Point cloud registration is an important task in robotics and autonomous driving to estimate the ego-motion of the vehicle. Recent advances following the coarse-to-fine manner show promising potential in point cloud registration. However, existing methods rely on good superpoint correspondences, which are hard to be obtained reliably and efficiently, thus resulting in less robust and accurate point cloud registration. In this paper, we propose a novel network, named RDMNet, to find dense point correspondences coarse-to-fine and improve final pose estimation based on such reliable correspondences. Our RDMNet uses a devised 3D-RoFormer mechanism to first extract distinctive superpoints and generates reliable superpoints matches between two point clouds. The proposed 3D-RoFormer fuses 3D position information into the transformer network, efficiently exploiting point clouds' contextual and geometric information to generate robust superpoint correspondences. RDMNet then propagates the sparse superpoints matches to dense point matches using the neighborhood information for accurate point cloud registration. We extensively evaluate our method on multiple datasets from different environments. The experimental results demonstrate that our method outperforms existing state-of-the-art approaches in all tested datasets with a strong generalization ability.

Contrastive learning methods have shown an impressive ability to learn meaningful representations for image or time series classification. However, these methods are less effective for time series forecasting, as optimization of instance discrimination is not directly applicable to predicting the future state from the history context. Moreover, the construction of positive and negative pairs in current technologies strongly relies on specific time series characteristics, restricting their generalization across diverse types of time series data. To address these limitations, we propose SimTS, a simple representation learning approach for improving time series forecasting by learning to predict the future from the past in the latent space. SimTS does not rely on negative pairs or specific assumptions about the characteristics of the particular time series. Our extensive experiments on several benchmark time series forecasting datasets show that SimTS achieves competitive performance compared to existing contrastive learning methods. Furthermore, we show the shortcomings of the current contrastive learning framework used for time series forecasting through a detailed ablation study. Overall, our work suggests that SimTS is a promising alternative to other contrastive learning approaches for time series forecasting.

The variety of complex algorithmic approaches for tackling time-series classification problems has grown considerably over the past decades, including the development of sophisticated but challenging-to-interpret deep-learning-based methods. But without comparison to simpler methods it can be difficult to determine when such complexity is required to obtain strong performance on a given problem. Here we evaluate the performance of an extremely simple classification approach -- a linear classifier in the space of two simple features that ignore the sequential ordering of the data: the mean and standard deviation of time-series values. Across a large repository of 128 univariate time-series classification problems, this simple distributional moment-based approach outperformed chance on 69 problems, and reached 100% accuracy on two problems. With a neuroimaging time-series case study, we find that a simple linear model based on the mean and standard deviation performs better at classifying individuals with schizophrenia than a model that additionally includes features of the time-series dynamics. Comparing the performance of simple distributional features of a time series provides important context for interpreting the performance of complex time-series classification models, which may not always be required to obtain high accuracy.

Average-K classification is an alternative to top-K classification in which the number of labels returned varies with the ambiguity of the input image but must average to K over all the samples. A simple method to solve this task is to threshold the softmax output of a model trained with the cross-entropy loss. This approach is theoretically proven to be asymptotically consistent, but it is not guaranteed to be optimal for a finite set of samples. In this paper, we propose a new loss function based on a multi-label classification head in addition to the classical softmax. This second head is trained using pseudo-labels generated by thresholding the softmax head while guaranteeing that K classes are returned on average. We show that this approach allows the model to better capture ambiguities between classes and, as a result, to return more consistent sets of possible classes. Experiments on two datasets from the literature demonstrate that our approach outperforms the softmax baseline, as well as several other loss functions more generally designed for weakly supervised multi-label classification. The gains are larger the higher the uncertainty, especially for classes with few samples.

We study the fundamental question of how to define and measure the distance from calibration for probabilistic predictors. While the notion of perfect calibration is well-understood, there is no consensus on how to quantify the distance from perfect calibration. Numerous calibration measures have been proposed in the literature, but it is unclear how they compare to each other, and many popular measures such as Expected Calibration Error (ECE) fail to satisfy basic properties like continuity. We present a rigorous framework for analyzing calibration measures, inspired by the literature on property testing. We propose a ground-truth notion of distance from calibration: the $\ell_1$ distance to the nearest perfectly calibrated predictor. We define a consistent calibration measure as one that is polynomially related to this distance. Applying our framework, we identify three calibration measures that are consistent and can be estimated efficiently: smooth calibration, interval calibration, and Laplace kernel calibration. The former two give quadratic approximations to the ground truth distance, which we show is information-theoretically optimal in a natural model for measuring calibration which we term the prediction-only access model. Our work thus establishes fundamental lower and upper bounds on measuring the distance to calibration, and also provides theoretical justification for preferring certain metrics (like Laplace kernel calibration) in practice.

We improve upon previous oblivious sketching and turnstile streaming results for $\ell_1$ and logistic regression, giving a much smaller sketching dimension achieving $O(1)$-approximation and yielding an efficient optimization problem in the sketch space. Namely, we achieve for any constant $c>0$ a sketching dimension of $\tilde{O}(d^{1+c})$ for $\ell_1$ regression and $\tilde{O}(\mu d^{1+c})$ for logistic regression, where $\mu$ is a standard measure that captures the complexity of compressing the data. For $\ell_1$-regression our sketching dimension is near-linear and improves previous work which either required $\Omega(\log d)$-approximation with this sketching dimension, or required a larger $\operatorname{poly}(d)$ number of rows. Similarly, for logistic regression previous work had worse $\operatorname{poly}(\mu d)$ factors in its sketching dimension. We also give a tradeoff that yields a $1+\varepsilon$ approximation in input sparsity time by increasing the total size to $(d\log(n)/\varepsilon)^{O(1/\varepsilon)}$ for $\ell_1$ and to $(\mu d\log(n)/\varepsilon)^{O(1/\varepsilon)}$ for logistic regression. Finally, we show that our sketch can be extended to approximate a regularized version of logistic regression where the data-dependent regularizer corresponds to the variance of the individual logistic losses.

In this work, the authors develop regression approaches based on deep learning to perform thread density estimation for plain weave canvas analysis. Previous approaches were based on Fourier analysis, which is quite robust for some scenarios but fails in some others, in machine learning tools, that involve pre-labeling of the painting at hand, or the segmentation of thread crossing points, that provides good estimations in all scenarios with no need of pre-labeling. The segmentation approach is time-consuming as the estimation of the densities is performed after locating the crossing points. In this novel proposal, we avoid this step by computing the density of threads directly from the image with a regression deep learning model. We also incorporate some improvements in the initial preprocessing of the input image with an impact on the final error. Several models are proposed and analyzed to retain the best one. Furthermore, we further reduce the density estimation error by introducing a semi-supervised approach. The performance of our novel algorithm is analyzed with works by Ribera, Vel\'azquez, and Poussin where we compare our results to the ones of previous approaches. Finally, the method is put into practice to support the change of authorship or a masterpiece at the Museo del Prado.

Background: Alzheimer's disease (AD) is the most common type of age-related dementia, affecting 6.2 million people aged 65 or older according to CDC data. It is commonly agreed that discovering an effective AD diagnosis biomarker could have enormous public health benefits, potentially preventing or delaying up to 40% of dementia cases. Tau neurofibrillary tangles are the primary driver of downstream neurodegeneration and subsequent cognitive impairment in AD, resulting in structural deformations such as hippocampal atrophy that can be observed in magnetic resonance imaging (MRI) scans. Objective: To build a surface-based model to 1) detect differences between APOE subgroups in patterns of tau deposition and hippocampal atrophy, and 2) use the extracted surface-based features to predict cognitive decline. Methods: Using data obtained from different institutions, we develop a surface-based federated Chow test model to study the synergistic effects of APOE, a previously reported significant risk factor of AD, and tau on hippocampal surface morphometry. Results: We illustrate that the APOE-specific morphometry features correlate with AD progression and better predict future AD conversion than other MRI biomarkers. For example, a strong association between atrophy and abnormal tau was identified in hippocampal subregion cornu ammonis 1 (CA1 subfield) and subiculum in e4 homozygote cohort. Conclusion: Our model allows for identifying MRI biomarkers for AD and cognitive decline prediction and may uncover a corner of the neural mechanism of the influence of APOE and tau deposition on hippocampal morphology.

The information diffusion performance of GCN and its variant models is limited by the adjacency matrix, which can lower their performance. Therefore, we introduce a new framework for graph convolutional networks called Hybrid Diffusion-based Graph Convolutional Network (HD-GCN) to address the limitations of information diffusion caused by the adjacency matrix. In the HD-GCN framework, we initially utilize diffusion maps to facilitate the diffusion of information among nodes that are adjacent to each other in the feature space. This allows for the diffusion of information between similar points that may not have an adjacent relationship. Next, we utilize graph convolution to further propagate information among adjacent nodes after the diffusion maps, thereby enabling the spread of information among similar nodes that are adjacent in the graph. Finally, we employ the diffusion distances obtained through the use of diffusion maps to regularize and constrain the predicted labels of training nodes. This regularization method is then applied to the HD-GCN training, resulting in a smoother classification surface. The model proposed in this paper effectively overcomes the limitations of information diffusion imposed only by the adjacency matrix. HD-GCN utilizes hybrid diffusion by combining information diffusion between neighborhood nodes in the feature space and adjacent nodes in the adjacency matrix. This method allows for more comprehensive information propagation among nodes, resulting in improved model performance. We evaluated the performance of DM-GCN on three well-known citation network datasets and the results showed that the proposed framework is more effective than several graph-based semi-supervised learning methods.

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) in Euclidean and general $\ell_p^d$ spaces. Specifically, we focus on three settings that are still far from well understood: (1) DP-SCO over a constrained and bounded (convex) set in Euclidean space; (2) unconstrained DP-SCO in $\ell_p^d$ space; (3) DP-SCO with heavy-tailed data over a constrained and bounded set in $\ell_p^d$ space. For problem (1), for both convex and strongly convex loss functions, we propose methods whose outputs could achieve (expected) excess population risks that are only dependent on the Gaussian width of the constraint set rather than the dimension of the space. Moreover, we also show the bound for strongly convex functions is optimal up to a logarithmic factor. For problems (2) and (3), we propose several novel algorithms and provide the first theoretical results for both cases when $1