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In this paper, we introduce two robust, nonparametric methods for multiple change-point detection in the variability of a multivariate sequence of observations. We demonstrate that changes in ranks generated from data depth functions can be used to detect changes in the variability of a sequence of multivariate observations. In order to detect more than one change, the first algorithm uses methods similar to that of wild-binary segmentation. The second algorithm estimates change-points by maximizing a penalized version of the classical Kruskal Wallis ANOVA test statistic. We show that this objective function can be maximized via the well-known PELT algorithm. Under mild, nonparametric assumptions both of these algorithms are shown to be consistent for the correct number of change-points and the correct location(s) of the change-point(s). We demonstrate the efficacy of these methods with a simulation study, where we compare our new methods to several competing methods. We show our methods outperform existing methods in this problem setting, and our methods can estimate changes accurately when the data are heavy tailed or skewed.

Precision medicine is a clinical approach for disease prevention, detection and treatment, which considers each individual's genetic background, environment and lifestyle. The development of this tailored avenue has been driven by the increased availability of omics methods, large cohorts of temporal samples, and their integration with clinical data. Despite the immense progression, existing computational methods for data analysis fail to provide appropriate solutions for this complex, high-dimensional and longitudinal data. In this work we have developed a new method termed TCAM, a dimensionality reduction technique for multi-way data, that overcomes major limitations when doing trajectory analysis of longitudinal omics data. Using real-world data, we show that TCAM outperforms traditional methods, as well as state-of-the-art tensor-based approaches for longitudinal microbiome data analysis. Moreover, we demonstrate the versatility of TCAM by applying it to several different omics datasets, and the applicability of it as a drop-in replacement within straightforward ML tasks.

This paper studies an intelligent reflecting surface (IRS)-aided multiple-input-multiple-output (MIMO) full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) operating in FD broadcasts energy signals to multiple devices for their energy harvesting (EH) in the downlink (DL) and meanwhile receives information signals from devices in the uplink (UL) with the help of an IRS. Taking into account the practical finite self-interference (SI) and the non-linear EH model, we formulate the weighted sum throughput maximization optimization problem by jointly optimizing DL/UL time allocation, precoding matrices at devices, transmit covariance matrices at the HAP, and phase shifts at the IRS. Since the resulting optimization problem is non-convex, there are no standard methods to solve it optimally in general. To tackle this challenge, we first propose an element-wise (EW) based algorithm, where each IRS phase shift is alternately optimized in an iterative manner. To reduce the computational complexity, a minimum mean-square error (MMSE) based algorithm is proposed, where we transform the original problem into an equivalent form based on the MMSE method, which facilities the design of an efficient iterative algorithm. In particular, the IRS phase shift optimization problem is recast as an second-order cone program (SOCP), where all the IRS phase shifts are simultaneously optimized. For comparison, we also study two suboptimal IRS beamforming configurations in simulations, namely partially dynamic IRS beamforming (PDBF) and static IRS beamforming (SBF), which strike a balance between the system performance and practical complexity.

Sparse Conditional Random Field (CRF) is a powerful technique in computer vision and natural language processing for structured prediction. However, solving sparse CRFs in large-scale applications remains challenging. In this paper, we propose a novel safe dynamic screening method that exploits an accurate dual optimum estimation to identify and remove the irrelevant features during the training process. Thus, the problem size can be reduced continuously, leading to great savings in the computational cost without sacrificing any accuracy on the finally learned model. To the best of our knowledge, this is the first screening method which introduces the dual optimum estimation technique -- by carefully exploring and exploiting the strong convexity and the complex structure of the dual problem -- in static screening methods to dynamic screening. In this way, we can absorb the advantages of both the static and dynamic screening methods and avoid their drawbacks. Our estimation would be much more accurate than those developed based on the duality gap, which contributes to a much stronger screening rule. Moreover, our method is also the first screening method in sparse CRFs and even structure prediction models. Experimental results on both synthetic and real-world datasets demonstrate that the speedup gained by our method is significant.

We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Model reduction offers a variety of computational tools that seek to reduce this computational burden. In particular, balanced truncation is a system-theoretic approach to model reduction which obtains an efficient reduced-dimension dynamical system by projecting the system operators onto state directions which trade off the reachability and observability of state directions as expressed through the associated Gramians. We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance. Our definitions exploit natural connections between (i) the reachability Gramian and the prior covariance and (ii) the observability Gramian and the Fisher information. The resulting reduced model then inherits stability properties and error bounds from system theoretic considerations, and in some settings yields an optimal posterior covariance approximation. Numerical demonstrations on two benchmark problems in model reduction show that our method can yield near-optimal posterior covariance approximations with order-of-magnitude state dimension reduction.

We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases like $\exp(-cN/\log(N))$ for $N$ quadrature points. The method is parallisable, avoids having to resolve singularities of the solution as $t\downarrow 0$, and avoids the large memory consumption that can be a challenge for time-stepping methods applied to time-fractional PDEs. The ODEs resulting from quadrature are solved using adaptive sparse spectral methods that converge exponentially with optimal linear complexity. These solutions of ODEs are reused for different times. We provide a complete analysis of our approach for fractional beam equations used to model small-amplitude vibration of viscoelastic materials with a fractional Kelvin-Voigt stress-strain relationship. We calculate the system's energy evolution over time and the surface deformation in cases of both constant and non-constant viscoelastic parameters. An infinite-dimensional ``solve-then-discretise'' approach considerably simplifies the analysis, which studies the generalisation of the numerical range of a quasi-linearisation of a suitable operator pencil. This allows us to build an efficient algorithm with explicit error control. The approach can be readily adapted to other time-fractional PDEs and is not constrained to fractional parameters in the range $0<\nu<1$.

Satellite networks are promising to provide ubiquitous and high-capacity global wireless connectivity. Traditionally, satellite networks are modeled by placing satellites on a grid of multiple circular orbit geometries. Such a network model, however, requires intricate system-level simulations to evaluate coverage performance, and analytical understanding of the satellite network is limited. Continuing the success of stochastic geometry in a tractable analysis for terrestrial networks, in this paper, we develop novel models that are tractable for the coverage analysis of satellite networks using stochastic geometry. By modeling the locations of satellites and users using Poisson point processes on the surfaces of concentric spheres, we characterize analytical expressions for the coverage probability of a typical downlink user as a function of relevant parameters, including path-loss exponent, satellite height, density, and Nakagami fading parameter. Then, we also derive a tight lower bound of the coverage probability in closed-form expression while keeping full generality. Leveraging the derived expression, we identify the optimal density of satellites in terms of the height and the path-loss exponent. Our key finding is that the optimal average number of satellites decreases logarithmically with the network height to maximize the coverage performance. Simulation results verify the exactness of the derived expressions.

The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a small-scale SLAM; the joining of submaps mainly involves solving linear least squares and performing nonlinear coordinate transformations. Through approximating the local submap information as the state estimate and its corresponding information matrix, judiciously selecting the submap coordinate frames, and approximating the joining of a large number of submaps by joining only two maps at a time, either sequentially or in a more efficient Divide and Conquer manner, the nonlinear optimization process involved in most of the existing submap joining approaches is avoided. Thus the proposed submap joining algorithm does not require initial guess or iterations since linear least squares problems have closed-form solutions. The proposed Linear SLAM technique is applicable to feature-based SLAM, pose graph SLAM and D-SLAM, in both two and three dimensions, and does not require any assumption on the character of the covariance matrices. Simulations and experiments are performed to evaluate the proposed Linear SLAM algorithm. Results using publicly available datasets in 2D and 3D show that Linear SLAM produces results that are very close to the best solutions that can be obtained using full nonlinear optimization algorithm started from an accurate initial guess. The C/C++ and MATLAB source codes of Linear SLAM are available on OpenSLAM.

Simultaneous Localization And Mapping (SLAM) is a fundamental problem in mobile robotics. While point-based SLAM methods provide accurate camera localization, the generated maps lack semantic information. On the other hand, state of the art object detection methods provide rich information about entities present in the scene from a single image. This work marries the two and proposes a method for representing generic objects as quadrics which allows object detections to be seamlessly integrated in a SLAM framework. For scene coverage, additional dominant planar structures are modeled as infinite planes. Experiments show that the proposed points-planes-quadrics representation can easily incorporate Manhattan and object affordance constraints, greatly improving camera localization and leading to semantically meaningful maps. The performance of our SLAM system is demonstrated in //youtu.be/dR-rB9keF8M .

In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of the data fitting in this formulation allows for reasonable assumptions to be made about the solution that can improve the computational performance further. In particular, we employ a well known dual formulation of this problem and solve the corresponding equations in a restricted domain. We present experimental results that explore the dependence of the solution on this restriction and quantify imrovements in the computational performance. This approach can be extended to analogous methods simply and could provide an efficient alternative for problems of this type.