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We investigate the problem of estimating a function $f$ based on observations from its noisy convolution when the noise exhibits long-range dependence. We construct an adaptive estimator based on the kernel method, derive minimax lower…
We forecast a single time series using a high-dimensional set of predictors. When these predictors share common underlying dynamics, an approximate latent factor model provides a powerful characterization of their co-movements Bai(2003).…
The paper considers the application of reference governors to linear discrete-time systems with constraints given by polynomial inequalities. We propose a novel algorithm to compute the maximal output admissible invariant set in the case of…
We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional…
We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
Ensemble weather predictions typically show systematic errors that have to be corrected via post-processing. Even state-of-the-art post-processing methods based on neural networks often solely rely on location-specific predictors that…
Pre-trained language models demonstrate general intelligence and common sense, but long inputs quickly become a bottleneck for memorizing information at inference time. We resurface a simple method, Memorizing Transformers (Wu et al.,…
In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for best approximation by spaces of shifts in…
Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing…
Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance…
A low-complexity convolutional neural network estimator which learns the minimum mean squared error channel estimator for single-antenna users was recently proposed. We generalize the architecture to the estimation of MIMO channels with…
We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation. Opposed to related previous contributions suffering from the problem of reading out the optimal…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…
We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel.…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…