In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with nontrivial structure. The underlying network is unknown in many applications and should be inferred from observed data. We assume: i) Partial observability -- time series data is only available over a subset of the nodes; ii) Input noise -- it is correlated across distinct nodes while temporally independent, i.e., it is spatially colored. We present a feasibility condition on the noise correlation structure wherein there exists a consistent network inference estimator to recover the underlying fundamental dependencies among the observed nodes. Further, we describe a structure identification algorithm that exhibits competitive performance across distinct regimes of network connectivity, observability, and noise correlation.
Conventional Time Series Classification (TSC) methods are often black boxes that obscure inherent interpretation of their decision-making processes. In this work, we leverage Multiple Instance Learning (MIL) to overcome this issue, and propose a new framework called MILLET: Multiple Instance Learning for Locally Explainable Time series classification. We apply MILLET to existing deep learning TSC models and show how they become inherently interpretable without compromising (and in some cases, even improving) predictive performance. We evaluate MILLET on 85 UCR TSC datasets and also present a novel synthetic dataset that is specially designed to facilitate interpretability evaluation. On these datasets, we show MILLET produces sparse explanations quickly that are of higher quality than other well-known interpretability methods. To the best of our knowledge, our work with MILLET, which is available on GitHub (https://github.com/JAEarly/MILTimeSeriesClassification), is the first to develop general MIL methods for TSC and apply them to an extensive variety of domains
In this paper, we study a secure integrated sensing and communication (ISAC) system where one multi-antenna base station (BS) simultaneously communicates with one single-antenna user and senses the location parameter of a target which serves as a potential eavesdropper via its reflected echo signals. In particular, we consider a challenging scenario where the target's location is unknown and random, while its distribution information is known a priori. First, we derive the posterior Cram\'er-Rao bound (PCRB) of the mean-squared error (MSE) in target location sensing, which has a complicated expression. To draw more insights, we derive a tight approximation of it in closed form, which indicates that the transmit beamforming should achieve a "probability-dependent power focusing" effect over possible target locations, with more power focused on highly-probable locations. Next, considering an artificial noise based beamforming structure, we formulate the transmit beamforming optimization problem to maximize the worst-case secrecy rate among all possible target (eavesdropper) locations, subject to a threshold on the sensing PCRB. The formulated problem is non-convex and difficult to solve. We show that the problem can be solved via a two-stage method, by first obtaining the optimal beamforming corresponding to any given threshold on the signal-to-interference-plus-noise ratio (SINR) at the eavesdropper, and then obtaining the optimal threshold via one-dimensional search. By applying the semi-definite relaxation (SDR) technique, we relax the first problem into a convex form and further prove that the relaxation is tight, based on which the optimal solution of the original beamforming optimization problem can be obtained with polynomial-time complexity. Then, we further propose two suboptimal solutions with lower complexity. Numerical results validate the effectiveness of our designs.
We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical numerical algorithms for Lasso, our quantum algorithm provides the full regularisation path as the penalty term varies, but quadratically faster per iteration under specific conditions. A quadratic speedup on the number of features/predictors $d$ is possible by using the simple quantum minimum-finding subroutine from D\"urr and Hoyer (arXiv'96) in order to obtain the joining time at each iteration. We then improve upon this simple quantum algorithm and obtain a quadratic speedup both in the number of features $d$ and the number of observations $n$ by using the recent approximate quantum minimum-finding subroutine from Chen and de Wolf (ICALP'23). As one of our main contributions, we construct a quantum unitary based on quantum amplitude estimation to approximately compute the joining times to be searched over by the approximate quantum minimum finding. Since the joining times are no longer exactly computed, it is no longer clear that the resulting approximate quantum algorithm obtains a good solution. As our second main contribution, we prove, via an approximate version of the KKT conditions and a duality gap, that the LARS algorithm (and therefore our quantum algorithm) is robust to errors. This means that it still outputs a path that minimises the Lasso cost function up to a small error if the joining times are only approximately computed. Finally, in the model where the observations are generated by an underlying linear model with an unknown coefficient vector, we prove bounds on the difference between the unknown coefficient vector and the approximate Lasso solution, which generalises known results about convergence rates in classical statistical learning theory analysis.
In a privacy-focused era, Federated Learning (FL) has emerged as a promising machine learning technique. However, most existing FL studies assume that the data distribution remains nearly fixed over time, while real-world scenarios often involve dynamic and continual changes. To equip FL systems with continual model evolution capabilities, we focus on an important problem called Federated Continual Novel Class Learning (FedCN) in this work. The biggest challenge in FedCN is to merge and align novel classes that are discovered and learned by different clients without compromising privacy. To address this, we propose a Global Alignment Learning (GAL) framework that can accurately estimate the global novel class number and provide effective guidance for local training from a global perspective, all while maintaining privacy protection. Specifically, GAL first locates high-density regions in the representation space through a bi-level clustering mechanism to estimate the novel class number, with which the global prototypes corresponding to novel classes can be constructed. Then, GAL uses a novel semantic weighted loss to capture all possible correlations between these prototypes and the training data for mitigating the impact of pseudo-label noise and data heterogeneity. Extensive experiments on various datasets demonstrate GAL's superior performance over state-of-the-art novel class discovery methods. In particular, GAL achieves significant improvements in novel-class performance, increasing the accuracy by 5.1% to 10.6% in the case of one novel class learning stage and by 7.8% to 17.9% in the case of two novel class learning stages, without sacrificing known-class performance. Moreover, GAL is shown to be effective in equipping a variety of different mainstream FL algorithms with novel class discovery and learning capability, highlighting its potential for many real-world applications.
We consider problems in which a mobile robot samples an unknown function defined over its operating space, so as to find a global optimum of this function. The path traveled by the robot matters, since it influences energy and time requirements. We consider a branch-and-bound algorithm called deterministic optimistic optimization, and extend it to the path-aware setting, obtaining path-aware optimistic optimization (OOPA). In this new algorithm, the robot decides how to move next via an optimal control problem that maximizes the long-term impact of the robot trajectory on lowering the upper bound, weighted by bound and function values to focus the search on the optima. An online version of value iteration is used to solve an approximate version of this optimal control problem. OOPA is evaluated in extensive experiments in two dimensions, where it does better than path-unaware and local-optimization baselines.
We propose Diffusion Noise Optimization (DNO), a new method that effectively leverages existing motion diffusion models as motion priors for a wide range of motion-related tasks. Instead of training a task-specific diffusion model for each new task, DNO operates by optimizing the diffusion latent noise of an existing pre-trained text-to-motion model. Given the corresponding latent noise of a human motion, it propagates the gradient from the target criteria defined on the motion space through the whole denoising process to update the diffusion latent noise. As a result, DNO supports any use cases where criteria can be defined as a function of motion. In particular, we show that, for motion editing and control, DNO outperforms existing methods in both achieving the objective and preserving the motion content. DNO accommodates a diverse range of editing modes, including changing trajectory, pose, joint locations, or avoiding newly added obstacles. In addition, DNO is effective in motion denoising and completion, producing smooth and realistic motion from noisy and partial inputs. DNO achieves these results at inference time without the need for model retraining, offering great versatility for any defined reward or loss function on the motion representation.
Training-free guided sampling in diffusion models leverages off-the-shelf pre-trained networks, such as an aesthetic evaluation model, to guide the generation process. Current training-free guided sampling algorithms obtain the guidance energy function based on a one-step estimate of the clean image. However, since the off-the-shelf pre-trained networks are trained on clean images, the one-step estimation procedure of the clean image may be inaccurate, especially in the early stages of the generation process in diffusion models. This causes the guidance in the early time steps to be inaccurate. To overcome this problem, we propose Symplectic Adjoint Guidance (SAG), which calculates the gradient guidance in two inner stages. Firstly, SAG estimates the clean image via $n$ function calls, where $n$ serves as a flexible hyperparameter that can be tailored to meet specific image quality requirements. Secondly, SAG uses the symplectic adjoint method to obtain the gradients accurately and efficiently in terms of the memory requirements. Extensive experiments demonstrate that SAG generates images with higher qualities compared to the baselines in both guided image and video generation tasks.
Neural construction models have shown promising performance for Vehicle Routing Problems (VRPs) by adopting either the Autoregressive (AR) or Non-Autoregressive (NAR) learning approach. While AR models produce high-quality solutions, they generally have a high inference latency due to their sequential generation nature. Conversely, NAR models generate solutions in parallel with a low inference latency but generally exhibit inferior performance. In this paper, we propose a generic Guided Non-Autoregressive Knowledge Distillation (GNARKD) method to obtain high-performance NAR models having a low inference latency. GNARKD removes the constraint of sequential generation in AR models while preserving the learned pivotal components in the network architecture to obtain the corresponding NAR models through knowledge distillation. We evaluate GNARKD by applying it to three widely adopted AR models to obtain NAR VRP solvers for both synthesized and real-world instances. The experimental results demonstrate that GNARKD significantly reduces the inference time (4-5 times faster) with acceptable performance drop (2-3\%). To the best of our knowledge, this study is first-of-its-kind to obtain NAR VRP solvers from AR ones through knowledge distillation.
The present-day business landscape necessitates novel methodologies that integrate intelligent technologies and tools capable of swiftly providing precise and dependable information for decision-making purposes. Contemporary society is characterized by vast amounts of accumulated data across various domains, which hold considerable potential for informing and guiding decision-making processes. However, these data are typically collected and stored by disparate and unrelated software systems, stored in diverse formats, and offer varying levels of accessibility and security. To address the challenges associated with processing such large volumes of data, organizations often rely on data analysts. Nonetheless, a significant hurdle in harnessing the benefits of accumulated data lies in the lack of direct communication between technical specialists, decision-makers, and business process analysts. To overcome this issue, the application of collaborative business intelligence (CBI) emerges as a viable solution. This research focuses on the applications of data mining and aims to model CBI processes within distributed virtual teams through the interaction of users and a CBI Virtual Assistant. The proposed virtual assistant for CBI endeavors to enhance data exploration accessibility for a wider range of users and streamline the time and effort required for data analysis. The key contributions of this study encompass: 1) a reference model representing collaborative BI, inspired by linguistic theory; 2) an approach that enables the transformation of user queries into executable commands, thereby facilitating their utilization within data exploration software; and 3) the primary workflow of a conversational agent designed for data analytics.