A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al. (2008), which is based on an approach by Woolfe et al. (2008). Using tools from non-asymptotic random matrix theory, we provide the first theoretical guarantees characterizing the error between the output of the double sketch algorithm and the ground truth low-rank matrix. We apply our result to the problems of low-rank matrix approximation and low-tubal-rank tensor recovery.
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A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs.
In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference approximations of the derivatives. We use a special adaptive search procedure in our algorithms, which simultaneously fits both the regularization constant and the parameters of the finite difference approximations. It makes our schemes free from the need to know the actual Lipschitz constants. Additionally, we equip our algorithms with the lazy Hessian update that reuse a previously computed Hessian approximation matrix for several iterations. Specifically, we prove the global complexity bound of $\mathcal{O}( n^{1/2} \epsilon^{-3/2})$ function and gradient evaluations for our new Hessian-free method, and a bound of $\mathcal{O}( n^{3/2} \epsilon^{-3/2} )$ function evaluations for the derivative-free method, where $n$ is the dimension of the problem and $\epsilon$ is the desired accuracy for the gradient norm. These complexity bounds significantly improve the previously known ones in terms of the joint dependence on $n$ and $\epsilon$, for the first-order and zeroth-order non-convex optimization.
Previous researchers conducting Just-In-Time (JIT) defect prediction tasks have primarily focused on the performance of individual pre-trained models, without exploring the relationship between different pre-trained models as backbones. In this study, we build six models: RoBERTaJIT, CodeBERTJIT, BARTJIT, PLBARTJIT, GPT2JIT, and CodeGPTJIT, each with a distinct pre-trained model as its backbone. We systematically explore the differences and connections between these models. Specifically, we investigate the performance of the models when using Commit code and Commit message as inputs, as well as the relationship between training efficiency and model distribution among these six models. Additionally, we conduct an ablation experiment to explore the sensitivity of each model to inputs. Furthermore, we investigate how the models perform in zero-shot and few-shot scenarios. Our findings indicate that each model based on different backbones shows improvements, and when the backbone's pre-training model is similar, the training resources that need to be consumed are much more closer. We also observe that Commit code plays a significant role in defect detection, and different pre-trained models demonstrate better defect detection ability with a balanced dataset under few-shot scenarios. These results provide new insights for optimizing JIT defect prediction tasks using pre-trained models and highlight the factors that require more attention when constructing such models. Additionally, CodeGPTJIT and GPT2JIT achieved better performance than DeepJIT and CC2Vec on the two datasets respectively under 2000 training samples. These findings emphasize the effectiveness of transformer-based pre-trained models in JIT defect prediction tasks, especially in scenarios with limited training data.
Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods
In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.
In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset.
The non-identifiability of the competing risks model requires researchers to work with restrictions on the model to obtain informative results. We present a new identifiability solution based on an exclusion restriction. Many areas of applied research use methods that rely on exclusion restrcitions. It appears natural to also use them for the identifiability of competing risks models. By imposing the exclusion restriction couple with an Archimedean copula, we are able to avoid any parametric restriction on the marginal distributions. We introduce a semiparametric estimation approach for the nonparametric marginals and the parametric copula. Our simulation results demonstrate the usefulness of the suggested model, as the degree of risk dependence can be estimated without parametric restrictions on the marginal distributions.
In this work, we present an experimental setup and guide to enable the perching of large flapping-wing robots. The combination of forward flight, limited payload, and flight oscillations imposes challenging conditions for localized perching. The described method details the different operations that are concurrently performed within the 4 second perching flight. We validate this experiment with a 700 g ornithopter and demonstrate the first autonomous perching flight of a flapping-wing robot on a branch. This work paves the way towards the application of flapping-wing robots for long-range missions, bird observation, manipulation, and outdoor flight.
Speech emotion recognition (SER) often experiences reduced performance due to background noise. In addition, making a prediction on signals with only background noise could undermine user trust in the system. In this study, we propose a Noise Robust Speech Emotion Recognition system, NRSER. NRSER employs speech enhancement (SE) to effectively reduce the noise in input signals. Then, the signal-to-noise-ratio (SNR)-level detection structure and waveform reconstitution strategy are introduced to reduce the negative impact of SE on speech signals with no or little background noise. Our experimental results show that NRSER can effectively improve the noise robustness of the SER system, including preventing the system from making emotion recognition on signals consisting solely of background noise. Moreover, the proposed SNR-level detection structure can be used individually for tasks such as data selection.
We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good guarantees) or for theoretical purposes (e.g., to reveal that the landscape satisfies a strict saddle property). In both cases, the central question is: how do the landscapes of the two problems relate? More precisely: how do desirable points such as local minima and critical points in one problem relate to those in the other problem? A key finding in this paper is that these relations are often determined by the parametrization itself, and are almost entirely independent of the cost function. Accordingly, we introduce a general framework to study parametrizations by their effect on landscapes. The framework enables us to obtain new guarantees for an array of problems, some of which were previously treated on a case-by-case basis in the literature. Applications include: optimizing low-rank matrices and tensors through factorizations; solving semidefinite programs via the Burer-Monteiro approach; training neural networks by optimizing their weights and biases; and quotienting out symmetries.
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification.
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