We consider standard gradient descent, gradient flow and conjugate gradients as iterative algorithms for minimizing a penalized ridge criterion in linear regression. While it is well known that conjugate gradients exhibit fast numerical convergence, the statistical properties of their iterates are more difficult to assess due to inherent nonlinearities and dependencies. On the other hand, standard gradient flow is a linear method with well known regularizing properties when stopped early. By an explicit non-standard error decomposition we are able to bound the prediction error for conjugate gradient iterates by a corresponding prediction error of gradient flow at transformed iteration indices. This way, the risk along the entire regularisation path of conjugate gradient iterations can be compared to that for regularisation paths of standard linear methods like gradient flow and ridge regression. In particular, the oracle conjugate gradient iterate shares the optimality properties of the gradient flow and ridge regression oracles up to a constant factor. Numerical examples show the similarity of the regularisation paths in practice.

We study a contextual version of the repeated brokerage problem. In each interaction, two traders with private valuations for an item seek to buy or sell based on the learner's-a broker-proposed price, which is informed by some contextual information. The broker's goal is to maximize the traders' net utility-also known as the gain from trade-by minimizing regret compared to an oracle with perfect knowledge of traders' valuation distributions. We assume that traders' valuations are zero-mean perturbations of the unknown item's current market value-which can change arbitrarily from one interaction to the next-and that similar contexts will correspond to similar market prices. We analyze two feedback settings: full-feedback, where after each interaction the traders' valuations are revealed to the broker, and limited-feedback, where only transaction attempts are revealed. For both feedback types, we propose algorithms achieving tight regret bounds. We further strengthen our performance guarantees by providing a tight 1/2-approximation result showing that the oracle that knows the traders' valuation distributions achieves at least 1/2 of the gain from trade of the omniscient oracle that knows in advance the actual realized traders' valuations.

We provide a complete characterization of the entire regularization curve of a modified two-part-code Minimum Description Length (MDL) learning rule for binary classification, based on an arbitrary prior or description language. Grunwald and Langford [2004] previously established the lack of asymptotic consistency, from an agnostic PAC (frequentist worst case) perspective, of the MDL rule with a penalty parameter of $\lambda=1$, suggesting that it underegularizes. Driven by interest in understanding how benign or catastrophic under-regularization and overfitting might be, we obtain a precise quantitative description of the worst case limiting error as a function of the regularization parameter $\lambda$ and noise level (or approximation error), significantly tightening the analysis of Grunwald and Langford for $\lambda=1$ and extending it to all other choices of $\lambda$.

Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert knowledge or causal discovery algorithms to justify this assumption. In practice, neither may propose a single DAG with high confidence. Domain experts are hesitant to rule out dependencies with certainty or have ongoing disputes about relationships; causal discovery often relies on untestable assumptions itself or only provides an equivalence class of DAGs and is commonly sensitive to hyperparameter and threshold choices. We propose an efficient, gradient-based optimization method that provides bounds for causal queries over a collection of causal graphs -- compatible with imperfect prior knowledge -- that may still be too large for exhaustive enumeration. Our bounds achieve good coverage and sharpness for causal queries such as average treatment effects in linear and non-linear synthetic settings as well as on real-world data. Our approach aims at providing an easy-to-use and widely applicable rebuttal to the valid critique of `What if your assumed DAG is wrong?'.

With the recent development and advancement of Transformer and MLP architectures, significant strides have been made in time series analysis. Conversely, the performance of Convolutional Neural Networks (CNNs) in time series analysis has fallen short of expectations, diminishing their potential for future applications. Our research aims to enhance the representational capacity of Convolutional Neural Networks (CNNs) in time series analysis by introducing novel perspectives and design innovations. To be specific, We introduce a novel time series reshaping technique that considers the inter-patch, intra-patch, and cross-variable dimensions. Consequently, we propose TVNet, a dynamic convolutional network leveraging a 3D perspective to employ time series analysis. TVNet retains the computational efficiency of CNNs and achieves state-of-the-art results in five key time series analysis tasks, offering a superior balance of efficiency and performance over the state-of-the-art Transformer-based and MLP-based models. Additionally, our findings suggest that TVNet exhibits enhanced transferability and robustness. Therefore, it provides a new perspective for applying CNN in advanced time series analysis tasks.

In this paper we present the statistical analysis of data from inexpensive sensors. We also present the performance of machine learning algorithms when used for automatic calibration such sensors. In this we have used low-cost Non-Dispersive Infrared CO$_2$ sensor placed at a co-located site at Cape Point, South Africa (maintained by Weather South Africa). The collected low-cost sensor data and site truth data are investigated and compared. We compare and investigate the performance of Random Forest Regression, Support Vector Regression, 1D Convolutional Neural Network and 1D-CNN Long Short-Term Memory Network models as a method for automatic calibration and the statistical properties of these model predictions. In addition, we also investigate the drift in performance of these algorithms with time.

Existing LiDAR-Inertial Odometry (LIO) systems typically use sensor-specific or environment-dependent measurement covariances during state estimation, leading to laborious parameter tuning and suboptimal performance in challenging conditions (e.g., sensor degeneracy and noisy observations). Therefore, we propose an Adaptive Kalman Filter (AKF) framework that dynamically estimates time-varying noise covariances of LiDAR and Inertial Measurement Unit (IMU) measurements, enabling context-aware confidence weighting between sensors. During LiDAR degeneracy, the system prioritizes IMU data while suppressing contributions from unreliable inputs like moving objects or noisy point clouds. Furthermore, a compact Gaussian-based map representation is introduced to model environmental planarity and spatial noise. A correlated registration strategy ensures accurate plane normal estimation via pseudo-merge, even in unstructured environments like forests. Extensive experiments validate the robustness of the proposed system across diverse environments, including dynamic scenes and geometrically degraded scenarios. Our method achieves reliable localization results across all MARS-LVIG sequences and ranks 8th on the KITTI Odometry Benchmark. The code will be released at https://github.com/xpxie/AKF-LIO.git.

In this paper, we describe the design of an inexpensive and agile climate sensor system which can be repurposed easily to measure various pollutants. We also propose the use of machine learning regression methods to calibrate CO2 data from this cost-effective sensing platform to a reference sensor at the South African Weather Service's Cape Point measurement facility. We show the performance of these methods and found that Random Forest Regression was the best in this scenario. This shows that these machine learning methods can be used to improve the performance of cost-effective sensor platforms and possibly extend the time between manual calibration of sensor networks.

This work suggests faster and space-efficient index construction algorithms for LSH for Euclidean distance (\textit{a.k.a.}~\ELSH) and cosine similarity (\textit{a.k.a.}~\SRP). The index construction step of these LSHs relies on grouping data points into several bins of hash tables based on their hashcode. To generate an $m$-dimensional hashcode of the $d$-dimensional data point, these LSHs first project the data point onto a $d$-dimensional random Gaussian vector and then discretise the resulting inner product. The time and space complexity of both \ELSH~and \SRP~for computing an $m$-sized hashcode of a $d$-dimensional vector is $O(md)$, which becomes impractical for large values of $m$ and $d$. To overcome this problem, we propose two alternative LSH hashcode generation algorithms both for Euclidean distance and cosine similarity, namely, \CSELSH, \HCSELSH~and \CSSRP, \HCSSRP, respectively. \CSELSH~and \CSSRP~are based on count sketch \cite{count_sketch} and \HCSELSH~and \HCSSRP~utilize higher-order count sketch \cite{shi2019higher}. These proposals significantly reduce the hashcode computation time from $O(md)$ to $O(d)$. Additionally, both \CSELSH~and \CSSRP~reduce the space complexity from $O(md)$ to $O(d)$; ~and \HCSELSH, \HCSSRP~ reduce the space complexity from $O(md)$ to $O(N \sqrt[N]{d})$ respectively, where $N\geq 1$ denotes the size of the input/reshaped tensor. Our proposals are backed by strong mathematical guarantees, and we validate their performance through simulations on various real-world datasets.

Soft robots have become increasingly popular for complex manipulation tasks requiring gentle and safe contact. However, their softness makes accurate control challenging, and high-fidelity sensing is a prerequisite to adequate control performance. To this end, many flexible and embedded sensors have been created over the past decade, but they inevitably increase the robot's complexity and stiffness. This study demonstrates a novel approach that uses simple bending strain gauges embedded inside a modular arm to extract complex information regarding its deformation and working conditions. The core idea is based on physical reservoir computing (PRC): A soft body's rich nonlinear dynamic responses, captured by the inter-connected bending sensor network, could be utilized for complex multi-modal sensing with a simple linear regression algorithm. Our results show that the soft modular arm reservoir can accurately predict body posture (bending angle), estimate payload weight, determine payload orientation, and even differentiate two payloads with only minimal difference in weight -- all using minimal digital computing power.