Related papers: Evaluations of The Hierarchical Subspace Iteration…
In this work, we propose a hierarchical subspace model for acoustic unit discovery. In this approach, we frame the task as one of learning embeddings on a low-dimensional phonetic subspace, and simultaneously specify the subspace itself as…
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]
Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…
We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…
The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a…
Deploying deep neural networks for risk-sensitive tasks necessitates an uncertainty estimation mechanism. This paper introduces hierarchical selective classification, extending selective classification to a hierarchical setting. Our…
In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
For stochastic approximation algorithms with discontinuous dynamics, it is shown that under suitable distributional assumptions, the interpolated iterates track a Fillipov solution of the limiting differential inclusion. In addition, we…
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
This paper is a review of the developments in Instruction level parallelism. It takes into account all the changes made in speeding up the execution. The various drawbacks and dependencies due to pipelining are discussed and various…
We introduce a version of RSK that captures the dynamics of periodic TASEP. This work is building towards a cylindrical analogue of (AB Dieker, J Warren, 2008).
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
In this paper, further extensions of the result of the paper "A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024" concerning a…
In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
The experimental evaluation of algorithms results in a large set of data which generally do not follow a normal distribution or are not heteroscedastic. Besides, some of its entries may be missing, due to the inability of an algorithm to…
In this paper, we propose a data representation model that demonstrates hierarchical feature learning using nsNMF. We extend unit algorithm into several layers. Experiments with document and image data successfully discovered feature…
Humans can leverage hierarchical structures to split a task into sub-tasks and solve problems efficiently. Both imitation and reinforcement learning or a combination of them with hierarchical structures have been proven to be an efficient…