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We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…
In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…
Autonomous systems with machine learning-based perception can exhibit unpredictable behaviors that are difficult to quantify, let alone verify. Such behaviors are convenient to capture in probabilistic models, but probabilistic model…
To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…
In this paper, we consider the automated planning of optimal paths for a robotic team satisfying a high level mission specification. Each robot in the team is modeled as a weighted transition system where the weights have associated…
Signal Temporal Logic (STL) is widely used to specify timed and safety-critical tasks for cyber-physical systems, but writing STL formulas directly is difficult for non-expert users. Natural language (NL) provides a convenient interface,…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian…
Runtime verification encompasses several lightweight techniques for checking whether a system's current execution satisfies a given specification. We focus on runtime verification for Linear Temporal Logic (LTL). Previous work describes…
The logistic regression estimator is known to inflate the magnitude of its coefficients if the sample size $n$ is small, the dimension $p$ is (moderately) large or the signal-to-noise ratio $1/\sigma$ is large (probabilities of observing a…
Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
This paper investigates the online monitoring problem for cyber-physical systems under signal temporal logic (STL) specifications. The objective is to design an online monitor that evaluates system correctness at runtime based on partial…
In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…
The majority of existing Linear Temporal Logic (LTL) planning methods rely on the construction of a discrete product automaton, that combines a discrete abstraction of robot mobility and a B$\ddot{\text{u}}$chi automaton that captures the…
Perception is one of the key abilities of autonomous mobile robotic systems, which often relies on fusion of heterogeneous sensors. Although this heterogeneity presents a challenge for sensor calibration, it is also the main prospect for…
As learned control policies become increasingly common in autonomous systems, there is increasing need to ensure that they are interpretable and can be checked by human stakeholders. Formal specifications have been proposed as ways to…
We introduce a new family of temporal logics intended for specifications in motion planning (MP). It builds upon the signal temporal logic (STL), which is a linear-time logic over real-valued signals that possess quantitative semantics and…