arXiv subjects

Arash Amini

Publications and source records attributed to Arash Amini.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantification of Distributionally Robust Risk of Cascade of Failures in Platoon of Vehicles

Achieving safety is a critical aspect of attaining autonomy in a platoon of autonomous vehicles. In this paper, we propose a distributionally robust risk framework to investigate cascading failures in platoons. To examine the impact of network connectivity and system dynamics on the emergence of cascading failures, we consider a time-delayed network model of the platoon of vehicles as a benchmark. To study the cascading effects among pairs of vehicles in the platoon, we use the measure of conditional distributionally robust functional. We extend the risk framework to quantify cascading failures by utilizing a bi-variate normal distribution. Our work establishes closed-form risk formulas that illustrate the effects of time-delay, noise statistics, underlying communication graph, and sets of soft failures. The insights gained from our research can be applied to design safe platoons that are robust to the risk of cascading failures. We validate our results through extensive simulations.

eess.SY↗

arXiv2023

YOLOPose V2: Understanding and Improving Transformer-based 6D Pose Estimation

6D object pose estimation is a crucial prerequisite for autonomous robot manipulation applications. The state-of-the-art models for pose estimation are convolutional neural network (CNN)-based. Lately, Transformers, an architecture originally proposed for natural language processing, is achieving state-of-the-art results in many computer vision tasks as well. Equipped with the multi-head self-attention mechanism, Transformers enable simple single-stage end-to-end architectures for learning object detection and 6D object pose estimation jointly. In this work, we propose YOLOPose (short form for You Only Look Once Pose estimation), a Transformer-based multi-object 6D pose estimation method based on keypoint regression and an improved variant of the YOLOPose model. In contrast to the standard heatmaps for predicting keypoints in an image, we directly regress the keypoints. Additionally, we employ a learnable orientation estimation module to predict the orientation from the keypoints. Along with a separate translation estimation module, our model is end-to-end differentiable. Our method is suitable for real-time applications and achieves results comparable to state-of-the-art methods. We analyze the role of object queries in our architecture and reveal that the object queries specialize in detecting objects in specific image regions. Furthermore, we quantify the accuracy trade-off of using datasets of smaller sizes to train our model.

cs.CV↗

arXiv2023

Bayesian community detection for networks with covariates

The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and algorithms. Among the various learning tasks with network data, community detection, the discovery of node clusters or "communities," has arguably received the most attention in the scientific community. In many real-world applications, the network data often come with additional information in the form of node or edge covariates that should ideally be leveraged for inference. In this paper, we add to a limited literature on community detection for networks with covariates by proposing a Bayesian stochastic block model with a covariate-dependent random partition prior. Under our prior, the covariates are explicitly expressed in specifying the prior distribution on the cluster membership. Our model has the flexibility of modeling uncertainties of all the parameter estimates including the community membership. Importantly, and unlike the majority of existing methods, our model has the ability to learn the number of the communities via posterior inference without having to assume it to be known. Our model can be applied to community detection in both dense and sparse networks, with both categorical and continuous covariates, and our MCMC algorithm is very efficient with good mixing properties. We demonstrate the superior performance of our model over existing models in a comprehensive simulation study and an application to two real datasets.

stat.ME↗

arXiv2023

RoboCup 2022 AdultSize Winner NimbRo: Upgraded Perception, Capture Steps Gait and Phase-based In-walk Kicks

Beating the human world champions by 2050 is an ambitious goal of the Humanoid League that provides a strong incentive for RoboCup teams to further improve and develop their systems. In this paper, we present upgrades of our system which enabled our team NimbRo to win the Soccer Tournament, the Drop-in Games, and the Technical Challenges in the Humanoid AdultSize League of RoboCup 2022. Strong performance in these competitions resulted in the Best Humanoid award in the Humanoid League. The mentioned upgrades include: hardware upgrade of the vision module, balanced walking with Capture Steps, and the introduction of phase-based in-walk kicks.

cs.RO↗

arXiv2022

Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectory

We consider a class of stochastic dynamical networks whose governing dynamics can be modeled using a coupling function. It is shown that the dynamics of such networks can generate geometrically ergodic trajectories under some reasonable assumptions. We show that a general class of coupling functions can be learned using only one sample trajectory from the network. This is practically plausible as in numerous applications it is desired to run an experiment only once but for a longer period of time, rather than repeating the same experiment multiple times from different initial conditions. Building upon ideas from the concentration inequalities for geometrically ergodic Markov chains, we formulate several results about the convergence of the empirical estimator to the true coupling function. Our theoretical findings are supported by extensive simulation results.

eess.SY↗

arXiv2022

Carleman Linearization of Nonlinear Systems and Its Finite-Section Approximations

The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original nonlinear system over larger regions around the equilibrium for longer time horizons with respect to the conventional first-order linearization approach. Finite-section approximations of the lifted system has been widely used to study dynamical and control properties of the original nonlinear system. In this context, some of the outstanding problems are to determine under what conditions, as the finite-section order (i.e., truncation length) increases, the trajectory of the resulting approximate linear system from the finite-section scheme converges to that of the original nonlinear system and whether the time interval over which the convergence happens can be quantified explicitly. In this paper, we provide explicit error bounds for the finite-section approximation and prove that the convergence is indeed exponential with respect to the finite-section order. For a class of nonlinear systems, it is shown that one can achieve exponential convergence over the entire time horizon up to infinity. Our results are practically plausible as our proposed error bound estimates can be used to compute proper truncation lengths for a given application, e.g., determining proper sampling period for model predictive control and reachability analysis for safety verifications. We validate our theoretical findings through several illustrative simulations.

math.DS↗

arXiv2022

Complex-Order Scale-Invariant Operators and Self-Similar Processes

Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also belong to this family. In this paper, we extend the fractional operators to complex-order operators by constructing them in the Fourier domain. We analyze these operators in details with a special emphasis on the decay properties of the outputs. We further use these operators to introduce a family of complex-valued stable processes that are self-similar with complex-valued Hurst indices. These processes are expressed via the characteristic functionals over the Schwartz space of functions. Besides the self-similarity and stationarity, we study the regularity (in terms of Sobolev spaces) of the proposed processes.

math.FA↗

arXiv2022

YOLOPose: Transformer-based Multi-Object 6D Pose Estimation using Keypoint Regression

6D object pose estimation is a crucial prerequisite for autonomous robot manipulation applications. The state-of-the-art models for pose estimation are convolutional neural network (CNN)-based. Lately, Transformers, an architecture originally proposed for natural language processing, is achieving state-of-the-art results in many computer vision tasks as well. Equipped with the multi-head self-attention mechanism, Transformers enable simple single-stage end-to-end architectures for learning object detection and 6D object pose estimation jointly. In this work, we propose YOLOPose (short form for You Only Look Once Pose estimation), a Transformer-based multi-object 6D pose estimation method based on keypoint regression. In contrast to the standard heatmaps for predicting keypoints in an image, we directly regress the keypoints. Additionally, we employ a learnable orientation estimation module to predict the orientation from the keypoints. Along with a separate translation estimation module, our model is end-to-end differentiable. Our method is suitable for real-time applications and achieves results comparable to state-of-the-art methods.

cs.CV↗

arXiv2022

Robustness Analysis of Classification Using Recurrent Neural Networks with Perturbed Sequential Input

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be perturbed in various ways, e.g., streaming images can be deformed due to robot motion or imperfect camera lens. Using the notion of the Voronoi diagram and Lipschitz properties of stable RNNs, we provide a thorough analysis and characterize the maximum allowable perturbations while guaranteeing the full accuracy of the classification task. We illustrate and validate our theoretical results using a map dataset with clouds as well as the MNIST dataset.

cs.LG↗

arXiv2022

Compressibility Measures for Affinely Singular Random Vectors

There are several ways to measure the compressibility of a random measure; they include general approaches such as using the rate-distortion curve, as well as more specific notions, such as the Renyi information dimension (RID). The RID parameter indicates the concentration of the measure around lower-dimensional subsets of the space. While the evaluation of such compressibility parameters is well-studied for continuous and discrete measures, the case of discrete-continuous measures is quite subtle. In this paper, we focus on a class of multi-dimensional random measures that have singularities on affine lower-dimensional subsets. This class of distributions naturally arises when considering linear transformation of component-wise independent discrete-continuous random variables. To measure the compressibility of such distributions, we introduce the new notion of dimensional-rate bias (DRB) which is closely related to the entropy and differential entropy in discrete and continuous cases, respectively. Similar to entropy and differential entropy, DRB is useful in evaluating the mutual information between distributions of the aforementioned type. Besides the DRB, we also evaluate the the RID of these distributions. We further provide an upper-bound for the RID of multi-dimensional random measures that are obtained by Lipschitz functions of component-wise independent discrete-continuous random variables ($\mathbf{X}$). The upper-bound is shown to be achievable when the Lipschitz function is $A \mathbf{X}$, where $A$ satisfies {\changed$\spark({A_{m\times n}}) = m+1$} (e.g., Vandermonde matrices). When considering discrete-domain moving-average processes with non-Gaussian excitation noise, the above results allow us to evaluate the block-average RID and DRB, as well as to determine a relationship between these parameters and other existing compressibility measures.

cs.IT↗

arXiv2022

Two-snapshot DOA Estimation via Hankel-structured Matrix Completion

In this paper, we study the problem of estimating the direction of arrival (DOA) using a sparsely sampled uniform linear array (ULA). Based on an initial incomplete ULA measurement, our strategy is to choose a sparse subset of array elements for measuring the next snapshot. Then, we use a Hankel-structured matrix completion to interpolate for the missing ULA measurements. Finally, the source DOAs are estimated using a subspace method such as Prony on the fully recovered ULA. We theoretically provide a sufficient bound for the number of required samples (array elements) for perfect recovery. The numerical comparisons of the proposed method with existing techniques such as atomic-norm minimization and off-the-grid approaches confirm the superiority of the proposed method.

eess.SP↗

arXiv2021

T6D-Direct: Transformers for Multi-Object 6D Pose Direct Regression

6D pose estimation is the task of predicting the translation and orientation of objects in a given input image, which is a crucial prerequisite for many robotics and augmented reality applications. Lately, the Transformer Network architecture, equipped with a multi-head self-attention mechanism, is emerging to achieve state-of-the-art results in many computer vision tasks. DETR, a Transformer-based model, formulated object detection as a set prediction problem and achieved impressive results without standard components like region of interest pooling, non-maximal suppression, and bounding box proposals. In this work, we propose T6D-Direct, a real-time single-stage direct method with a transformer-based architecture built on DETR to perform 6D multi-object pose direct estimation. We evaluate the performance of our method on the YCB-Video dataset. Our method achieves the fastest inference time, and the pose estimation accuracy is comparable to state-of-the-art methods.

cs.CV↗

arXiv2021

Real-time Pose Estimation from Images for Multiple Humanoid Robots

Pose estimation commonly refers to computer vision methods that recognize people's body postures in images or videos. With recent advancements in deep learning, we now have compelling models to tackle the problem in real-time. Since these models are usually designed for human images, one needs to adapt existing models to work on other creatures, including robots. This paper examines different state-of-the-art pose estimation models and proposes a lightweight model that can work in real-time on humanoid robots in the RoboCup Humanoid League environment. Additionally, we present a novel dataset called the HumanoidRobotPose dataset. The results of this work have the potential to enable many advanced behaviors for soccer-playing robots.

cs.RO↗

arXiv2021

Robust Learning of Recurrent Neural Networks in Presence of Exogenous Noise

Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture of RNNs exacerbates the problem. In this paper, we will use ideas from control and estimation theories to propose a tractable robustness analysis for RNN models that are subject to input noise. The variance of the output of the noisy system is adopted as a robustness measure to quantify the impact of noise on learning. It is shown that the robustness measure can be estimated efficiently using linearization techniques. Using these results, we proposed a learning method to enhance robustness of a RNN with respect to exogenous Gaussian noise with known statistics. Our extensive simulations on benchmark problems reveal that our proposed methodology significantly improves robustness of recurrent neural networks.

cs.LG↗

arXiv2021

Distributed Map Classification using Local Observations

We consider the problem of classifying a map using a team of communicating robots. It is assumed that all robots have localized visual sensing capabilities and can exchange their information with neighboring robots. Using a graph decomposition technique, we proposed an offline learning structure that makes every robot capable of communicating with and fusing information from its neighbors to plan its next move towards the most informative parts of the environment for map classification purposes. The main idea is to decompose a given undirected graph into a union of directed star graphs and train robots w.r.t a bounded number of star graphs. This will significantly reduce the computational cost of offline training and makes learning scalable (independent of the number of robots). Our approach is particularly useful for fast map classification in large environments using a large number of communicating robots. We validate the usefulness of our proposed methodology through extensive simulations.

cs.RO↗

arXiv2019

Living near the edge: A lower-bound on the phase transition of total variation minimization

This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on this threshold in case of any random measurement matrix whose null space is distributed uniformly with respect to the Haar measure. In contrast to the conventional TV phase transition results that depend on the simple gradient-sparsity level, our bound is highly affected by generalized notions of gradient-sparsity. Our proposed bound is very close to the true phase transition of TV minimization confirmed by simulation results.

cs.IT↗

arXiv2019

Exploiting Prior Information in Block Sparse Signals

We study the problem of recovering a block-sparse signal from under-sampled observations. The non-zero values of such signals appear in few blocks, and their recovery is often accomplished using a $\ell_{1,2}$ optimization problem. In applications such as DNA micro-arrays, some prior information about the block support, i.e., blocks containing non-zero elements, is available. A typical way to consider the extra information in recovery procedures is to solve a weighted $\ell_{1,2}$ problem. In this paper, we consider a block sparse model, where the block support has intersection with some given subsets of blocks with known probabilities. Our goal in this work is to minimize the number of required linear Gaussian measurements for perfect recovery of the signal by tuning the weights of a weighted $\ell_{1,2}$ problem. For this goal, we apply tools from conic integral geometry and derive closed-form expressions for the optimal weights. We show through precise analysis and simulations that the weighted $\ell_{1,2}$ problem with optimal weights significantly outperforms the regular $\ell_{1,2}$ problem. We further examine the sensitivity of the optimal weights to the mismatch of block probabilities, and conclude stability under small probability deviations.

cs.IT↗

arXiv2019

On the Error in Phase Transition Computations for Compressed Sensing

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. To ensure that this technique is suitable, [1] has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in [1] in some low-dimensional models such as total variation and $\ell_1$ analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap compared to [1]. In particular, unlike the bound in [1] that is not applicable to settings with overcomplete dictionaries, our bound exhibits a decaying behavior in such cases.

cs.IT↗