This paper addresses uncertainty propagation on unimodular matrix Lie groups that have a surjective exponential map. We derive the exact formula for the propagation of mean and covariance in a continuous-time setting from the governing Fokker-Planck equation. Two approximate propagation methods are discussed based on the exact formula. One uses numerical quadrature and another utilizes the expansion of moments. A closed-form second-order propagation formula is derived. We apply the general theory to the joint attitude and angular momentum uncertainty propagation problem and numerical experiments demonstrate two approximation methods. These results show that our new methods have high accuracy while being computationally efficient.
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Offline reinforcement learning (RL) is challenged by the distributional shift problem. To address this problem, existing works mainly focus on designing sophisticated policy constraints between the learned policy and the behavior policy. However, these constraints are applied equally to well-performing and inferior actions through uniform sampling, which might negatively affect the learned policy. To alleviate this issue, we propose Offline Prioritized Experience Replay (OPER), featuring a class of priority functions designed to prioritize highly-rewarding transitions, making them more frequently visited during training. Through theoretical analysis, we show that this class of priority functions induce an improved behavior policy, and when constrained to this improved policy, a policy-constrained offline RL algorithm is likely to yield a better solution. We develop two practical strategies to obtain priority weights by estimating advantages based on a fitted value network (OPER-A) or utilizing trajectory returns (OPER-R) for quick computation. OPER is a plug-and-play component for offline RL algorithms. As case studies, we evaluate OPER on five different algorithms, including BC, TD3+BC, Onestep RL, CQL, and IQL. Extensive experiments demonstrate that both OPER-A and OPER-R significantly improve the performance for all baseline methods. Codes and priority weights are availiable at //github.com/sail-sg/OPER.
Although continuous advances in theoretical modelling of Molecular Communications (MC) are observed, there is still an insuperable gap between theory and experimental testbeds, especially at the microscale. In this paper, the development of the first testbed incorporating engineered yeast cells is reported. Different from the existing literature, eukaryotic yeast cells are considered for both the sender and the receiver, with {\alpha}-factor molecules facilitating the information transfer. The use of such cells is motivated mainly by the well understood biological mechanism of yeast mating, together with their genetic amenability. In addition, recent advances in yeast biosensing establish yeast as a suitable detector and a neat interface to in-body sensor networks. The system under consideration is presented first, and the mathematical models of the underlying biological processes leading to an end-to-end (E2E) system are given. The experimental setup is then described and used to obtain experimental results which validate the developed mathematical models. Beyond that, the ability of the system to effectively generate output pulses in response to repeated stimuli is demonstrated, reporting one event per two hours. However, fast RNA fluctuations indicate cell responses in less than three minutes, demonstrating the potential for much higher rates in the future.
The family of log-concave density functions contains various kinds of common probability distributions. Due to the shape restriction, it is possible to find the nonparametric estimate of the density, for example, the nonparametric maximum likelihood estimate (NPMLE). However, the associated uncertainty quantification of the NPMLE is less well developed. The current techniques for uncertainty quantification are Bayesian, using a Dirichlet process prior combined with the use of Markov chain Monte Carlo (MCMC) to sample from the posterior. In this paper, we start with the NPMLE and use a version of the martingale posterior distribution to establish uncertainty about the NPMLE. The algorithm can be implemented in parallel and hence is fast. We prove the convergence of the algorithm by constructing suitable submartingales. We also illustrate results with different models and settings and some real data, and compare our method with that within the literature.
We deal with a normal form for context-free grammars, called Dyck normal form. This normal form is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired nonterminals. This pairwise property, along with several other terminal rewriting conditions, makes it possible to define a homomorphism from Dyck words to words generated by a grammar in Dyck normal form. We prove that for each context-free language L, there exist an integer K and a homomorphism phi such that L=phi(D'_K), where D'_K is a subset of D_K and D_K is the one-sided Dyck language over K letters. As an application we give an alternative proof of the inclusion of the class of even linear languages in AC1.
The extraction of modular object-centric representations for downstream tasks is an emerging area of research. Learning grounded representations of objects that are guaranteed to be stable and invariant promises robust performance across different tasks and environments. Slot Attention (SA) learns object-centric representations by assigning objects to \textit{slots}, but presupposes a \textit{single} distribution from which all slots are randomly initialised. This results in an inability to learn \textit{specialized} slots which bind to specific object types and remain invariant to identity-preserving changes in object appearance. To address this, we present \emph{\textsc{Co}nditional \textsc{S}lot \textsc{A}ttention} (\textsc{CoSA}) using a novel concept of \emph{Grounded Slot Dictionary} (GSD) inspired by vector quantization. Our proposed GSD comprises (i) canonical object-level property vectors and (ii) parametric Gaussian distributions, which define a prior over the slots. We demonstrate the benefits of our method in multiple downstream tasks such as scene generation, composition, and task adaptation, whilst remaining competitive with SA in popular object discovery benchmarks.
Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap, this paper presents a novel Gaussian variational estimation algorithm for the multidimensional generalized partial credit model (MGPCM). The proposed algorithm demonstrates both fast and accurate performance, as illustrated through a series of simulation studies and two real data analyses.
Federated learning (FL) has been proposed to protect data privacy and virtually assemble the isolated data silos by cooperatively training models among organizations without breaching privacy and security. However, FL faces heterogeneity from various aspects, including data space, statistical, and system heterogeneity. For example, collaborative organizations without conflict of interest often come from different areas and have heterogeneous data from different feature spaces. Participants may also want to train heterogeneous personalized local models due to non-IID and imbalanced data distribution and various resource-constrained devices. Therefore, heterogeneous FL is proposed to address the problem of heterogeneity in FL. In this survey, we comprehensively investigate the domain of heterogeneous FL in terms of data space, statistical, system, and model heterogeneity. We first give an overview of FL, including its definition and categorization. Then, We propose a precise taxonomy of heterogeneous FL settings for each type of heterogeneity according to the problem setting and learning objective. We also investigate the transfer learning methodologies to tackle the heterogeneity in FL. We further present the applications of heterogeneous FL. Finally, we highlight the challenges and opportunities and envision promising future research directions toward new framework design and trustworthy approaches.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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