A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it canonical correlation analysis} (CCA) provably identify the shared components up to minor ambiguities, when samples in each modality are generated from a linear mixture of shared and private components. Such identifiability results were obtained under the condition that the cross-modality samples are aligned/paired according to their shared information. This work takes a step further, investigating shared component identifiability from multi-modal linear mixtures where cross-modality samples are unaligned. A distribution divergence minimization-based loss is proposed, under which a suite of sufficient conditions ensuring identifiability of the shared components are derived. Our conditions are based on cross-modality distribution discrepancy characterization and density-preserving transform removal, which are much milder than existing studies relying on independent component analysis. More relaxed conditions are also provided via adding reasonable structural constraints, motivated by available side information in various applications. The identifiability claims are thoroughly validated using synthetic and real-world data.

Machine learning can significantly improve performance for decision-making under uncertainty in a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve in high-capacity prediction models such as deep neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with their own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn the uncertainty estimates for conditional robust optimization, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent arbitrary convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization.

Multiplex networks have emerged as a promising approach for modeling complex systems, where each layer represents a different mode of interaction among entities of the same type. A core task in analyzing these networks is to identify the community structure for a better understanding of the overall functioning of the network. While different methods have been proposed to detect the community structure of multiplex networks, the majority deal with extracting the consensus community structure across layers. In this paper, we address the community detection problem across two closely related multiplex networks. For example in neuroimaging studies, it is common to have multiple multiplex brain networks where each layer corresponds to an individual and each group to different experimental conditions. In this setting, one may be interested in both learning the community structure representing each experimental condition and the discriminative community structure between two groups. In this paper, we introduce two discriminative community detection algorithms based on spectral clustering. The first approach aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously. The proposed approaches are evaluated on both simulated and real world multiplex networks.

Tactile information effectively enables faster training and better task performance for learning-based in-hand manipulation. Existing approaches are validated in simulated environments with a large number of tactile sensors. However, attaching such sensors to a real robot hand is not applicable due to high cost and physical limitations. To enable real-world adoption of tactile sensors, this study investigates the impact of tactile sensors, including their varying quantities and placements on robot hands, on the dexterous manipulation task performance and analyzes the importance of each. Through empirically decreasing the sensor quantities, we successfully find an optimized set of tactile sensors (21 sensors) configuration, which keeps over 93% task performance with only 20% sensor quantities compared to the original set (92 sensors) for the block manipulation task, leading to a potential reduction of over 80% in sensor manufacturing and design costs. To transform the empirical results into a generalizable understanding, we build a task performance prediction model with a weighted linear regression algorithm and use it to forecast the task performance with different sensor configurations. To show its generalizability, we verified this model in egg and pen manipulation tasks and achieved an average prediction error of 3.12%.

Recent advances in federated learning have shown that asynchronous variants can be faster and more scalable than their synchronous counterparts. However, their design does not include quantization, which is necessary in practice to deal with the communication bottleneck. To bridge this gap, we develop a novel algorithm, Quantized Asynchronous Federated Learning (QAFeL), which introduces a hidden-state quantization scheme to avoid the error propagation caused by direct quantization. QAFeL also includes a buffer to aggregate client updates, ensuring scalability and compatibility with techniques such as secure aggregation. Furthermore, we prove that QAFeL achieves an $\mathcal{O}(1/\sqrt{T})$ ergodic convergence rate for stochastic gradient descent on non-convex objectives, which is the optimal order of complexity, without requiring bounded gradients or uniform client arrivals. We also prove that the cross-term error between staleness and quantization only affects the higher-order error terms. We validate our theoretical findings on standard benchmarks.

Cluster analysis plays a crucial role in various domains and applications, such as customer segmentation in marketing. These contexts often involve multimodal data, including both tabular and textual datasets, making it challenging to represent hidden patterns for obtaining meaningful clusters. This study introduces ERASMO, a framework designed to fine-tune a pretrained language model on textually encoded tabular data and generate embeddings from the fine-tuned model. ERASMO employs a textual converter to transform tabular data into a textual format, enabling the language model to process and understand the data more effectively. Additionally, ERASMO produces contextually rich and structurally representative embeddings through techniques such as random feature sequence shuffling and number verbalization. Extensive experimental evaluations were conducted using multiple datasets and baseline approaches. Our results demonstrate that ERASMO fully leverages the specific context of each tabular dataset, leading to more precise and nuanced embeddings for accurate clustering. This approach enhances clustering performance by capturing complex relationship patterns within diverse tabular data.

Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute Shrinkage and Selection Operator (LASSO) approaches by jointly estimating the permutation, resulting in shuffled LS and shuffled LASSO formulations. Existing methods, constrained by the combinatorial complexity of permutation recovery, often address small-scale cases with limited measurements. In contrast, we focus on large-scale SLR, particularly suited for environments with abundant measurement samples. We propose a spectral matching method that efficiently resolves permutations by aligning spectral components of the measurement and feature covariances. Rigorous theoretical analyses demonstrate that our method achieves accurate estimates in both shuffled LS and shuffled LASSO settings, given a sufficient number of samples. Furthermore, we extend our approach to address simultaneous pose and correspondence estimation in image registration tasks. Experiments on synthetic datasets and real-world image registration scenarios show that our method outperforms existing algorithms in both estimation accuracy and registration performance.

Specialist language models (LMs) focus on a specific task or domain on which they often outperform generalist LMs of the same size. However, the specialist data needed to pretrain these models is only available in limited amount for most tasks. In this work, we build specialist models from large generalist training sets instead. We adjust the training distribution of the generalist data with guidance from the limited domain-specific data. We explore several approaches, with clustered importance sampling standing out. This method clusters the generalist dataset and samples from these clusters based on their frequencies in the smaller specialist dataset. It is scalable, suitable for pretraining and continued pretraining, it works well in multi-task settings. Our findings demonstrate improvements across different domains in terms of language modeling perplexity and accuracy on multiple-choice question tasks. We also present ablation studies that examine the impact of dataset sizes, clustering configurations, and model sizes. Generalist language models (LMs) can address a wide variety of tasks, but this generality comes at a cost (Brown et al., 2020). It necessitates a large training set representative of all prospective tasks, as well as a large model to fit such a comprehensive dataset.

Intersecting manifold segmentation has been a focus of research, where individual manifolds, that intersect with other manifolds, are separated to discover their distinct properties. The proposed method is based on the intuition that when a manifold in $D$ dimensional space with an intrinsic dimension of $d$ intersects with another manifold, the data variance grows in more than $d$ directions. The proposed method measures local data variances and determines their vector directions. It counts the number of vectors with non-zero variance, which determines the manifold's intrinsic dimension. For detection of the intersection region, the method adapts to the changes in the angular gaps between the corresponding direction vectors of the child and parent using exponential moving averages using a tree structure construction. Accordingly, it includes those data points in the same manifold whose neighborhood is within the adaptive angular difference and eventually identifies the data points in the intersection area of manifolds. Data points whose inclusion in the neighborhood-identified data points increases their intrinsic dimensionality are removed based on data variance and distance. The proposed method performs better than 18 SOTA manifold segmentation methods in ARI and NMI scores over 14 real-world datasets with lesser time complexity and better stability.

Identifying and classifying shutdown initiating events (SDIEs) is critical for developing low power shutdown probabilistic risk assessment for nuclear power plants. Existing computational approaches cannot achieve satisfactory performance due to the challenges of unavailable large, labeled datasets, imbalanced event types, and label noise. To address these challenges, we propose a hybrid pipeline that integrates a knowledge-informed machine learning mode to prescreen non-SDIEs and a large language model (LLM) to classify SDIEs into four types. In the prescreening stage, we proposed a set of 44 SDIE text patterns that consist of the most salient keywords and phrases from six SDIE types. Text vectorization based on the SDIE patterns generates feature vectors that are highly separable by using a simple binary classifier. The second stage builds Bidirectional Encoder Representations from Transformers (BERT)-based LLM, which learns generic English language representations from self-supervised pretraining on a large dataset and adapts to SDIE classification by fine-tuning it on an SDIE dataset. The proposed approaches are evaluated on a dataset with 10,928 events using precision, recall ratio, F1 score, and average accuracy. The results demonstrate that the prescreening stage can exclude more than 97% non-SDIEs, and the LLM achieves an average accuracy of 93.4% for SDIE classification.