We study the task of list-decodable linear regression using batches. A batch is called clean if it consists of i.i.d. samples from an unknown linear regression distribution. For a parameter $\alpha \in (0, 1/2)$, an unknown $\alpha$-fraction of the batches are clean and no assumptions are made on the remaining ones. The goal is to output a small list of vectors at least one of which is close to the true regressor vector in $\ell_2$-norm. [DJKS23] gave an efficient algorithm, under natural distributional assumptions, with the following guarantee. Assuming that the batch size $n$ satisfies $n \geq \tilde{\Omega}(\alpha^{-1})$ and the number of batches is $m = \mathrm{poly}(d, n, 1/\alpha)$, their algorithm runs in polynomial time and outputs a list of $O(1/\alpha^2)$ vectors at least one of which is $\tilde{O}(\alpha^{-1/2}/\sqrt{n})$ close to the target regressor. Here we design a new polynomial time algorithm with significantly stronger guarantees under the assumption that the low-degree moments of the covariates distribution are Sum-of-Squares (SoS) certifiably bounded. Specifically, for any constant $\delta>0$, as long as the batch size is $n \geq \Omega_{\delta}(\alpha^{-\delta})$ and the degree-$\Theta(1/\delta)$ moments of the covariates are SoS certifiably bounded, our algorithm uses $m = \mathrm{poly}((dn)^{1/\delta}, 1/\alpha)$ batches, runs in polynomial-time, and outputs an $O(1/\alpha)$-sized list of vectors one of which is $O(\alpha^{-\delta/2}/\sqrt{n})$ close to the target. That is, our algorithm achieves substantially smaller minimum batch size and final error, while achieving the optimal list size. Our approach uses higher-order moment information by carefully combining the SoS paradigm interleaved with an iterative method and a novel list pruning procedure. In the process, we give an SoS proof of the Marcinkiewicz-Zygmund inequality that may be of broader applicability.

Explainable AI is a crucial component for edge services, as it ensures reliable decision making based on complex AI models. Surrogate models are a prominent approach of XAI where human-interpretable models, such as a linear regression model, are trained to approximate a complex (black-box) model's predictions. This paper delves into the balance between the predictive accuracy of complex AI models and their approximation by surrogate ones, advocating that both these models benefit from being learned simultaneously. We derive a joint (bi-level) training scheme for both models and we introduce a new algorithm based on multi-objective optimization (MOO) to simultaneously minimize both the complex model's prediction error and the error between its outputs and those of the surrogate. Our approach leads to improvements that exceed 99% in the approximation of the black-box model through the surrogate one, as measured by the metric of Fidelity, for a compromise of less than 3% absolute reduction in the black-box model's predictive accuracy, compared to single-task and multi-task learning baselines. By improving Fidelity, we can derive more trustworthy explanations of the complex model's outcomes from the surrogate, enabling reliable AI applications for intelligent services at the network edge.

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.

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.

Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many real-world problems involve more complex relationships that cannot be adequately captured by simple linear interactions. One way to model such relationships is via multilinear transformations. This paper introduces Higher Order Reduced Rank Regression (HORRR), an extension of RRR that leverages multi-linear transformations, and as such is capable of capturing nonlinear interactions in multi-response regression. HORRR employs tensor representations for the coefficients and a Tucker decomposition to impose multilinear rank constraints as regularization akin to the rank constraints in RRR. Encoding these constraints as a manifold allows us to use Riemannian optimization to solve this HORRR problems. We theoretically and empirically analyze the use of Riemannian optimization for solving HORRR problems.

In the rapidly evolving digital era, comprehending the intricate dynamics influencing server power consumption, efficiency, and performance is crucial for sustainable data center operations. However, existing models lack the ability to provide a detailed and reliable understanding of these intricate relationships. This study employs a machine learning-based approach, using the SPECPower_ssj2008 database, to facilitate user-friendly and generalizable server modeling. The resulting models demonstrate high accuracy, with errors falling within approximately 10% on the testing dataset, showcasing their practical utility and generalizability. Through meticulous analysis, predictive features related to hardware availability date, server workload level, and specifications are identified, providing insights into optimizing energy conservation, efficiency, and performance in server deployment and operation. By systematically measuring biases and uncertainties, the study underscores the need for caution when employing historical data for prospective server modeling, considering the dynamic nature of technology landscapes. Collectively, this work offers valuable insights into the sustainable deployment and operation of servers in data centers, paving the way for enhanced resource use efficiency and more environmentally conscious practices.

This work presents a physics-based machine learning framework to predict and analyze oxides of nitrogen (NOx) emissions from compression-ignition engine-powered vehicles using on-board diagnostics (OBD) data as input. Accurate NOx prediction from OBD datasets is difficult because NOx formation inside an engine combustion chamber is governed by complex processes occurring on timescales much shorter than the data collection rate. Thus, emissions generally cannot be predicted accurately using simple empirically derived physics models. Black box models like genetic algorithms or neural networks can be more accurate, but have poor interpretability. The transparent model presented in this paper has both high accuracy and can explain potential sources of high emissions. The proposed framework consists of two major steps: a physics-based NOx prediction model combined with a novel Divergent Window Co-occurrence (DWC) Pattern detection algorithm to analyze operating conditions that are not adequately addressed by the physics-based model. The proposed framework is validated for generalizability with a second vehicle OBD dataset, a sensitivity analysis is performed, and model predictions are compared with that from a deep neural network. The results show that NOx emissions predictions using the proposed model has around 55% better root mean square error, and around 60% higher mean absolute error compared to the baseline NOx prediction model from previously published work. The DWC Pattern Detection Algorithm identified low engine power conditions to have high statistical significance, indicating an operating regime where the model can be improved. This work shows that the physics-based machine learning framework is a viable method for predicting NOx emissions from engines that do not incorporate NOx sensing.

We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing techniques with dynamic programming strategies, and is applicable in various settings, including binary fields, general finite fields, and integer matrices. In particular, our algorithms achieve a runtime of $\mathcal{O}\left(dk \cdot \left(nM\right)^{\lceil k / 2 \rceil}\right)$ while ensuring high-probability correctness. Our contributions include: A unified framework for verifying Kruskal rank across different algebraic settings; Rigorous runtime and high-probability guarantees that nearly match known lower bounds; Practical implications for identifiability in tensor decompositions and deep learning, particularly for the estimation of noise transition matrices.

In the rapidly advancing field of materials informatics, nonlinear machine learning models have demonstrated exceptional predictive capabilities for material properties. However, their black-box nature limits interpretability, and they may incorporate features that do not contribute to--or even deteriorate--model performance. This study employs explainable ML (XML) techniques, including permutation feature importance and the SHapley Additive exPlanation, applied to a pristine support vector regression model designed to predict band gaps at the GW level using 18 input features. Guided by XML-derived individual feature importance, a simple framework is proposed to construct reduced-feature predictive models. Model evaluations indicate that an XML-guided compact model, consisting of the top five features, achieves comparable accuracy to the pristine model on in-domain datasets while demonstrating superior generalization with lower prediction errors on out-of-domain data. Additionally, the study underscores the necessity for eliminating strongly correlated features to prevent misinterpretation and overestimation of feature importance before applying XML. This study highlights XML's effectiveness in developing simplified yet highly accurate machine learning models by clarifying feature roles.

This research addresses the challenges of handling unbalanced datasets for binary classification tasks. In such scenarios, standard evaluation metrics are often biased by the disproportionate representation of the minority class. Conducting experiments across seven datasets, we uncovered inconsistencies in evaluation metrics when determining the model that outperforms others for each binary classification problem. This justifies the need for a metric that provides a more consistent and unbiased evaluation across unbalanced datasets, thereby supporting robust model selection. To mitigate this problem, we propose a novel metric, the Unbiased Integration Coefficients (UIC), which exhibits significantly reduced bias ($p < 10^{-4}$) towards the minority class compared to conventional metrics. The UIC is constructed by aggregating existing metrics while penalising those more prone to imbalance. In addition, we introduce the Identical Partitions for Imbalance Problems (IPIP) algorithm for imbalanced ML problems, an ensemble-based approach. Our experimental results show that IPIP outperforms other baseline imbalance-aware approaches using Random Forest and Logistic Regression models in three out of seven datasets as assessed by the UIC metric, demonstrating its effectiveness in addressing imbalanced data challenges in binary classification tasks. This new framework for dealing with imbalanced datasets is materialized in the FILM (Framework for Imbalanced Learning Machines) R Package, accessible at https://github.com/antoniogt/FILM.