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In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
We propose a projection method to estimate risk-neutral moments from option prices. We derive a finite-sample bound implying that the projection estimator attains (up to a constant) the smallest pricing error within the span of traded…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a…
We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus let down a curtain on a possible formulation of a principle of…
Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori-Zwanzig (MZ) perspective, projecting the full dynamics onto a…
Algorithmic recourse suggests actions to individuals who have been adversely affected by automated decision-making, helping them to achieve the desired outcome. Knowing the recourse, however, does not guarantee that users can implement it…
Time series with missing data are signals encountered in important settings for machine learning. Some of the most successful prior approaches for modeling such time series are based on recurrent neural networks that transform the input and…
In this paper, we reveal a general relationship between model simplification and irreversibility based on the model of continuous-time Markov chains with time-scale separation. According to the topological structure of the fast process, we…
Most approaches to cross-modal retrieval (CMR) focus either on object-centric datasets, meaning that each document depicts or describes a single object, or on scene-centric datasets, meaning that each image depicts or describes a complex…
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount…
Inverse reinforcement learning (IRL) recovers reward functions from observed behavior, yet traditional methods assume a single stationary reward that cannot capture goal switching within an episode. Recent multi-intention IRL methods…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a…
This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the…
Consider a subject or unit in a longitudinal biomedical, public health, engineering, economic, or social science study which is being monitored over a possibly random duration. Over time this unit experiences competing recurrent events and…
Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision…
We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set ${\cal X}$ from indirect observation $\omega=Ax+\xi$ of $x$ corrupted by random noise $\xi$ with finite covariance matrix.…
Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work…
This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…