Efficient kernel surrogates for neural network-based regression

Despite their immense promise in performing a variety of learning tasks, a theoretical understanding of the effectiveness and limitations of Deep Neural Networks (DNNs) has so far eluded practitioners. This is partly due to the inability to determine the closed forms of the learned functions, making it harder to assess their precise dependence on the training data and to study their generalization properties on unseen datasets. Recent work has shown that randomly initialized DNNs in the infinite width limit converge to kernel machines relying on a Neural Tangent Kernel (NTK) with known closed form. These results suggest, and experimental evidence corroborates, that empirical kernel machines can also act as surrogates for finite width DNNs. The high computational cost of assembling the full NTK, however, makes this approach infeasible in practice, motivating the need for low-cost approximations. In the current work, we study the performance of the Conjugate Kernel (CK), an efficient approximation to the NTK that has been observed to yield fairly similar results. For the regression problem of smooth functions and classification using logistic regression, we show that the CK performance is only marginally worse than that of the NTK and, in certain cases, is shown to be superior. In particular, we establish bounds for the relative test losses, verify them with numerical tests, and identify the regularity of the kernel as the key determinant of performance. In addition to providing a theoretical grounding for using CKs instead of NTKs, our framework provides insights into understanding the robustness of the various approximants and suggests a recipe for improving DNN accuracy inexpensively. We present a demonstration of this on the foundation model GPT-2 by comparing its performance on a classification task using a conventional approach and our prescription.Comment: 29 pages. software used to reach results available upon request, approved for release by Pacific Northwest National Laborator

Improving Shape Retrieval by Integrating AIR and Modified Mutual k

In computer vision, image retrieval remained a significant problem and recent resurgent of image retrieval also relies on other postprocessing methods to improve the accuracy instead of solely relying on good feature representation. Our method addressed the shape retrieval of binary images. This paper proposes a new integration scheme to best utilize feature representation along with contextual information. For feature representation we used articulation invariant representation; dynamic programming is then utilized for better shape matching followed by manifold learning based postprocessing modified mutual kNN graph to further improve the similarity score. We conducted extensive experiments on widely used MPEG-7 database of shape images by so-called bulls-eye score with and without normalization of modified mutual kNN graph which clearly indicates the importance of normalization. Finally, our method demonstrated better results compared to other methods. We also computed the computational time with another graph transduction method which clearly shows that our method is computationally very fast. Furthermore, to show consistency of postprocessing method, we also performed experiments on challenging ORL and YALE face datasets and improved baseline results

2017 HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: executive summary.

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withdrawn 2017 hrs ehra ecas aphrs solaece expert consensus statement on catheter and surgical ablation of atrial fibrillation

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2017 HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: executive summary.

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Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Simulating Nonlinear Faraday Waves on a Cylinder

In 1831, Michael Faraday observed the formation of standing waves on the surface of a vibrating fluid body. Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude of the vibration and have spurred vast research in hydrodynamics and pattern formation. These include linear analyses to determine the conditions for the onset of the patterns, weakly nonlinear studies to understand pattern selection, and dynamical systems approaches to study mode competition and chaos. Recently, there has been some work towards numerical simulations in various three-dimensional geometries. These methods however possess low orders of accuracy, making them unsuitable for nonlinear regimes.We present a new technique for fast and accurate simulations of nonlinear Faraday waves in a cylinder. Beginning from a viscous potential flow model, we generalize the Transformed Field Expansion to this geometry for finding the highly non-local Dirichlet-to-Neumann operator (DNO) for the Laplace equation. A spectral method relying on Zernike polynomials is developed to rapidly compute the bulk potential. We prove the effectiveness of representing functions on the unit disc in terms of these polynomials and also show that the DNO algorithm possesses spectral accuracy, unlike a method based on Bessel functions. The free surface evolution equations are solved in time using Picard iterations carried out by left-Radau quadrature. The results are in perfect agreement with the instability thresholds and surface patterns predicted for the linearized problem. The nonlinear simulations reproduce several qualitative features observed experimentally. In addition, by enabling one to switch between various nonlinear regimes, the technique allows a precise determination of the mechanisms triggering various experimental observations

Simulating Nonlinear Faraday Waves on a Cylinder

In 1831, Michael Faraday observed the formation of standing waves on the surface of a vibrating fluid body. Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude of the vibration and have spurred vast research in hydrodynamics and pattern formation. These include linear analyses to determine the conditions for the onset of the patterns, weakly nonlinear studies to understand pattern selection, and dynamical systems approaches to study mode competition and chaos. Recently, there has been some work towards numerical simulations in various three-dimensional geometries. These methods however possess low orders of accuracy, making them unsuitable for nonlinear regimes.We present a new technique for fast and accurate simulations of nonlinear Faraday waves in a cylinder. Beginning from a viscous potential flow model, we generalize the Transformed Field Expansion to this geometry for finding the highly non-local Dirichlet-to-Neumann operator (DNO) for the Laplace equation. A spectral method relying on Zernike polynomials is developed to rapidly compute the bulk potential. We prove the effectiveness of representing functions on the unit disc in terms of these polynomials and also show that the DNO algorithm possesses spectral accuracy, unlike a method based on Bessel functions. The free surface evolution equations are solved in time using Picard iterations carried out by left-Radau quadrature. The results are in perfect agreement with the instability thresholds and surface patterns predicted for the linearized problem. The nonlinear simulations reproduce several qualitative features observed experimentally. In addition, by enabling one to switch between various nonlinear regimes, the technique allows a precise determination of the mechanisms triggering various experimental observations