To Reviewer 2/4/5/7: The neuroimaging field is still limited to *either* using unsupervised methods to find "resting-state networks" (PCA,SparsePCA,ICA,etc.) *or* using supervised methods on experimental data to predict psychological processes (logistic regression,SVMs,etc.). The unsupervised discovery of special structure and supervised prediction of mental tasks are unfortunately seldom combined in brain imaging.

General comments: The paper is well written. I would just remove "cryptographic" in the abstract. Not a lot of people are familiar with differential privacy and many of them would get confused with the notion of cryptography in which there exists an algorithm that reverts the "encrypted" data to its original form (I consider that once the data is noisified, its original form is essentially "lost"). Technical comments: Following the argument in the supplementary information of ref. [30], the authors argue that being able to find a perfect SSC clustering breaches the notion of differential privacy (DP). Consider the following problem: Name: SSC approximation.

We consider the problem in Electrical Impedance Tomography (EIT) of identifying one or multiple inclusions in a background-conducting body $\Omega\subset\mathbb{R}^2$, from the knowledge of a finite number of electrostatic measurements taken on its boundary $\partial\Omega$ and modelled by the Dirichlet-to-Neumann (D-N) matrix. Once the presence of one inclusion in $\Omega$ is established, our model, combined with the machine learning techniques of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), may be used to determine the size of the inclusion, the presence of multiple inclusions, and also that of anisotropy within the inclusion(s). Utilising both real and simulated datasets within a 16-electrode setup, we achieve a high rate of inclusion detection and show that two measurements are sufficient to achieve a good level of accuracy when predicting the size of an inclusion. This underscores the substantial potential of integrating machine learning approaches with the more classical analysis of EIT and the inverse inclusion problem to extract critical insights, such as the presence of anisotropy.

We consider the noisy matrix sensing problem in the over-parameterization setting, where the estimated rank $r$ is larger than the true rank $r_\star$. Specifically, our main objective is to recover a matrix $ X_\star \in \mathbb{R}^{n_1 \times n_2} $ with rank $ r_\star $ from noisy measurements using an over-parameterized factorized form $ LR^\top $, where $ L \in \mathbb{R}^{n_1 \times r}, \, R \in \mathbb{R}^{n_2 \times r} $ and $ \min\{n_1, n_2\} \ge r > r_\star $, with the true rank $ r_\star $ being unknown. Recently, preconditioning methods have been proposed to accelerate the convergence of matrix sensing problem compared to vanilla gradient descent, incorporating preconditioning terms $ (L^\top L + \lambda I)^{-1} $ and $ (R^\top R + \lambda I)^{-1} $ into the original gradient. However, these methods require careful tuning of the damping parameter $\lambda$ and are sensitive to initial points and step size. To address these limitations, we propose the alternating preconditioned gradient descent (APGD) algorithm, which alternately updates the two factor matrices, eliminating the need for the damping parameter and enabling faster convergence with larger step sizes. We theoretically prove that APGD achieves near-optimal error convergence at a linear rate, starting from arbitrary random initializations. Through extensive experiments, we validate our theoretical results and demonstrate that APGD outperforms other methods, achieving the fastest convergence rate. Notably, both our theoretical analysis and experimental results illustrate that APGD does not rely on the initialization procedure, making it more practical and versatile.

In object detection, the instance count is typically used to define whether a dataset exhibits a long-tail distribution, implicitly assuming that models will underperform on categories with fewer instances. This assumption has led to extensive research on category bias in datasets with imbalanced instance counts. However, models still exhibit category bias even in datasets where instance counts are relatively balanced, clearly indicating that instance count alone cannot explain this phenomenon. In this work, we first introduce the concept and measurement of category information amount. We observe a significant negative correlation between category information amount and accuracy, suggesting that category information amount more accurately reflects the learning difficulty of a category. Based on this observation, we propose Information Amount-Guided Angular Margin (IGAM) Loss. The core idea of IGAM is to dynamically adjust the decision space of each category based on its information amount, thereby reducing category bias in long-tail datasets. IGAM Loss not only performs well on long-tailed benchmark datasets such as LVIS v1.0 and COCO-LT but also shows significant improvement for underrepresented categories in the non-long-tailed dataset Pascal VOC. Comprehensive experiments demonstrate the potential of category information amount as a tool and the generality of our proposed method.

This paper is dedicated to using a classifier to predict whether a Weibo post would be censored under the Chinese internet. Through randomized sampling from \citeauthor{Fu2021} and Chinese tokenizing strategies, we constructed a cleaned Chinese phrase dataset with binary censorship markings. Utilizing various probability-based information retrieval methods on the data, we were able to derive 4 logistic regression models for classification. Furthermore, we experimented with pre-trained transformers to perform similar classification tasks. After evaluating both the macro-F1 and ROC-AUC metrics, we concluded that the Fined-Tuned BERT model exceeds other strategies in performance.

Machine Learning models are being extensively used in safety critical applications where errors from these models could cause harm to the user. Such risks are amplified when multiple machine learning models, which are deployed concurrently, interact and make errors simultaneously. This paper explores three scenarios where error correlations between multiple models arise, resulting in such aggregated risks. Using real-world data, we simulate these scenarios and quantify the correlations in errors of different models. Our findings indicate that aggregated risks are substantial, particularly when models share similar algorithms, training datasets, or foundational models. Overall, we observe that correlations across models are pervasive and likely to intensify with increased reliance on foundational models and widely used public datasets, highlighting the need for effective mitigation strategies to address these challenges.

Focusing on the expert problem in online learning, this paper studies the interpolation of several performance metrics via $\phi$-regret minimization, which measures the performance of an algorithm by its regret with respect to an arbitrary action modification rule $\phi$. With $d$ experts and $T\gg d$ rounds in total, we present a single algorithm achieving the instance-adaptive $\phi$-regret bound \begin{equation*} \tilde O\left(\min\left\{\sqrt{d-d^{\mathrm{unif}}_\phi+1},\sqrt{d-d^{\mathrm{self}}_\phi}\right\}\cdot\sqrt{T}\right), \end{equation*} where $d^{\mathrm{unif}}_\phi$ is the maximum amount of experts modified identically by $\phi$, and $d^{\mathrm{self}}_\phi$ is the amount of experts that $\phi$ trivially modifies to themselves. By recovering the optimal $O(\sqrt{T\log d})$ external regret bound when $d^{\mathrm{unif}}_\phi=d$, the standard $\tilde O(\sqrt{T})$ internal regret bound when $d^{\mathrm{self}}_\phi=d-1$ and the optimal $\tilde O(\sqrt{dT})$ swap regret bound in the worst case, we improve existing results in the intermediate regimes. In addition, the same algorithm achieves the optimal quantile regret bound, which corresponds to even easier settings of $\phi$ than the external regret. Building on the classical reduction from $\phi$-regret minimization to external regret minimization on stochastic matrices, our main idea is to further convert the latter to online linear regression using Haar-wavelet-inspired matrix features. Then, we apply a particular $L_1$-version of comparator-adaptive online learning algorithms to exploit the sparsity in this regression subroutine.

This paper tackles the problem of jointly estimating the noise covariance matrix alongside primary parameters (such as poses and points) from measurements corrupted by Gaussian noise. In such settings, the noise covariance matrix determines the weights assigned to individual measurements in the least squares problem. We show that the joint problem exhibits a convex structure and provide a full characterization of the optimal noise covariance estimate (with analytical solutions) within joint maximum a posteriori and likelihood frameworks and several variants. Leveraging this theoretical result, we propose two novel algorithms that jointly estimate the primary parameters and the noise covariance matrix. To validate our approach, we conduct extensive experiments across diverse scenarios and offer practical insights into their application in robotics and computer vision estimation problems with a particular focus on SLAM.

In recent years, advances in machine learning (ML) models have inspired researchers to revisit the design of classic online algorithms, incorporating insights from ML-based advice to improve decision-making in real-world environments. This research area, termed algorithms with predictions, seeks to design algorithms that are both robust to worst-case inputs and achieve performance that improves with prediction accuracy (a desideratum termed consistency) (Lykouris and Vassilvitskii, 2018). Many prediction-aided algorithms have been developed for online decision-making tasks ranging from rent-or-buy problems like ski rental (Purohit et al., 2018; Anand et al., 2020; Sun et al., 2024) to sequencing problems like job scheduling (Cho et al., 2022). Algorithms in this framework often rely on global uncertainty parameters intended to summarize the trustworthiness of all of the model's predictions, with extreme settings indicating that predictions are either all perfect or all uninformative (e.g., Mahdian et al., 2007; Lykouris and Vassilvitskii, 2018; Purohit et al., 2018; Rohatgi, 2020; Wei and Zhang, 2020; Antoniadis et al., 2020). However, ML models often produce local, input-specific uncertainty estimates, exposing a disconnect between theory and practice.