Power of the Spacing test for Least-Angle Regression

Recent advances in Post-Selection Inference have shown that conditional testing is relevant and tractable in high-dimensions. In the Gaussian linear model, further works have derived unconditional test statistics such as the Kac-Rice Pivot for general penalized problems. In order to test the global null, a prominent offspring of this breakthrough is the spacing test that accounts the relative separation between the first two knots of the celebrated least-angle regression (LARS) algorithm. However, no results have been shown regarding the distribution of these test statistics under the alternative. For the first time, this paper addresses this important issue for the spacing test and shows that it is unconditionally unbiased. Furthermore, we provide the first extension of the spacing test to the frame of unknown noise variance. More precisely, we investigate the power of the spacing test for LARS and prove that it is unbiased: its power is always greater or equal to the significance level $\alpha$. In particular, we describe the power of this test under various scenarii: we prove that its rejection region is optimal when the predictors are orthogonal; as the level $\alpha$ goes to zero, we show that the probability of getting a true positive is much greater than $\alpha$; and we give a detailed description of its power in the case of two predictors. Moreover, we numerically investigate a comparison between the spacing test for LARS and the Pearson's chi-squared test (goodness of fit).Comment: 22 pages, 8 figure

Linear diffusion with singular absorption potential and/or unbounded convective flow: the weighted space approach

In this paper we prove the existence and uniqueness of very weak solutions to linear diffusion equations involving a singular absorption potential and/or an unbounded convective flow on a bounded open set of $\mathbb R^N$. In most of the paper we consider homogeneous Dirichlet boundary conditions but we prove that when the potential function grows faster than the distance to the boundary to the power -2 then no boundary condition is required to get the uniqueness of very weak solutions. This result is new in the literature and must be distinguished from other previous results in which such uniqueness of solutions without any boundary condition was proved for degenerate diffusion operators (which is not our case). Our approach, based on the treatment on some distance to the boundary weighted spaces, uses a suitable regularity of the solution of the associated dual problem which is here established. We also consider the delicate question of the differentiability of the very weak solution and prove that some suitable additional hypothesis on the data is required since otherwise the gradient of the solution may not be integrable on the domain

Conscientiously Creating Content: AI-Powered Social Media Strategies for Promoting Digital Collections

As cultural institutions continue to digitize their collections and make them available online, social media platforms offer a promising method for promoting and providing access to these digital archives. By incorporating Artificial Intelligence (AI), it is possible to create engaging and accessible content that can reach a wider, measurable audience. However, concerns about bias, inaccurate information and ethical considerations abound and must be considered. In this presentation, we will explore the evolution of practices in incorporating AI into digital archive work at the Digital Collections Center at Florida International University Libraries to extend into social media content. We will examine the potential of social media platforms for promoting and providing access to partner collections in the digital repository. We will also address the ethical considerations of using AI in creating social media content and discuss the question of whether this is a worthwhile endeavor. Attendees will gain a deeper understanding of the potential of AI-generated social media content (using platforms such as ChatGPT) as a means of access to digital archives, as well as practical insights into the considerations that should be taken into account. By showcasing the successes and challenges of using AI in social media content creation and promotion, we hope to inspire discussion and critical thinking about the role of social media and AI in promoting access to digitized collection materials

Underwater acoustic slant range measurements related to weather and sea state

Underwater range measurements are key factor in underwater acoustic positioning, used in Long Base-Line (LBL) or Ultra Short Base-Line (USBL) computing techniques. These measurements are commonly carried out through acoustic communications between modems and their accuracy can be affected by different factors, such as sea state, weather conditions, and obstacles in the line of sight propagation. This is especially important in shallow waters areas, where others phenomena such as multi-path have to be considered. Therefore, range accuracy and the associated position estimation errors are an important area of research. Here, we addressed the relation between range measurements variability and sea state (i.e. currents or waves height) as proxy of real-world conditions, affecting acoustic positioning performances. For that purpose, a long-term deployment have been carried out in the underwater cabled observatory OBSEA, which provide different measurements of the sea and weather state.Peer ReviewedPostprint (published version

Validation of Experts versus Atlas-based and Automatic Registration Methods for Subthalamic Nucleus Targeting on MRI

Objects In functional stereotactic neurosurgery, one of the cornerstones upon which the success and the operating time depends is an accurate targeting. The subthalamic nucleus (STN) is the usual target involved when applying deep brain stimulation for Parkinson's disease (PD). Unfortunately, STN is usually not clearly visible in common medical imaging modalities, which justifies the use of atlas-based segmentation techniques to infer the STN location. Materials and methods Eight bilaterally implanted PD patients were included in this study. A three-dimensional T1-weighted sequence and inversion recovery T2-weighted coronal slices were acquired pre-operatively. We propose a methodology for the construction of a ground truth of the STN location and a scheme that allows both, to perform a comparison between different non-rigid registration algorithms and to evaluate their usability to locate the STN automatically. Results The intra-expert variability in identifying the STN location is 1.06±0.61mm while the best non-rigid registration method gives an error of 1.80±0.62mm. On the other hand, statistical tests show that an affine registration with only 12 degrees of freedom is not enough for this application. Conclusions Using our validation-evaluation scheme, we demonstrate that automatic STN localization is possible and accurate with non-rigid registration algorithm