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We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned…
Adaptive time stepping methods for metastable dynamics of the Allen Cahn and Cahn Hilliard equations are investigated in the spatially continuous, semi-discrete setting. We analyse the performance of a number of first and second order…
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence…
Suppose we can choose from a set of linear autonomous systems with bounded process noise, the dynamics of each system are unknown, and we would like to design a stabilizing policy. The underlying question is how to estimate the dynamics of…
Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing…
The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence…
Uncertainty estimation methods using deep learning approaches strive against separating how uncertain the state of the world manifests to us via measurement (objective end) from the way this gets scrambled with the model specification and…
We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…
A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback…
Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given…
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…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…
Approximating time-varying unobserved heterogeneity by discrete types has become increasingly popular in economics. Yet, provably valid post-clustering inference for target parameters in models that do not impose an exact group structure is…