arXiv subjects

Maryann Rui

Publications and source records attributed to Maryann Rui.

4 recordsLinked to original sources

arXiv2025

Learning clusters of partially observed linear dynamical systems

We study the problem of learning clusters of partially observed linear dynamical systems from multiple input-output trajectories. This setting is particularly relevant when there are limited observations (e.g., short trajectories) from individual data sources, making direct estimation challenging. In such cases, incorporating data from multiple related sources can improve learning. We propose an estimation algorithm that leverages different data requirements for the tasks of clustering and system identification. First, short impulse responses are estimated from individual trajectories and clustered. Then, refined models for each cluster are jointly estimated using multiple trajectories. We establish end-to-end finite sample guarantees for estimating Markov parameters and state space realizations and highlight trade-offs among the number of observed systems, the trajectory lengths, and the complexity of the underlying models.

eess.SY↗

arXiv2024

Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems

We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response parameters of the mixture models. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexity bounds for estimating MLDS in the presence of noise, in terms of both the number of trajectories $N$ and the trajectory length $T$, and demonstrate the performance of the estimator through simulations.

eess.SY↗

arXiv2023

Estimation of Models with Limited Data by Leveraging Shared Structure

Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters. If there is shared structure among systems however, it may be possible to leverage data from other systems to help estimate individual parameters, which could otherwise be non-identifiable. In this paper, we assume systems share a latent low-dimensional parameter space and propose a method for recovering $d$-dimensional parameters for $N$ different linear systems, even when there are only $T<d$ observations per system. To do so, we develop a three-step algorithm which estimates the low-dimensional subspace spanned by the systems' parameters and produces refined parameter estimates within the subspace. We provide finite sample subspace estimation error guarantees for our proposed method. Finally, we experimentally validate our method on simulations with i.i.d. regression data and as well as correlated time series data.

cs.LG↗

arXiv2020

Towards Data Auctions with Externalities

The design of data markets has gained importance as firms increasingly use machine learning models fueled by externally acquired training data. A key consideration is the externalities firms face when data, though inherently freely replicable, is allocated to competing firms. In this setting, we demonstrate that a data seller's optimal revenue increases as firms can pay to prevent allocations to others. To do so, we first reduce the combinatorial problem of allocating and pricing multiple datasets to the auction of a single digital good by modeling utility for data through the increase in prediction accuracy it provides. We then derive welfare and revenue maximizing mechanisms, highlighting how the form of firms' private information - whether the externalities one exerts on others is known, or vice-versa - affects the resulting structures. In all cases, under appropriate assumptions, the optimal allocation rule is a single threshold per firm, where either all data is allocated or none is.

cs.GT↗