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Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
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…
The focus of this paper is the estimation of a delay between two signals. Such a problem is common in signal processing and particularly challenging when the delay is non-stationary in nature. Our proposed solution is based on an all-pass…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
We develop and analyze a general technique for learning with an unknown distribution drift. Given a sequence of independent observations from the last $T$ steps of a drifting distribution, our algorithm agnostically learns a family of…
In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying descriptor systems with uncertain parameters.…
Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid of constant mass…
We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
In the context of filtering chaotic dynamical systems it is well-known that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both…
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…
In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of…
The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of Statistics…
An algorithm called MUSIC-like algorithm was originally proposed as an alternative method to the MUltiple SIgnal Classification (MUSIC) algorithm for direction-of-arrival (DOA) estimation. Without requiring explicit model order estimation,…
We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly…
It is well-known that saturated output observations are prevalent in various practical systems and that the $\ell_1$-norm is more robust than the $\ell_2$-norm-based parameter estimation. Unfortunately, adaptive identification based on both…
This study investigates the use of continuous-time dynamical systems for sparse signal recovery. The proposed dynamical system is in the form of a nonlinear ordinary differential equation (ODE) derived from the gradient flow of the Lasso…
The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. Error estimates are…