Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

Personalisation and recommender systems in digital libraries

Widespread use of the Internet has resulted in digital libraries that are increasingly used by diverse communities of users for diverse purposes and in which sharing and collaboration have become important social elements. As such libraries become commonplace, as their contents and services become more varied, and as their patrons become more experienced with computer technology, users will expect more sophisticated services from these libraries. A simple search function, normally an integral part of any digital library, increasingly leads to user frustration as user needs become more complex and as the volume of managed information increases. Proactive digital libraries, where the library evolves from being passive and untailored, are seen as offering great potential for addressing and overcoming these issues and include techniques such as personalisation and recommender systems. In this paper, following on from the DELOS/NSF Working Group on Personalisation and Recommender Systems for Digital Libraries, which met and reported during 2003, we present some background material on the scope of personalisation and recommender systems in digital libraries. We then outline the working group’s vision for the evolution of digital libraries and the role that personalisation and recommender systems will play, and we present a series of research challenges and specific recommendations and research priorities for the field

Non-Redundant Spectral Dimensionality Reduction

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding coordinates they produce typically capture the same direction along the data manifold. This leads to redundant and inefficient representations that do not reveal the true intrinsic dimensionality of the data. In this paper, we propose a general method for avoiding redundancy in spectral algorithms. Our approach relies on replacing the orthogonality constraints underlying those methods by unpredictability constraints. Specifically, we require that each embedding coordinate be unpredictable (in the statistical sense) from all previous ones. We prove that these constraints necessarily prevent redundancy, and provide a simple technique to incorporate them into existing methods. As we illustrate on challenging high-dimensional scenarios, our approach produces significantly more informative and compact representations, which improve visualization and classification tasks

User interfaces for information systems

This paper presents descriptions of four information-system interface projects in progress at ESRIN, each demonstrating a somewhat different approach to interface design, but ali sharing the commonality of responding to user goals, tasks and characteristics. It is suggested that next-generation scientific information systems will have to be designed for direct access by end users to a large variety of information sources, through a commom interface. Design of such systems, including their interfaces, should be based on a multi-level analysis of user goals, tasks and domain views.Se describen cuatro proyectos de interfaces de sistemas de información que se están desarrollando en ESRIN (establecimiento de la Agencia Espacial Europea, en Frascati). Cada uno de ellos muestra un enfoque diferente del diseño de interfaces, pero todos tienen en común el responder a los objetivos, tareas y características de los usuarios. Se sugiere que la próxima generación de sistemas de información científica se tendrá que diseñar para permitir el acceso directo de los usuarios finales a una gran variedad de fuentes de información a través de una interfaz común. El diseño de tales sistemas y de sus interfaces debería basarse en un análisis multinivel de objetivos, tareas y puntos de vista propios de la materia de trabajo de cada usuario

Semi-Supervised Learning of Lift Optimization of Multi-Element Three-Segment Variable Camber Airfoil

This chapter describes a new intelligent platform for learning optimal designs of morphing wings based on Variable Camber Continuous Trailing Edge Flaps (VCCTEF) in conjunction with a leading edge flap called the Variable Camber Krueger (VCK). The new platform consists of a Computational Fluid Dynamics (CFD) methodology coupled with a semi-supervised learning methodology. The CFD component of the intelligent platform comprises of a full Navier-Stokes solution capability (NASA OVERFLOW solver with Spalart-Allmaras turbulence model) that computes flow over a tri-element inboard NASA Generic Transport Model (GTM) wing section. Various VCCTEF/VCK settings and configurations were considered to explore optimal design for high-lift flight during take-off and landing. To determine globally optimal design of such a system, an extremely large set of CFD simulations is needed. This is not feasible to achieve in practice. To alleviate this problem, a recourse was taken to a semi-supervised learning (SSL) methodology, which is based on manifold regularization techniques. A reasonable space of CFD solutions was populated and then the SSL methodology was used to fit this manifold in its entirety, including the gaps in the manifold where there were no CFD solutions available. The SSL methodology in conjunction with an elastodynamic solver (FiDDLE) was demonstrated in an earlier study involving structural health monitoring. These CFD-SSL methodologies define the new intelligent platform that forms the basis for our search for optimal design of wings. Although the present platform can be used in various other design and operational problems in engineering, this chapter focuses on the high-lift study of the VCK-VCCTEF system. Top few candidate design configurations were identified by solving the CFD problem in a small subset of the design space. The SSL component was trained on the design space, and was then used in a predictive mode to populate a selected set of test points outside of the given design space. The new design test space thus populated was evaluated by using the CFD component by determining the error between the SSL predictions and the true (CFD) solutions, which was found to be small. This demonstrates the proposed CFD-SSL methodologies for isolating the best design of the VCK-VCCTEF system, and it holds promise for quantitatively identifying best designs of flight systems, in general

Semantic distillation: a method for clustering objects by their contextual specificity

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence, Springer-Verla

Nonmonotonic Decay of Nonequilibrium Polariton Condensate in Direct-Gap Semiconductors

Time evolution of a nonequilibrium polariton condensate has been studied in the framework of a microscopic approach. It has been shown that due to polariton-polariton scattering a significant condensate depletion takes place in a comparatively short time interval. The condensate decay occurs in the form of multiple echo signals. Distribution-function dynamics of noncondensate polaritons have been investigated. It has been shown that at the initial stage of evolution the distribution function has the form of a bell. Then oscillations arise in the contour of the distribution function, which further transform into small chaotic ripples. The appearance of a short-wavelength wing of the distribution function has been demonstrated. We have pointed out the enhancement and then partial extinction of the sharp extra peak arising within the time interval characterized by small values of polariton condensate density and its relatively slow changes.Comment: 20 pages, LaTeX 2.09; in press in PR

Risk factors for myocardial infarction during carotid endarterectomy in high-risk patients with coronary artery disease

Aim. To determine the value of various risk factors for predicting the myocardial infarction (MI) during carotid endarterectomy in high-risk patients with coronary artery disease (CAD).Material and methods. The single-center cohort prospective study included 204 high-risk patients with CAD who required carotid endarterectomy (CEA). Before surgery, all patients underwent treatment of CAD, and all patients were clinically stabilized. The first step was CEA. Clinical and diagnostic factors associated with the risk of perioperative MI were studied. There were following end points of the study: stroke, MI, death due to MI. The diagnosis of MI was established when there was a combination of an increase in cTn-I troponin above the 99th percentile upper reference limit with electrocardiographic manifestations of myocardial ischemia, or with chest pain or equivalent symptoms consistent with myocardial ischemia.Results. There were no strokes. There were no deaths due to MI. Perioperative MI developed in 8 (3,9%) patients. There were following most significant predictors of perioperative MI: severe impairment of local left ventricular (LV) contractility (hazard ratio (HR), 13,57; 95% confidence interval (CI), 1,427-124,782, p<0,05) and a decrease in left ventricular ejection fraction <50% (HR, 10,909; 95% CI, 1,052-271,229, p<0,05). However, following factors were insignificant for predicting perioperative MI (p>0,05): SYNTAX score, prior cerebrovascular accident, myocardial infarction, insulin-dependent diabetes mellitus, obesity, chronic obstructive pulmonary disease.Conclusion. In high-risk patients with CAD, severe impairment of local LV contractility and global LV systolic dysfunction are the most significant risk factors for perioperative MI during CEA

Investigation of the microstructure of the fine-grained YPO4_4:Gd ceramics with xenotime structure after Xe irradiation

The paper reports on the preparation of xenotime-structured ceramics by the Spark Plasma Sintering (SPS) method. Phosphates Y$_{0.95}$Gd$_{0.05}$PO$_4$ (YPO$_4$:Gd) were obtained by the sol-gel method. The synthesized nanopowders are collected in large agglomerates 10-50 mkm in size. Ceramics has a fine-grained microstructure and a high relative density (98.67%). The total time of the SPS process was approximately 18 min. High-density sintered ceramics YPO$_4$:Gd with a xenotime structure were irradiated with Xe$^{+26}$ ions (E = 167 MeV) to fluences of $1\times10^{12}$-$3\times 10^{13}$ cm$^{-2}$. Complete amorphization at maximum fluence was not achieved. As the fluence increases, an insignificant increase in the depth of the amorphous layer is observed. According to the results of grazing incidence XRD (GIXRD), with an increase in fluence from $1\times10^{12}$-$3\times 10^{13}$ cm$^{-2}$, an increase in the volume fraction of the amorphous structure from 20 to 70% is observed. The intensity of XRD peak 200 YPO$_4$:Gd after recovery annealing (700$^\circ$C, 18 h) reached a value of ~80% of the initial intensity I0.Comment: 16 pages, 10 figure

Self-explaining AI as an alternative to interpretable AI

The ability to explain decisions made by AI systems is highly sought after, especially in domains where human lives are at stake such as medicine or autonomous vehicles. While it is often possible to approximate the input-output relations of deep neural networks with a few human-understandable rules, the discovery of the double descent phenomena suggests that such approximations do not accurately capture the mechanism by which deep neural networks work. Double descent indicates that deep neural networks typically operate by smoothly interpolating between data points rather than by extracting a few high level rules. As a result, neural networks trained on complex real world data are inherently hard to interpret and prone to failure if asked to extrapolate. To show how we might be able to trust AI despite these problems we introduce the concept of self-explaining AI. Self-explaining AIs are capable of providing a human-understandable explanation of each decision along with confidence levels for both the decision and explanation. For this approach to work, it is important that the explanation actually be related to the decision, ideally capturing the mechanism used to arrive at the explanation. Finally, we argue it is important that deep learning based systems include a "warning light" based on techniques from applicability domain analysis to warn the user if a model is asked to extrapolate outside its training distribution. For a video presentation of this talk see https://www.youtube.com/watch?v=Py7PVdcu7WY& .Comment: 10pgs, 2 column forma