We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints, including the "classical" case of changes in the mean, and even changes in the whole distribution. Our statistics are based on a generalisation of the empirical energy distance; we propose weighted functionals of the energy distance process, which are designed in order to enhance the ability to detect breaks occurring at sample endpoints. The limiting distribution of the maximally selected version of our statistics requires only the computation of the eigenvalues of the covariance function, thus being readily implementable in the most commonly employed packages, e.g. R. We show that, under the alternative, our statistics are able to detect changepoints occurring even very close to the beginning/end of the sample. In the presence of multiple changepoints, we propose a binary segmentation algorithm to estimate the number of breaks and the locations thereof. Simulations show that our procedures work very well in finite samples. We complement our theory with applications to financial and temperature data.
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We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly logconcave data distributions while our approximating class of functions used for score estimation is made of Lipschitz continuous functions. We demonstrate via a motivating example, sampling from a Gaussian distribution with unknown mean, the powerfulness of our approach. In this case, explicit estimates are provided for the associated optimization problem, i.e. score approximation, while these are combined with the corresponding sampling estimates. As a result, we obtain the best known upper bound estimates in terms of key quantities of interest, such as the dimension and rates of convergence, for the Wasserstein-2 distance between the data distribution (Gaussian with unknown mean) and our sampling algorithm. Beyond the motivating example and in order to allow for the use of a diverse range of stochastic optimizers, we present our results using an $L^2$-accurate score estimation assumption, which crucially is formed under an expectation with respect to the stochastic optimizer and our novel auxiliary process that uses only known information. This approach yields the best known convergence rate for our sampling algorithm.
Mediation analysis assesses the extent to which the exposure affects the outcome indirectly through a mediator and the extent to which it operates directly through other pathways. As the most popular method in empirical mediation analysis, the Baron-Kenny approach estimates the indirect and direct effects of the exposure on the outcome based on linear structural equation models. However, when the exposure and the mediator are not randomized, the estimates may be biased due to unmeasured confounding among the exposure, mediator, and outcome. Building on Cinelli and Hazlett (2020), we derive general omitted-variable bias formulas in linear regressions with vector responses and regressors. We then use the formulas to develop a sensitivity analysis method for the Baron-Kenny approach to mediation in the presence of unmeasured confounding. To ensure interpretability, we express the sensitivity parameters to correspond to the natural factorization of the joint distribution of the direct acyclic graph for mediation analysis. They measure the partial correlation between the unmeasured confounder and the exposure, mediator, outcome, respectively. With the sensitivity parameters, we propose a novel measure called the "robustness value for mediation" or simply the "robustness value", to assess the robustness of results based on the Baron-Kenny approach with respect to unmeasured confounding. Intuitively, the robustness value measures the minimum value of the maximum proportion of variability explained by the unmeasured confounding, for the exposure, mediator and outcome, to overturn the results of the point estimate or confidence interval for the direct and indirect effects. Importantly, we prove that all our sensitivity bounds are attainable and thus sharp.
We consider the task of estimating functions belonging to a specific class of nonsmooth functions, namely so-called tame functions. These functions appear in a wide range of applications: training deep learning, value functions of mixed-integer programs, or wave functions of small molecules. We show that tame functions are approximable by piecewise polynomials on any full-dimensional cube. We then present the first ever mixed-integer programming formulation of piecewise polynomial regression. Together, these can be used to estimate tame functions. We demonstrate promising computational results.
A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad-Shafranov equation by using Physics-Informed Neural Networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the PDE as a loss function. We show that PINNs can accurately and effectively solve the Grad-Shafranov equation with several different boundary conditions. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various trade-offs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parametrized PINNs could be used in future work to solve inverse problems such as shape optimization.
Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few different ways, discussed in the pertaining literature. The present contribution proposes a different way of tackling this problem, by constructing a numeric variable in an alternative way with respect to the current methodology. The proposed techniques appears to retain the data fitting capability of the existing methodology, but with a simpler interpretation of the model components.
Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. $\overline{X|Y}$ as random variable containing information from $X$, but with removed information about $Y$, by using $(x,y) \leftrightarrow (\bar{x}=\textrm{CDF}_{X|Y=y}(x),y)$ reversible normalization. One application can be decoupling of individual information of variables: reversibly transform $(X_1,\ldots,X_n)\leftrightarrow(\tilde{X}_1,\ldots \tilde{X}_n)$ together containing the same information, but being independent: $\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$. It requires detailed models of complex conditional probability distributions - it is generally a difficult task, but here can be done through multiple dependency reducing iterations, using imperfect methods (here HCR: Hierarchical Correlation Reconstruction). It could be also used for direct mutual information - evaluating direct information transfer: without use of intermediate variables. For causality direction there is discussed multi-feature Granger causality, e.g. to trace various types of individual information transfers between such decoupled variables, including propagation time (delay).
Navigating the challenges of data-driven speech processing, one of the primary hurdles is accessing reliable pathological speech data. While public datasets appear to offer solutions, they come with inherent risks of potential unintended exposure of patient health information via re-identification attacks. Using a comprehensive real-world pathological speech corpus, with over n=3,800 test subjects spanning various age groups and speech disorders, we employed a deep-learning-driven automatic speaker verification (ASV) approach. This resulted in a notable mean equal error rate (EER) of 0.89% with a standard deviation of 0.06%, outstripping traditional benchmarks. Our comprehensive assessments demonstrate that pathological speech overall faces heightened privacy breach risks compared to healthy speech. Specifically, adults with dysphonia are at heightened re-identification risks, whereas conditions like dysarthria yield results comparable to those of healthy speakers. Crucially, speech intelligibility does not influence the ASV system's performance metrics. In pediatric cases, particularly those with cleft lip and palate, the recording environment plays a decisive role in re-identification. Merging data across pathological types led to a marked EER decrease, suggesting the potential benefits of pathological diversity in ASV, accompanied by a logarithmic boost in ASV effectiveness. In essence, this research sheds light on the dynamics between pathological speech and speaker verification, emphasizing its crucial role in safeguarding patient confidentiality in our increasingly digitized healthcare era.
We give a fully polynomial-time randomized approximation scheme (FPRAS) for two terminal reliability in directed acyclic graphs.
We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large variety in the robotic landscape is considered. If we can learn the correspondences between the sensorimotor spaces of different robots, we can expect a skill that is learned in one robot can be more directly and easily transferred to other robots. In this paper, we propose a method to learn correspondences among two or more robots that may have different morphologies. To be specific, besides robots with similar morphologies with different degrees of freedom, we show that a fixed-based manipulator robot with joint control and a differential drive mobile robot can be addressed within the proposed framework. To set up the correspondence among the robots considered, an initial base task is demonstrated to the robots to achieve the same goal. Then, a common latent representation is learned along with the individual robot policies for achieving the goal. After the initial learning stage, the observation of a new task execution by one robot becomes sufficient to generate a latent space representation pertaining to the other robots to achieve the same task. We verified our system in a set of experiments where the correspondence between robots is learned (1) when the robots need to follow the same paths to achieve the same task, (2) when the robots need to follow different trajectories to achieve the same task, and (3) when complexities of the required sensorimotor trajectories are different for the robots. We also provide a proof-of-the-concept realization of correspondence learning between a real manipulator robot and a simulated mobile robot.
Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.
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