Abstract-- This paper investigates a passivity-based approach to output consensus analysis in heterogeneous networks com - posed of non-identical agents coupled via nonlinear intera ctions, in the presence of measurement and/or communication noise. Focusing on agents that are input-feedforward passive (IFP), we first examine whether a shortage of passivity in some agents can be compensated by a passivity surplus in others, in the sense of preserving the passivity of the transformed open-l oop system defined by the agent dynamics and network topology. We show that such compensation is only feasible when at most one agent lacks passivity, and we characterise how this defic it can be offset using the excess passivity within the group of agents. For general networks, we then investigate passivit y compensation within the feedback interconnection by lever aging the passivity surplus in the coupling links to locally compe nsate for the lack of passivity in the adjacent agents. In particul ar, a distributed condition, expressed in terms of passivity in dices and coupling gains, is derived to ensure output consensus of the interconnected network.

Topic modeling is a powerful technique for uncovering hidden themes within a collection of documents. However, the effectiveness of traditional topic models often relies on sufficient word co-occurrence, which is lacking in short texts. Therefore, existing approaches, whether probabilistic or neural, frequently struggle to extract meaningful patterns from such data, resulting in incoherent topics. To address this challenge, we propose a novel approach that leverages large language models (LLMs) to extend short texts into more detailed sequences before applying topic modeling. To further improve the efficiency and solve the problem of semantic inconsistency from LLM-generated texts, we propose to use prefix tuning to train a smaller language model coupled with a variational autoencoder for short-text topic modeling. Our method significantly improves short-text topic modeling performance, as demonstrated by extensive experiments on real-world datasets with extreme data sparsity, outperforming current state-of-the-art topic models.

Bayesian Optimization (BO) (Shahriari et al., 2015) is a popular sample-efficient optimization technique to solve problems where the objective is expensive. It has been successfully applied in diverse areas (Greenhill et al., 2020) including material discovery (Li et al., 2017), alloy design (Barnett et al., 2020) and molecular design (Gómez-Bombarelli et al., 2018). However, standard BO typically operates tabula rasa, building its model of the objective from minimal priors that do not include domain-specific information. While there has been some progress made incorporating domain-specific knowledge to accelerate BO (Li et al., 2018; Hvarfner et al., 2022) or transfer learning from previous experiments (Shilton et al., 2017), it remains the case that there is a significant corpus of knowledge and expertise that could potentially accelerate BO even further but which remain largely untapped due to the inherent complexities involved in knowledge extraction and exploitation. In particular, this often arises from the fact that experts tend to organize their knowledge in complex schema containing concepts, attributes and relationships (Rousseau, 2001), making the elicitation of relevant expert knowledge, both quantitative and qualitative, a difficult task.

An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions designed such that the resulting hypothesis space is permutation invariant. Prior work on deep sets indicates that such readouts might require complex node embeddings that can be difficult to learn via standard neighborhood aggregation schemes. Motivated by this, we investigate the potential of adaptive readouts given by neural networks that do not necessarily give rise to permutation invariant hypothesis spaces. We argue that in some problems such as binding affinity prediction where molecules are typically presented in a canonical form it might be possible to relax the constraints on permutation invariance of the hypothesis space and learn a more effective model of the affinity by employing an adaptive readout function. Our empirical results demonstrate the effectiveness of neural readouts on more than 40 datasets spanning different domains and graph characteristics. Moreover, we observe a consistent improvement over standard readouts (i.e., sum, max, and mean) relative to the number of neighborhood aggregation iterations and different convolutional operators.

Unsupervised ensemble learning has long been an interesting yet challenging problem that comes to prominence in recent years with the increasing demand of crowdsourcing in various applications. In this paper, we propose a novel method-- unsupervised ensemble learning via Ising model approximation (unElisa) that combines a pruning step with a predicting step. We focus on the binary case and use an Ising model to characterize interactions between the ensemble and the underlying true classifier. The presence of an edge between an observed classifier and the true classifier indicates a direct dependence whereas the absence indicates the corresponding one provides no additional information and shall be eliminated. This observation leads to the pruning step where the key is to recover the neighborhood of the true classifier. We show that it can be recovered successfully with exponentially decaying error in the high-dimensional setting by performing nodewise $\ell_1$-regularized logistic regression. The pruned ensemble allows us to get a consistent estimate of the Bayes classifier for predicting. We also propose an augmented version of majority voting by reversing all labels given by a subgroup of the pruned ensemble. We demonstrate the efficacy of our method through extensive numerical experiments and through the application to EHR-based phenotyping prediction on Rheumatoid Arthritis (RA) using data from Partners Healthcare System.

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these hypotheses may concern a wide range of parameters, with complex and unknown dependence structures among variables. In analyzing such hypothesis testing procedures, gains in efficiency and power can be achieved by performing variable reduction on the set of hypotheses prior to testing. We present in this paper an approach using data-adaptive multiple testing that serves exactly this purpose. This approach applies data mining techniques to screen the full set of covariates on equally sized partitions of the whole sample via cross-validation. This generalized screening procedure is used to create average ranks for covariates, which are then used to generate a reduced (sub)set of hypotheses, from which we compute test statistics that are subsequently subjected to standard multiple testing corrections. The principal advantage of this methodology lies in its providing valid statistical inference without the \textit{a priori} specifying which hypotheses will be tested. Here, we present the theoretical details of this approach, confirm its validity via a simulation study, and exemplify its use by applying it to the analysis of data on microRNA differential expression.