We study the problem of drawing samples from a logconcave distribution truncated on a polytope, motivated by computational challenges in Bayesian statistical models with indicator variables, such as probit regression. Building on interior point methods and the Dikin walk for sampling from uniform distributions, we analyze the mixing time of regularized Dikin walks. Our contributions are threefold. First, for a logconcave and log-smooth distribution with condition number $\kappa$, truncated on a polytope in $\mathbb{R}^n$ defined with $m$ linear constraints, we prove that the soft-threshold Dikin walk mixes in $\widetilde{O}((m+\kappa)n)$ iterations from a warm initialization. It improves upon prior work which required the polytope to be bounded and involved a bound dependent on the radius of the bounded region. Moreover, we introduce the regularized Dikin walk using Lewis weights for approximating the John ellipsoid. We show that it mixes in $\widetilde{O}((n^{2.5}+\kappa n)$. Second, we extend the mixing time guarantees mentioned above to weakly log-concave distributions truncated on polytopes, provided that they have a finite covariance matrix. Third, going beyond worst-case mixing time analysis, we demonstrate that soft-threshold Dikin walk can mix significantly faster when only a limited number of constraints intersect the high-probability mass of the distribution, improving the $\widetilde{O}((m+\kappa)n)$ upper bound to $\widetilde{O}(m + \kappa n)$. Additionally, per-iteration complexity of regularized Dikin walk and ways to generate a warm initialization are discussed to facilitate practical implementation.

This paper presents a comprehensive exploration of the phenomenon of data redundancy in video understanding, with the aim to improve computational efficiency. Our investigation commences with an examination of spatial redundancy, which refers to the observation that the most informative region in each video frame usually corresponds to a small image patch, whose shape, size and location shift smoothly across frames. Motivated by this phenomenon, we formulate the patch localization problem as a dynamic decision task, and introduce a spatially adaptive video recognition approach, termed AdaFocus. In specific, a lightweight encoder is first employed to quickly process the full video sequence, whose features are then utilized by a policy network to identify the most task-relevant regions. Subsequently, the selected patches are inferred by a high-capacity deep network for the final prediction. The full model can be trained in end-to-end conveniently. Furthermore, AdaFocus can be extended by further considering temporal and sample-wise redundancies, i.e., allocating the majority of computation to the most task-relevant frames, and minimizing the computation spent on relatively "easier" videos. Our resulting approach, Uni-AdaFocus, establishes a comprehensive framework that seamlessly integrates spatial, temporal, and sample-wise dynamic computation, while it preserves the merits of AdaFocus in terms of efficient end-to-end training and hardware friendliness. In addition, Uni-AdaFocus is general and flexible as it is compatible with off-the-shelf efficient backbones (e.g., TSM and X3D), which can be readily deployed as our feature extractor, yielding a significantly improved computational efficiency. Empirically, extensive experiments based on seven benchmark datasets and three application scenarios substantiate that Uni-AdaFocus is considerably more efficient than the competitive baselines.

This study presents a novel representation learning model tailored for dynamic networks, which describes the continuously evolving relationships among individuals within a population. The problem is encapsulated in the dimension reduction topic of functional data analysis. With dynamic networks represented as matrix-valued functions, our objective is to map this functional data into a set of vector-valued functions in a lower-dimensional learning space. This space, defined as a metric functional space, allows for the calculation of norms and inner products. By constructing this learning space, we address (i) attribute learning, (ii) community detection, and (iii) link prediction and recovery of individual nodes in the dynamic network. Our model also accommodates asymmetric low-dimensional representations, enabling the separate study of nodes' regulatory and receiving roles. Crucially, the learning method accounts for the time-dependency of networks, ensuring that representations are continuous over time. The functional learning space we define naturally spans the time frame of the dynamic networks, facilitating both the inference of network links at specific time points and the reconstruction of the entire network structure without direct observation. We validated our approach through simulation studies and real-world applications. In simulations, we compared our methods link prediction performance to existing approaches under various data corruption scenarios. For real-world applications, we examined a dynamic social network replicated across six ant populations, demonstrating that our low-dimensional learning space effectively captures interactions, roles of individual ants, and the social evolution of the network. Our findings align with existing knowledge of ant colony behavior.

Constructing compact and informative 3D scene representations is essential for effective embodied exploration and reasoning, especially in complex environments over extended periods. Existing representations, such as object-centric 3D scene graphs, oversimplify spatial relationships by modeling scenes as isolated objects with restrictive textual relationships, making it difficult to address queries requiring nuanced spatial understanding. Moreover, these representations lack natural mechanisms for active exploration and memory management, hindering their application to lifelong autonomy. In this work, we propose 3D-Mem, a novel 3D scene memory framework for embodied agents. 3D-Mem employs informative multi-view images, termed Memory Snapshots, to represent the scene and capture rich visual information of explored regions. It further integrates frontier-based exploration by introducing Frontier Snapshots-glimpses of unexplored areas-enabling agents to make informed decisions by considering both known and potential new information. To support lifelong memory in active exploration settings, we present an incremental construction pipeline for 3D-Mem, as well as a memory retrieval technique for memory management. Experimental results on three benchmarks demonstrate that 3D-Mem significantly enhances agents' exploration and reasoning capabilities in 3D environments, highlighting its potential for advancing applications in embodied AI.

Predictive models often face performance degradation due to evolving data distributions, a phenomenon known as data drift. Among its forms, concept drift, where the relationship between explanatory variables and the response variable changes, is particularly challenging to detect and adapt to. Traditional drift detection methods often rely on metrics such as accuracy or variable distributions, which may fail to capture subtle but significant conceptual changes. This paper introduces drifter, an R package designed to detect concept drift, and proposes a novel method called Profile Drift Detection (PDD) that enables both drift detection and an enhanced understanding of the cause behind the drift by leveraging an explainable AI tool - Partial Dependence Profiles (PDPs). The PDD method, central to the package, quantifies changes in PDPs through novel metrics, ensuring sensitivity to shifts in the data stream without excessive computational costs. This approach aligns with MLOps practices, emphasizing model monitoring and adaptive retraining in dynamic environments. The experiments across synthetic and real-world datasets demonstrate that PDD outperforms existing methods by maintaining high accuracy while effectively balancing sensitivity and stability. The results highlight its capability to adaptively retrain models in dynamic environments, making it a robust tool for real-time applications. The paper concludes by discussing the advantages, limitations, and future extensions of the package for broader use cases.

Electroencephalogram (EEG) is a valuable technique to record brain electrical activity through electrodes placed on the scalp. Analyzing EEG signals contributes to the understanding of neurological conditions and developing brain-computer interface. Graph Signal Processing (GSP) has emerged as a promising method for EEG spatial-temporal analysis, by further considering the topological relationships between electrodes. However, existing GSP studies lack interpretability of electrode importance and the credibility of prediction confidence. This work proposes an EEG Graph Mutual Attention Convolutional Network (EEG-GMACN), by introducing an 'Inverse Graph Weight Module' to output interpretable electrode graph weights, enhancing the clinical credibility and interpretability of EEG classification results. Additionally, we incorporate a mutual attention mechanism module into the model to improve its capability to distinguish critical electrodes and introduce credibility calibration to assess the uncertainty of prediction results. This study enhances the transparency and effectiveness of EEG analysis, paving the way for its widespread use in clinical and neuroscience research.

In causal inference, randomized experiment is a de facto method to overcome various theoretical issues in observational study. However, the experimental design requires expensive costs, so an efficient experimental design is necessary. We propose ABC3, a Bayesian active learning policy for causal inference. We show a policy minimizing an estimation error on conditional average treatment effect is equivalent to minimizing an integrated posterior variance, similar to Cohn criteria \citep{cohn1994active}. We theoretically prove ABC3 also minimizes an imbalance between the treatment and control groups and the type 1 error probability. Imbalance-minimizing characteristic is especially notable as several works have emphasized the importance of achieving balance. Through extensive experiments on real-world data sets, ABC3 achieves the highest efficiency, while empirically showing the theoretical results hold.

In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss, compression introduces a penalty on the number of iterations needed to reach a solution. In this work, we investigate how the iteration penalty depends on the interaction between compression and problem structure, in the context of non-convex stochastic optimization. We focus on linear compression schemes, where compression and decompression can be modeled as multiplication with a random matrix. We consider several distributions of matrices, among them random orthogonal matrices and matrices with random Gaussian entries. We find that in each case, the impact of compression on convergence can be quantified in terms of the norm of the Hessian of the objective, using a norm defined by the compression scheme. The analysis reveals that in certain cases, compression performance is related to low-rank structure or other spectral properties of the problem. In these cases, our bounds predict that the penalty introduced by compression is significantly reduced compared to worst-case bounds that only consider the compression level, ignoring problem data. We verify the theoretical findings on several optimization problems, including fine-tuning an image classification model.

Stochastic configuration networks (SCNs), as a class of randomized learner models, are featured by its way of random parameters assignment in the light of a supervisory mechanism, resulting in the universal approximation property at algorithmic level. This paper presents a kernel version of SCNs, termed KSCNs, aiming to enhance model's representation learning capability and performance stability. The random bases of a built SCN model can be used to span a reproducing kernel Hilbert space (RKHS), followed by our proposed algorithm for constructing KSCNs. It is shown that the data distribution in the reconstructive space is favorable for regression solving and the proposed KSCN learner models hold the universal approximation property. Three benchmark datasets including two industrial datasets are used in this study for performance evaluation. Experimental results with comparisons against existing solutions clearly demonstrate that the proposed KSCN remarkably outperforms the original SCNs and some typical kernel methods for resolving nonlinear regression problems in terms of the learning performance, the model's stability and robustness with respect to the kernel parameter settings.

Continual Learning (CL) is a highly relevant setting gaining traction in recent machine learning research. Among CL works, architectural and hybrid strategies are particularly effective due to their potential to adapt the model architecture as new tasks are presented. However, many existing solutions do not efficiently exploit model sparsity, and are prone to capacity saturation due to their inefficient use of available weights, which limits the number of learnable tasks. In this paper, we propose TinySubNets (TSN), a novel architectural CL strategy that addresses the issues through the unique combination of pruning with different sparsity levels, adaptive quantization, and weight sharing. Pruning identifies a subset of weights that preserve model performance, making less relevant weights available for future tasks. Adaptive quantization allows a single weight to be separated into multiple parts which can be assigned to different tasks. Weight sharing between tasks boosts the exploitation of capacity and task similarity, allowing for the identification of a better trade-off between model accuracy and capacity. These features allow TSN to efficiently leverage the available capacity, enhance knowledge transfer, and reduce computational resource consumption. Experimental results involving common benchmark CL datasets and scenarios show that our proposed strategy achieves better results in terms of accuracy than existing state-of-the-art CL strategies. Moreover, our strategy is shown to provide a significantly improved model capacity exploitation. Code released at: https://github.com/lifelonglab/tinysubnets.