6,728 research outputs found
Literacy Data Map
A Map by The Program for Culture and Conflict Studies at the Naval Postgraduate SchoolA Map of the Literacy DATA for the FATA
Online Local Volatility Calibration by Convex Regularization with Morozov's Principle and Convergence Rates
We address the inverse problem of local volatility surface calibration from
market given option prices. We integrate the ever-increasing flow of option
price information into the well-accepted local volatility model of Dupire. This
leads to considering both the local volatility surfaces and their corresponding
prices as indexed by the observed underlying stock price as time goes by in
appropriate function spaces. The resulting parameter to data map is defined in
appropriate Bochner-Sobolev spaces. Under this framework, we prove key
regularity properties. This enable us to build a calibration technique that
combines online methods with convex Tikhonov regularization tools. Such
procedure is used to solve the inverse problem of local volatility
identification. As a result, we prove convergence rates with respect to noise
and a corresponding discrepancy-based choice for the regularization parameter.
We conclude by illustrating the theoretical results by means of numerical
tests.Comment: 23 pages, 5 figure
Symmetrized Perturbation Determinants and Applications to Boundary Data Maps and Krein-Type Resolvent Formulas
The aim of this paper is twofold: On one hand we discuss an abstract approach
to symmetrized Fredholm perturbation determinants and an associated trace
formula for a pair of operators of positive-type, extending a classical trace
formula. On the other hand, we continue a recent systematic study of boundary
data maps, that is, 2 \times 2 matrix-valued Dirichlet-to-Neumann and more
generally, Robin-to-Robin maps, associated with one-dimensional Schr\"odinger
operators on a compact interval [0,R] with separated boundary conditions at 0
and R. One of the principal new results in this paper reduces an appropriately
symmetrized (Fredholm) perturbation determinant to the 2\times 2 determinant of
the underlying boundary data map. In addition, as a concrete application of the
abstract approach in the first part of this paper, we establish the trace
formula for resolvent differences of self-adjoint Schr\"odinger operators
corresponding to different (separated) boundary conditions in terms of boundary
data maps.Comment: 38 page
STG-MTL: Scalable Task Grouping for Multi-Task Learning Using Data Map
Multi-Task Learning (MTL) is a powerful technique that has gained popularity
due to its performance improvement over traditional Single-Task Learning (STL).
However, MTL is often challenging because there is an exponential number of
possible task groupings, which can make it difficult to choose the best one,
and some groupings might produce performance degradation due to negative
interference between tasks. Furthermore, existing solutions are severely
suffering from scalability issues, limiting any practical application. In our
paper, we propose a new data-driven method that addresses these challenges and
provides a scalable and modular solution for classification task grouping based
on hand-crafted features, specifically Data Maps, which capture the training
behavior for each classification task during the MTL training. We experiment
with the method demonstrating its effectiveness, even on an unprecedented
number of tasks (up to 100).Comment: Accepted submission to DMLR workshop @ ICML 2
Calibrate, emulate, sample
Many parameter estimation problems arising in applications can be cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates. Often in such problems the parameter-to-data map is very expensive to evaluate, and computing derivatives of the map, or derivative-adjoints, may not be feasible. Additionally, in many applications only noisy evaluations of the map may be available. We propose an approach to Bayesian inversion in such settings that builds on the derivative-free optimization capabilities of ensemble Kalman inversion methods. The overarching approach is to first use ensemble Kalman sampling (EKS) to calibrate the unknown parameters to fit the data; second, to use the output of the EKS to emulate the parameter-to-data map; third, to sample from an approximate Bayesian posterior distribution in which the parameter-to-data map is replaced by its emulator. This results in a principled approach to approximate Bayesian inference that requires only a small number of evaluations of the (possibly noisy approximation of the) parameter-to-data map. It does not require derivatives of this map, but instead leverages the documented power of ensemble Kalman methods. Furthermore, the EKS has the desirable property that it evolves the parameter ensemble towards the regions in which the bulk of the parameter posterior mass is located, thereby locating them well for the emulation phase of the methodology. In essence, the EKS methodology provides a cheap solution to the design problem of where to place points in parameter space to efficiently train an emulator of the parameter-to-data map for the purposes of Bayesian inversion
Comparison of cattail (Typha sp.) occurrence on a photo-interpreted map versus a satellite data map
A comparison between a 1985 photo-interpreted vegetation map
and a vegetation map made from classified 1987 satellite data of
the Loxahatchee National Wildlife Refuge showed that 81% of
samples taken in areas occupied by cattail (Typha sp.) on the
photo-interpreted map corresponded with cattail on the satellite
data map.(5 page document
Sigmoid(x): secure distributed network storage
Secure data storage is a serious problem for computer users today, particularly in enterprise environments. As data requirements grow, traditional approaches of secured silos are showing their limitations. They represent a single – or at least, limited – point of failure, and require significant, and increasing, maintenance and overhead. Such solutions are totally unsuitable for consumers, who want a ‘plug and play’ secure solution for their increasing datasets – something with the ubiquity of access of Facebook or webmail. Network providers can provide centralised solutions, but that returns us to the first problem. Sigmoid(x) takes a completely different approach – a scalable, distributed, secure storage mechanism which shares data storage between the users themselves
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