrated that soilless cultivation can be successfully used for green bean Si biofortification

Biodiversity of vegetable crops, a living heritage

Biodiversity is the natural heritage of the planet and is one of the key factors of sustainable development, due to its importance not only for the environmental aspects of sustainability but also for the social and economic ones. The purpose of this Special Issue is to publish high-quality research papers addressing recent progress and perspectives while focusing on different aspects related to the biodiversity of vegetable crops. Original, high-quality contributions that have not yet been published, or that are not currently under review by other journals, have been gathered. A broad range of aspects such as genetic, crop production, environments, customs and traditions were covered. All contributions are of significant relevance and could stimulate further research in this area

On instabilities of deep learning in image reconstruction - Does AI come at a cost?

Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field. In this paper we demonstrate a crucial phenomenon: deep learning typically yields unstablemethods for image reconstruction. The instabilities usually occur in several forms: (1) tiny, almost undetectable perturbations, both in the image and sampling domain, may result in severe artefacts in the reconstruction, (2) a small structural change, for example a tumour, may not be captured in the reconstructed image and (3) (a counterintuitive type of instability) more samples may yield poorer performance. Our new stability test with algorithms and easy to use software detects the instability phenomena. The test is aimed at researchers to test their networks for instabilities and for government agencies, such as the Food and Drug Administration (FDA), to secure safe use of deep learning methods