Conformal prediction is a distribution-free technique for establishing valid prediction intervals. Although conventionally people conduct conformal prediction in the output space, this is not the only possibility. In this paper, we propose feature conformal prediction, which extends the scope of conformal prediction to semantic feature spaces by leveraging the inductive bias of deep representation learning. From a theoretical perspective, we demonstrate that feature conformal prediction provably outperforms regular conformal prediction under mild assumptions. Our approach could be combined with not only vanilla conformal prediction, but also other adaptive conformal prediction methods. Apart from experiments on existing predictive inference benchmarks, we also demonstrate the state-of-the-art performance of the proposed methods on large-scale tasks such as ImageNet classification and Cityscapes image segmentation.The code is available at \url{https://github.com/AlvinWen428/FeatureCP}.

Integrating Global Navigation Satellite Systems (GNSS) in Simultaneous Localization and Mapping (SLAM) systems draws increasing attention to a global and continuous localization solution. Nonetheless, in dense urban environments, GNSS-based SLAM systems will suffer from the Non-Line-Of-Sight (NLOS) measurements, which might lead to a sharp deterioration in localization results. In this paper, we propose to detect the sky area from the up-looking camera to improve GNSS measurement reliability for more accurate position estimation. We present Sky-GVINS: a sky-aware GNSS-Visual-Inertial system based on a recent work called GVINS. Specifically, we adopt a global threshold method to segment the sky regions and non-sky regions in the fish-eye sky-pointing image and then project satellites to the image using the geometric relationship between satellites and the camera. After that, we reject satellites in non-sky regions to eliminate NLOS signals. We investigated various segmentation algorithms for sky detection and found that the Otsu algorithm reported the highest classification rate and computational efficiency, despite the algorithm's simplicity and ease of implementation. To evaluate the effectiveness of Sky-GVINS, we built a ground robot and conducted extensive real-world experiments on campus. Experimental results show that our method improves localization accuracy in both open areas and dense urban environments compared to the baseline method. Finally, we also conduct a detailed analysis and point out possible further directions for future research. For detailed information, visit our project website at https://github.com/SJTU-ViSYS/Sky-GVINS.

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support sizes. We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (https://github.com/MathBioCU/WENDy).

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative latent variable tensor model that incorporates both high rank and low rank models, including but not limited to, simple hypergraphon models, single index models, low-rank CP models, and low-rank Tucker models. Comprehensive results are developed on both the statistical and computational limits for the signal tensor estimation. We find that high-dimensional latent variable tensors are of log-rank; the fact explains the pervasiveness of low-rank tensors in applications. Furthermore, we propose a polynomial-time spectral algorithm that achieves the computationally optimal rate. We show that the statistical-computational gap emerges only for latent variable tensors of order 3 or higher. Numerical experiments and two real data applications are presented to demonstrate the practical merits of our methods.

We introduce OFTER, a time series forecasting pipeline tailored for mid-sized multivariate time series. OFTER utilizes the non-parametric models of k-nearest neighbors and Generalized Regression Neural Networks, integrated with a dimensionality reduction component. To circumvent the curse of dimensionality, we employ a weighted norm based on a modified version of the maximal correlation coefficient. The pipeline we introduce is specifically designed for online tasks, has an interpretable output, and is able to outperform several state-of-the art baselines. The computational efficacy of the algorithm, its online nature, and its ability to operate in low signal-to-noise regimes, render OFTER an ideal approach for financial multivariate time series problems, such as daily equity forecasting. Our work demonstrates that while deep learning models hold significant promise for time series forecasting, traditional methods carefully integrating mainstream tools remain very competitive alternatives with the added benefits of scalability and interpretability.

Starting from 2021, more demanding $\text{NO}_\text{x}$ emission restrictions were introduced for ships operating in the North and Baltic Sea waters. Since all methods currently used for ship compliance monitoring are financially and time demanding, it is important to prioritize the inspection of ships that have high chances of being non-compliant. The current state-of-the-art approach for a large-scale ship $\text{NO}_\text{2}$ estimation is a supervised machine learning-based segmentation of ship plumes on TROPOMI/S5P images. However, challenging data annotation and insufficiently complex ship emission proxy used for the validation limit the applicability of the model for ship compliance monitoring. In this study, we present a method for the automated selection of potentially non-compliant ships using a combination of machine learning models on TROPOMI satellite data. It is based on a proposed regression model predicting the amount of $\text{NO}_\text{2}$ that is expected to be produced by a ship with certain properties operating in the given atmospheric conditions. The model does not require manual labeling and is validated with TROPOMI data directly. The differences between the predicted and actual amount of produced $\text{NO}_\text{2}$ are integrated over observations of the ship in time and are used as a measure of the inspection worthiness of a ship. To assure the robustness of the results, we compare the obtained results with the results of the previously developed segmentation-based method. Ships that are also highly deviating in accordance with the segmentation method require further attention. If no other explanations can be found by checking the TROPOMI data, the respective ships are advised to be the candidates for inspection.

In this work we derive the performance achievable by a network of distributed agents that solve, adaptively and in the presence of communication constraints, a regression problem. Agents employ the recently proposed ACTC (adapt-compress-then-combine) diffusion strategy, where the signals exchanged locally by neighboring agents are encoded with randomized differential compression operators. We provide a detailed characterization of the mean-square estimation error, which is shown to comprise a term related to the error that agents would achieve without communication constraints, plus a term arising from compression. The analysis reveals quantitative relationships between the compression loss and fundamental attributes of the distributed regression problem, in particular, the stochastic approximation error caused by the gradient noise and the network topology (through the Perron eigenvector). We show that knowledge of such relationships is critical to allocate optimally the communication resources across the agents, taking into account their individual attributes, such as the quality of their data or their degree of centrality in the network topology. We devise an optimized allocation strategy where the parameters necessary for the optimization can be learned online by the agents. Illustrative examples show that a significant performance improvement, as compared to a blind (i.e., uniform) resource allocation, can be achieved by optimizing the allocation by means of the provided mean-square-error formulas.

Nonsmooth composite optimization with orthogonality constraints has a broad spectrum of applications in statistical learning and data science. However, this problem is generally challenging to solve due to its non-convex and non-smooth nature. Existing solutions are limited by one or more of the following restrictions: (i) they are full gradient methods that require high computational costs in each iteration; (ii) they are not capable of solving general nonsmooth composite problems; (iii) they are infeasible methods and can only achieve the feasibility of the solution at the limit point; (iv) they lack rigorous convergence guarantees; (v) they only obtain weak optimality of critical points. In this paper, we propose \textit{\textbf{OBCD}}, a new Block Coordinate Descent method for solving general nonsmooth composite problems under Orthogonality constraints. \textit{\textbf{OBCD}} is a feasible method with low computation complexity footprints. In each iteration, our algorithm updates $k$ rows of the solution matrix ($k\geq2$ is a parameter) to preserve the constraints. Then, it solves a small-sized nonsmooth composite optimization problem under orthogonality constraints either exactly or approximately. We demonstrate that any exact block-$k$ stationary point is always an approximate block-$k$ stationary point, which is equivalent to the critical stationary point. We are particularly interested in the case where $k=2$ as the resulting subproblem reduces to a one-dimensional nonconvex problem. We propose a breakpoint searching method and a fifth-order iterative method to solve this problem efficiently and effectively. We also propose two novel greedy strategies to find a good working set to further accelerate the convergence of \textit{\textbf{OBCD}}. Finally, we have conducted extensive experiments on several tasks to demonstrate the superiority of our approach.

Autonomous robots are required to reason about the behaviour of dynamic agents in their environment. The creation of models to describe these relationships is typically accomplished through the application of causal discovery techniques. However, as it stands observational causal discovery techniques struggle to adequately cope with conditions such as causal sparsity and non-stationarity typically seen during online usage in autonomous agent domains. Meanwhile, interventional techniques are not always feasible due to domain restrictions. In order to better explore the issues facing observational techniques and promote further discussion of these topics we carry out a benchmark across 10 contemporary observational temporal causal discovery methods in the domain of autonomous driving. By evaluating these methods upon causal scenes drawn from real world datasets in addition to those generated synthetically we highlight where improvements need to be made in order to facilitate the application of causal discovery techniques to the aforementioned use-cases. Finally, we discuss potential directions for future work that could help better tackle the difficulties currently experienced by state of the art techniques.

Clinical trials are essential to drug development but time-consuming, costly, and prone to failure. Accurate trial outcome prediction based on historical trial data promises better trial investment decisions and more trial success. Existing trial outcome prediction models were not designed to model the relations among similar trials, capture the progression of features and designs of similar trials, or address the skewness of trial data which causes inferior performance for less common trials. To fill the gap and provide accurate trial outcome prediction, we propose Sequential Predictive mOdeling of clinical Trial outcome (SPOT) that first identifies trial topics to cluster the multi-sourced trial data into relevant trial topics. It then generates trial embeddings and organizes them by topic and time to create clinical trial sequences. With the consideration of each trial sequence as a task, it uses a meta-learning strategy to achieve a point where the model can rapidly adapt to new tasks with minimal updates. In particular, the topic discovery module enables a deeper understanding of the underlying structure of the data, while sequential learning captures the evolution of trial designs and outcomes. This results in predictions that are not only more accurate but also more interpretable, taking into account the temporal patterns and unique characteristics of each trial topic. We demonstrate that SPOT wins over the prior methods by a significant margin on trial outcome benchmark data: with a 21.5\% lift on phase I, an 8.9\% lift on phase II, and a 5.5\% lift on phase III trials in the metric of the area under precision-recall curve (PR-AUC).