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We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
This work provides a data-driven framework that combines coprime factorization with a lifting linearization technique to model the discrepancy between a nonlinear system and its nominal linear approximation using a linear time-invariant…
Given the recent surge of interest in data-driven control, this paper proposes a two-step method to study robust data-driven control for a parameter-unknown linear time-invariant (LTI) system that is affected by energy-bounded noises.…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction, and…
This work develops a data-based construction of inverse dynamics for LTI systems. Specifically, the problem addressed here is to find an input sequence from the corresponding output sequence based on pre-collected input and output data. The…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller…
Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…
Autonomous robots require high degrees of cognitive and motoric intelligence to come into our everyday life. In non-structured environments and in the presence of uncertainties, such degrees of intelligence are not easy to obtain.…
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector. We address the question of how long the…
Stochastic Interpolants (SI) is a powerful framework for generative modeling, capable of flexibly transforming between two probability distributions. However, its use in jointly optimized latent variable models remains unexplored as it…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is…