Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation of complex latent-state posteriors. In this work, we build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference by combining particle methods and variational inference. While standard VSMC operates in the offline mode, by re-processing repeatedly a given batch of data, we distribute the approximation of the gradient of the VSMC surrogate ELBO in time using stochastic approximation, allowing for online learning in the presence of streams of data. This results in an algorithm, online VSMC, that is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation. In addition, we provide rigorous theoretical results describing the algorithm's convergence properties as the number of data tends to infinity as well as numerical illustrations of its excellent convergence properties and usefulness also in batch-processing settings.
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Hypergraphs, with hyperedges connecting more than two nodes, are key for modelling higher-order interactions in real-world data. The success of graph neural networks (GNNs) reveals the capability of neural networks to process data with pairwise interactions. This inspires the usage of neural networks for data with higher-order interactions, thereby leading to the development of hypergraph neural networks (HyperGNNs). GNNs and HyperGNNs are typically considered distinct since they are designed for data on different geometric topologies. However, in this paper, we theoretically demonstrate that, in the context of node classification, most HyperGNNs can be approximated using a GNN with a weighted clique expansion of the hypergraph. This leads to WCE-GNN, a simple and efficient framework comprising a GNN and a weighted clique expansion (WCE), for hypergraph node classification. Experiments on nine real-world hypergraph node classification benchmarks showcase that WCE-GNN demonstrates not only higher classification accuracy compared to state-of-the-art HyperGNNs, but also superior memory and runtime efficiency.
Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many subtasks, which compete for resources (measured by the number of neurons allocated to subtasks). On toy problems, we empirically find that: (1) The loss of a subtask is inversely proportional to its allocated neurons. (2) When multiple subtasks are present in a composite task, the resources acquired by each subtask uniformly grow as models get larger, keeping the ratios of acquired resources constants. We hypothesize these findings to be generally true and build a model to predict neural scaling laws for general composite tasks, which successfully replicates the neural scaling law of Chinchilla models reported in arXiv:2203.15556. We believe that the notion of resource used in this paper will be a useful tool for characterizing and diagnosing neural networks.
We study online changepoint detection in the context of a linear regression model. We propose a class of heavily weighted statistics based on the CUSUM process of the regression residuals, which are specifically designed to ensure timely detection of breaks occurring early on during the monitoring horizon. We subsequently propose a class of composite statistics, constructed using different weighing schemes; the decision rule to mark a changepoint is based on the largest statistic across the various weights, thus effectively working like a veto-based voting mechanism, which ensures fast detection irrespective of the location of the changepoint. Our theory is derived under a very general form of weak dependence, thus being able to apply our tests to virtually all time series encountered in economics, medicine, and other applied sciences. Monte Carlo simulations show that our methodologies are able to control the procedure-wise Type I Error, and have short detection delays in the presence of breaks.
Current clustering priors for deep latent variable models (DLVMs) require defining the number of clusters a-priori and are susceptible to poor initializations. Addressing these deficiencies could greatly benefit deep learning-based scRNA-seq analysis by performing integration and clustering simultaneously. We adapt the VampPrior (Tomczak & Welling, 2018) into a Dirichlet process Gaussian mixture model, resulting in the VampPrior Mixture Model (VMM), a novel prior for DLVMs. We propose an inference procedure that alternates between variational inference and Empirical Bayes to cleanly distinguish variational and prior parameters. Using the VMM in a Variational Autoencoder attains highly competitive clustering performance on benchmark datasets. Augmenting scVI (Lopez et al., 2018), a popular scRNA-seq integration method, with the VMM significantly improves its performance and automatically arranges cells into biologically meaningful clusters.
Graph learning architectures based on the k-dimensional Weisfeiler-Leman (k-WL) hierarchy offer a theoretically well-understood expressive power. However, such architectures often fail to deliver solid predictive performance on real-world tasks, limiting their practical impact. In contrast, global attention-based models such as graph transformers demonstrate strong performance in practice, but comparing their expressive power with the k-WL hierarchy remains challenging, particularly since these architectures rely on positional or structural encodings for their expressivity and predictive performance. To address this, we show that the recently proposed Edge Transformer, a global attention model operating on node pairs instead of nodes, has at least 3-WL expressive power. Empirically, we demonstrate that the Edge Transformer surpasses other theoretically aligned architectures regarding predictive performance while not relying on positional or structural encodings.
Maximum likelihood estimation (MLE) of latent variable models is often recast as an optimization problem over the extended space of parameters and probability distributions. For example, the Expectation Maximization (EM) algorithm can be interpreted as coordinate descent applied to a suitable free energy functional over this space. Recently, this perspective has been combined with insights from optimal transport and Wasserstein gradient flows to develop particle-based algorithms applicable to wider classes of models than standard EM. Drawing inspiration from prior works which interpret `momentum-enriched' optimisation algorithms as discretizations of ordinary differential equations, we propose an analogous dynamical systems-inspired approach to minimizing the free energy functional over the extended space of parameters and probability distributions. The result is a dynamic system that blends elements of Nesterov's Accelerated Gradient method, the underdamped Langevin diffusion, and particle methods. Under suitable assumptions, we establish quantitative convergence of the proposed system to the unique minimiser of the functional in continuous time. We then propose a numerical discretization of this system which enables its application to parameter estimation in latent variable models. Through numerical experiments, we demonstrate that the resulting algorithm converges faster than existing methods and compares favourably with other (approximate) MLE algorithms.
Training machine learning models can be very expensive or even unaffordable. This may be, for example, due to data limitations (unavailability or being too large), or computational power limitations. Therefore, it is a common practice to rely on open-source pre-trained models whenever possible. However, this practice is alarming from a security perspective. Pre-trained models can be infected with Trojan attacks, in which the attacker embeds a trigger in the model such that the model's behavior can be controlled by the attacker when the trigger is present in the input. In this paper, we present a novel method for detecting Trojan models. Our method creates a signature for a model based on activation optimization. A classifier is then trained to detect a Trojan model given its signature. We call our method TRIGS for TRojan Identification from Gradient-based Signatures. TRIGS achieves state-of-the-art performance on two public datasets of convolutional models. Additionally, we introduce a new challenging dataset of ImageNet models based on the vision transformer architecture. TRIGS delivers the best performance on the new dataset, surpassing the baseline methods by a large margin. Our experiments also show that TRIGS requires only a small amount of clean samples to achieve good performance, and works reasonably well even if the defender does not have prior knowledge about the attacker's model architecture. Our dataset will be released soon.
Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.
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.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
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