Related papers: Uniform Oscillatory Integral estimates for Convex …
This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are…
The extremal dependence structure of a regularly varying random vector Xis fully described by its limiting spectral measure. In this paper, we investigate how torecover characteristics of the measure, such as extremal coefficients, from the…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
A number of results related to statistical classification on convex sets are presented. In particular, the focus is on the case where some of the covariates in the data and observation being classified can be missing. The form of the…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
This paper presents a joint optimisation framework for optimal estimation and stochastic optimal control with imperfect information. It provides a estimation and control scheme that can be decomposed into a classical optimal estimation step…
In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of $L^2 \mapsto L^2$ type for the operator, as well as for the corresponding maximal function. If…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
In large-scale modern data analysis, first-order optimization methods are usually favored to obtain sparse estimators in high dimensions. This paper performs theoretical analysis of a class of iterative thresholding based estimators defined…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
We study numerically the oscillation death state in the phase oscillator model proposed byWinfree. We found that the phases in this state follow very simple rules, actually, besides intrinsic properties of the oscillators, such as natural…
In this paper we consider the uniform estimates for oscillatory integrals with a two-order homogeneous polynomial phase. The estimate is sharp and the result is an analogue of the more general theorem of V. N. Karpushkin…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…