Federated Learning (FL) has gained significant recent attention in machine learning for its enhanced privacy and data security, making it indispensable in fields such as healthcare, finance, and personalized services. This paper investigates federated PCA and estimation for spiked covariance matrices under distributed differential privacy constraints. We establish minimax rates of convergence, with a key finding that the central server's optimal rate is the harmonic mean of the local clients' minimax rates. This guarantees consistent estimation at the central server as long as at least one local client provides consistent results. Notably, consistency is maintained even if some local estimators are inconsistent, provided there are enough clients. These findings highlight the robustness and scalability of FL for reliable statistical inference under privacy constraints. To establish minimax lower bounds, we derive a matrix version of van Trees' inequality, which is of independent interest. Furthermore, we propose an efficient algorithm that preserves differential privacy while achieving near-optimal rates at the central server, up to a logarithmic factor. We address significant technical challenges in analyzing this algorithm, which involves a three-layer spectral decomposition. Numerical performance of the proposed algorithm is investigated using both simulated and real data.

Large Language Models (LLMs) have demonstrated the ability to solve complex tasks through In-Context Learning (ICL), where models learn from a few input-output pairs without explicit fine-tuning. In this paper, we explore the capacity of LLMs to solve non-linear numerical computations, with specific emphasis on functions of the Singular Value Decomposition. Our experiments show that while LLMs perform comparably to traditional models such as Stochastic Gradient Descent (SGD) based Linear Regression and Neural Networks (NN) for simpler tasks, they outperform these models on more complex tasks, particularly in the case of top-k Singular Values. Furthermore, LLMs demonstrate strong scalability, maintaining high accuracy even as the matrix size increases. Additionally, we found that LLMs can achieve high accuracy with minimal prior examples, converging quickly and avoiding the overfitting seen in classical models. These results suggest that LLMs could provide an efficient alternative to classical methods for solving high-dimensional problems. Future work will focus on extending these findings to larger matrices and more complex matrix operations while exploring the effect of using different numerical representations in ICL.

Water plays a fundamental role in the structure and function of proteins and other biomolecules. The thermodynamic profile of water molecules surrounding a protein are critical for ligand binding and recognition. Therefore, identifying the location and thermodynamic behavior of relevant water molecules is important for generating and optimizing lead compounds for affinity and selectivity to a given target. Computational methods have been developed to identify these hydration sites, but are largely limited to simplified models that fail to capture multi-body interactions, or dynamics-based methods that rely on extensive sampling. Here we present a method for fast and accurate localization and thermodynamic profiling of hydration sites for protein structures. The method is based on a geometric deep neural network trained on a large, novel dataset of explicit water molecular dynamics simulations. We confirm the accuracy and robustness of our model on experimental data and demonstrate it's utility on several case studies.

This paper proposes a novel analytical framework: Transition Network Analysis (TNA), an approach that integrates Stochastic Process Mining and probabilistic graph representation to model, visualize, and identify transition patterns in the learning process data. Combining the relational and temporal aspects into a single lens offers capabilities beyond either framework, including centralities to capture important learning events, community finding to identify patterns of behavior, and clustering to reveal temporal patterns. This paper introduces the theoretical and mathematical foundations of TNA. To demonstrate the functionalities of TNA, we present a case study with students (n=191) engaged in small-group collaboration to map patterns of group dynamics using the theories of co-regulation and socially-shared regulated learning. The analysis revealed that TNA could reveal the regulatory processes and identify important events, temporal patterns and clusters. Bootstrap validation established the significant transitions and eliminated spurious transitions. In doing so, we showcase TNA's utility to capture learning dynamics and provide a robust framework for investigating the temporal evolution of learning processes. Future directions include advancing estimation methods, expanding reliability assessment, exploring longitudinal TNA, and comparing TNA networks using permutation tests.

Objective: Shoulder exoskeletons can effectively assist with overhead work. However, their impacts on muscle synergy remain unclear. The objective is to systematically investigate the effects of the shoulder exoskeleton on muscle synergies during overhead work.Methods: Eight male participants were recruited to perform a screwing task both with (Intervention) and without (Normal) the exoskeleton. Eight muscles were monitored and muscle synergies were extracted using non-negative matrix factorization and electromyographic topographic maps. Results: The number of synergies extracted was the same (n = 2) in both conditions. Specifically, the first synergies in both conditions were identical, with the highest weight of AD and MD; while the second synergies were different between conditions, with highest weight of PM and MD, respectively. As for the first synergy in the Intervention condition, the activation profile significantly decreased, and the average recruitment level and activation duration were significantly lower (p<0.05). The regression analysis for the muscle synergies across conditions shows the changes of muscle synergies did not influence the sparseness of muscle synergies (p=0.7341). In the topographic maps, the mean value exhibited a significant decrease (p<0.001) and the entropy significantly increased (p<0.01). Conclusion: The exoskeleton does not alter the number of synergies and existing major synergies but may induce new synergies. It can also significantly decrease neural activation and may influence the heterogeneity of the distribution of monitored muscle activations. Significance: This study provides insights into the potential mechanisms of exoskeleton-assisted overhead work and guidance on improving the performance of exoskeletons.

State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that uses a pair of neural networks to learn the proposal distribution and transition distribution of a particle filter. Both distributions are approximated using multivariate Gaussian mixtures. The component means and covariances of these mixtures are learnt as outputs of learned functions. Our method is trained targeting the log-likelihood, thereby requiring only the observation series, and combines the interpretability of state-space models with the flexibility and approximation power of artificial neural networks. The proposed method significantly improves recovery of the hidden state in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.

The use of machine learning (ML) in critical domains such as medicine poses risks and requires regulation. One requirement is that decisions of ML systems in high-risk applications should be human-understandable. The field of "explainable artificial intelligence" (XAI) seemingly addresses this need. However, in its current form, XAI is unfit to provide quality control for ML; it itself needs scrutiny. Popular XAI methods cannot reliably answer important questions about ML models, their training data, or a given test input. We recapitulate results demonstrating that popular XAI methods systematically attribute importance to input features that are independent of the prediction target. This limits their utility for purposes such as model and data (in)validation, model improvement, and scientific discovery. We argue that the fundamental reason for this limitation is that current XAI methods do not address well-defined problems and are not evaluated against objective criteria of explanation correctness. Researchers should formally define the problems they intend to solve first and then design methods accordingly. This will lead to notions of explanation correctness that can be theoretically verified and objective metrics of explanation performance that can be assessed using ground-truth data.

Robotic manipulation of volumetric elastoplastic deformable materials, from foods such as dough to construction materials like clay, is in its infancy, largely due to the difficulty of modelling and perception in a high-dimensional space. Simulating the dynamics of such materials is computationally expensive. It tends to suffer from inaccurately estimated physics parameters of the materials and the environment, impeding high-precision manipulation. Estimating such parameters from raw point clouds captured by optical cameras suffers further from heavy occlusions. To address this challenge, this work introduces a novel Differentiable Physics-based System Identification (DPSI) framework that enables a robot arm to infer the physics parameters of elastoplastic materials and the environment using simple manipulation motions and incomplete 3D point clouds, aligning the simulation with the real world. Extensive experiments show that with only a single real-world interaction, the estimated parameters, Young's modulus, Poisson's ratio, yield stress and friction coefficients, can accurately simulate visually and physically realistic deformation behaviours induced by unseen and long-horizon manipulation motions. Additionally, the DPSI framework inherently provides physically intuitive interpretations for the parameters in contrast to black-box approaches such as deep neural networks.

Out-of-Distribution (OOD) detection is crucial when deploying machine learning models in open-world applications. The core challenge in OOD detection is mitigating the model's overconfidence on OOD data. While recent methods using auxiliary outlier datasets or synthesizing outlier features have shown promising OOD detection performance, they are limited due to costly data collection or simplified assumptions. In this paper, we propose a novel OOD detection framework FodFoM that innovatively combines multiple foundation models to generate two types of challenging fake outlier images for classifier training. The first type is based on BLIP-2's image captioning capability, CLIP's vision-language knowledge, and Stable Diffusion's image generation ability. Jointly utilizing these foundation models constructs fake outlier images which are semantically similar to but different from in-distribution (ID) images. For the second type, GroundingDINO's object detection ability is utilized to help construct pure background images by blurring foreground ID objects in ID images. The proposed framework can be flexibly combined with multiple existing OOD detection methods. Extensive empirical evaluations show that image classifiers with the help of constructed fake images can more accurately differentiate real OOD images from ID ones. New state-of-the-art OOD detection performance is achieved on multiple benchmarks. The code is available at \url{https://github.com/Cverchen/ACMMM2024-FodFoM}.

In the recent past, there were several works on the prediction of stock price using different methods. Sentiment analysis of news and tweets and relating them to the movement of stock prices have already been explored. But, when we talk about the news, there can be several topics such as politics, markets, sports etc. It was observed that most of the prior analyses dealt with news or comments associated with particular stock prices only or the researchers dealt with overall sentiment scores only. However, it is quite possible that different topics having different levels of impact on the movement of the stock price or an index. The current study focused on bridging this gap by analysing the movement of Nifty 50 index with respect to the sentiments associated with news items related to various different topic such as sports, politics, markets etc. The study established that sentiment scores of news items of different other topics also have a significant impact on the movement of the index.