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This work addresses human intention identification during physical Human-Robot Interaction (pHRI) tasks to include this information in an assistive controller. To this purpose, human intention is defined as the desired trajectory that the human wants to follow over a finite rolling prediction horizon so that the robot can assist in pursuing it. This work investigates a Recurrent Neural Network (RNN), specifically, Long-Short Term Memory (LSTM) cascaded with a Fully Connected layer. In particular, we propose an iterative training procedure to adapt the model. Such an iterative procedure is powerful in reducing the prediction error. Still, it has the drawback that it is time-consuming and does not generalize to different users or different co-manipulated objects. To overcome this issue, Transfer Learning (TL) adapts the pre-trained model to new trajectories, users, and co-manipulated objects by freezing the LSTM layer and fine-tuning the last FC layer, which makes the procedure faster. Experiments show that the iterative procedure adapts the model and reduces prediction error. Experiments also show that TL adapts to different users and to the co-manipulation of a large object. Finally, to check the utility of adopting the proposed method, we compare the proposed controller enhanced by the intention prediction with the other two standard controllers of pHRI.

This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper bound for the distance between the mean and the median for general absolutely continuous distributions in R^d, and examples of specific classes of distributions for which these bounds do not depend on the ambient dimension d; (b) exponential deviation inequalities for the distance between the sample and the population versions of the geometric median, which again depend only on the trace-type quantities and not on the ambient dimension. As a corollary, we deduce improved bounds for the (geometric) median of means estimator that hold for large classes of heavy-tailed distributions. Finally, we address the error of numerical approximation, which is an important practical aspect of any statistical estimation procedure. We demonstrate that the objective function minimized by the geometric median satisfies a "local quadratic growth" condition that allows one to translate suboptimality bounds for the objective function to the corresponding bounds for the numerical approximation to the median itself, and propose a simple stopping rule applicable to any optimization method which yields explicit error guarantees. We conclude with the numerical experiments including the application to estimation of mean values of log-returns for S&P 500 data.

For a manifold embedded in an inner product space, we express geometric quantities such as {\it Hamilton vector fields, affine and Levi-Civita connections, curvature} in global coordinates. Instead of coordinate indices, the global formulas for most quantities are expressed as {\it operator-valued} expressions, using an {\it affine projection} to the tangent bundle. For a submersion image of an embedded manifold, we introduce {\it liftings} of Hamilton vector fields, allowing us to use embedded coordinates on horizontal bundles. We derive a {\it Gauss-Codazzi equation} for affine connections on vector bundles. This approach allows us to evaluate geometric expressions globally, and could be used effectively with modern numerical frameworks in applications. Examples considered include rigid body mechanics and Hamilton mechanics on Grassmann manifolds. We show explicitly the cross-curvature (MTW-tensor) for the {\it Kim-McCann} metric with a reflector antenna-type cost function on the space of positive-semidefinite matrices of fixed rank has nonnegative cross-curvature, while the corresponding cost could have negative cross-curvature on Grassmann manifolds, except for projective spaces.

Network operators and researchers frequently use Internet measurement platforms (IMPs), such as RIPE Atlas, RIPE RIS, or RouteViews for, e.g., monitoring network performance, detecting routing events, topology discovery, or route optimization. To interpret the results of their measurements and avoid pitfalls or wrong generalizations, users must understand a platform's limitations. To this end, this paper studies an important limitation of IMPs, the \textit{bias}, which exists due to the non-uniform deployment of the vantage points. Specifically, we introduce a generic framework to systematically and comprehensively quantify the multi-dimensional (e.g., across location, topology, network types, etc.) biases of IMPs. Using the framework and open datasets, we perform a detailed analysis of biases in IMPs that confirms well-known (to the domain experts) biases and sheds light on less-known or unexplored biases. To facilitate IMP users to obtain awareness of and explore bias in their measurements, as well as further research and analyses (e.g., methods for mitigating bias), we publicly share our code and data, and provide online tools (API, Web app, etc.) that calculate and visualize the bias in measurement setups.

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to be able to detect all oscillatory frequencies and the corresponding change points within an accurate range with a prescribed probability asymptotically. This study is motivated by oscillatory frequency estimation and change point detection problems encountered in physiological time series analysis. An application to spindle detection and estimation in sleep EEG data is used to illustrate the usefulness of the proposed methodology. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional non-stationary time series without variance lower bounds are established, which could be of independent interest.

In this paper, we propose new Metropolis-Hastings and simulated annealing algorithms on finite state space via modifying the energy landscape. The core idea of landscape modification rests on introducing a parameter $c$, in which the landscape is modified once the algorithm is above this threshold parameter to encourage exploration, while the original landscape is utilized when the algorithm is below the threshold for exploitation purpose. We illustrate the power and benefits of landscape modification by investigating its effect on the classical Curie-Weiss model with Glauber dynamics and external magnetic field in the subcritical regime. This leads to a landscape-modified mean-field equation, and with appropriate choice of $c$ the free energy landscape can be transformed from a double-well into a single-well, while the location of the global minimum is preserved on the modified landscape. Consequently, running algorithms on the modified landscape can improve the convergence to the ground-state in the Curie-Weiss model. In the setting of simulated annealing, we demonstrate that landscape modification can yield improved or even subexponential mean tunneling time between global minima in the low-temperature regime by appropriate choice of $c$, and give convergence guarantee using an improved logarithmic cooling schedule with reduced critical height. We also discuss connections between landscape modification and other acceleration techniques such as Catoni's energy transformation algorithm, preconditioning, importance sampling and quantum annealing. The technique developed in this paper is not only limited to simulated annealing and is broadly applicable to any difference-based discrete optimization algorithm by a change of landscape.

Casimir preserving integrators for stochastic Lie-Poisson equations with Stratonovich noise are developed extending Runge-Kutta Munthe-Kaas methods. The underlying Lie-Poisson structure is preserved along stochastic trajectories. A related stochastic differential equation on the Lie algebra is derived. The solution of this differential equation updates the evolution of the Lie-Poisson dynamics by means of the exponential map. The constructed numerical method conserves Casimir-invariants exactly, which is important for long time integration. This is illustrated numerically for the case of the stochastic heavy top and the stochastic sine-Euler equations.

Networked control systems are closed-loop feedback control systems containing system components that may be distributed geographically in different locations and interconnected via a communication network such as the Internet. The quality of network communication is a crucial factor that significantly affects the performance of remote control. This is due to the fact that network uncertainties can occur in the transmission of packets in the forward and backward channels of the system. The two most significant among these uncertainties are network time delay and packet loss. To overcome these challenges, the networked predictive control system has been proposed to provide improved performance and robustness using predictive controllers and compensation strategies. In particular, the model predictive control method is well-suited as an advanced approach compared to conventional methods. In this paper, a networked model predictive control system consisting of a model predictive control method and compensation strategies is implemented to control and stabilize a robot arm as a physical system. In particular, this work aims to analyze the performance of the system under the influence of network time delay and packet loss. Using appropriate performance and robustness metrics, an in-depth investigation of the impacts of these network uncertainties is performed. Furthermore, the forward and backward channels of the network are examined in detail in this study.

Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links, between random variables in a dynamic setting, that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel statistical independence test on data collected from time-invariant dynamical systems in which rare but consequential events occur. In particular, we exploit the time-invariance of the underlying data to construct a superimposed dataset of the system state before rare events happen at different timesteps. We then design a conditional independence test on the reorganized data. We provide non-asymptotic sample complexity bounds for the consistency of our method, and validate its performance across various simulated and real-world datasets, including incident data collected from the Caltrans Performance Measurement System (PeMS). Code containing the datasets and experiments is publicly available.

We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our first contribution is to formulate geometric perception as an optimization problem that jointly optimizes the feature descriptor and the geometric models given a large corpus of visual measurements (e.g., images, point clouds). Under this optimization formulation, we show that two important streams of research in vision, namely robust model fitting and deep feature learning, correspond to optimizing one block of the unknown variables while fixing the other block. This analysis naturally leads to our second contribution -- the SGP algorithm that performs alternating minimization to solve the joint optimization. SGP iteratively executes two meta-algorithms: a teacher that performs robust model fitting given learned features to generate geometric pseudo-labels, and a student that performs deep feature learning under noisy supervision of the pseudo-labels. As a third contribution, we apply SGP to two perception problems on large-scale real datasets, namely relative camera pose estimation on MegaDepth and point cloud registration on 3DMatch. We demonstrate that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.