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Probabilistic Methods · Bayesian Models and Methods

Cornelius Schröder, Jakob Macke

Many scientific models are composed of multiple discrete components, and scientists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in a simulation-based inference framework: We define model priors over candidate components and, from model simulations, train neural networks to infer joint probability distributions over both model components and associated parameters. Our method, simulation-based model inference (SBMI), represents distributions over model components as a conditional mixture of multivariate binary distributions in the Grassmann formalism. SBMI can be applied to any compositional stochastic simulator without requiring likelihood evaluations. We evaluate SBMI on a simple time series model and on two scientific models from neuroscience, and show that it can discover multiple data-consistent model configurations, and that it reveals non-identifiable model components and parameters. SBMI provides a powerful tool for data-driven scientific inquiry which will allow scientists to identify essential model components and make uncertainty-informed modelling decisions.

Deep Learning · Sequential Models, Time series

Weijieying Ren, Xiaoting Li, Huiyuan Chen, Vineeth Rakesh, Zhuoyi Wang, Mahashweta Das, Vasant Honavar

We consider the problem of test-time adaptation of predictive models trained on tabular data. Effective solution of this problem requires adaptation of predictive models trained on the source domain to a target domain, using only unlabeled target domain data, without access to source domain data. Existing test-time adaptation methods for tabular data have difficulty coping with the heterogeneous features and their complex dependencies inherent in tabular data. To overcome these limitations, we consider test-time adaptation in the setting wherein the logical structure of the rules is assumed to remain invariant despite distribution shift between source and target domains whereas the numerical parameters associated with the rules and the weights assigned to them can vary to accommodate distribution shift. TabLog discretizes numerical features, models dependencies between heterogeneous features, introduces a novel contrastive loss for coping with distribution shift, and presents an end-to-end framework for efficient training and test-time adaptation by taking advantage of a logical neural network representation of a rule ensemble. We present results of experiments using several benchmark data sets that demonstrate TabLog is competitive with or improves upon the state-of-the-art methods for test-time adaptation of predictive models trained on tabular data. Our code is available at https://github.com/WeijieyingRen/TabLog.

Ankit Pensia

We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a *corrupted* set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in \mathbb{R}^d$ is constrained to be $k$-sparse. A series of prior works has developed efficient algorithms for robust sparse mean estimation with sample complexity $\mathrm{poly}(k,\log d, 1/\epsilon)$ and runtime $d^2 \mathrm{poly}(k,\log d,1/\epsilon)$, where $\epsilon$ is the fraction of contamination. In particular, the fastest runtime of existing algorithms is quadratic in the dimension, which can be prohibitive in high dimensions. This quadratic barrier in the runtime stems from the reliance of these algorithms on the sample covariance matrix, which is of size $d^2$. Our main contribution is an algorithm for robust sparse mean estimation which runs in _subquadratic_ time using $\mathrm{poly}(k,\log d,1/\epsilon)$ samples. Our results build on algorithmic advances in detecting weak correlations, a generalized version of the light-bulb problem by Valiant (2015).

Deep Learning · Sequential Models, Time series

Rom N. Parnichkun, Stefano Massaroli, Alessandro Moro, Jimmy Smith, Ramin Hasani, Mathias Lechner, Qi An, Christopher Re, Hajime Asama, Stefano Ermon 等

We approach designing a state-space model for deep learning applications through its dual representation, the *transfer function*, and uncover a highly efficient sequence parallel inference algorithm that is *state-free*: unlike other proposed algorithms, state-free inference does not incur any significant memory or computational cost with an increase in state size. We achieve this using properties of the proposed frequency domain transfer function parametrization, which enables direct computation of its corresponding convolutional kernel's spectrum via a single Fast Fourier Transform. Our experimental results across multiple sequence lengths and state sizes illustrates, on average, a 35% training speed improvement over S4 layers -- parametrized in time-domain -- on the Long Range Arena benchmark, while delivering state-of-the-art downstream performances over other attention-free approaches. Moreover, we report improved perplexity in language modeling over a long convolutional Hyena baseline, by simply introducing our transfer function parametrization. Our code is available at https://github.com/ruke1ire/RTF.

Applications · Time Series

Zijie Pan, Yushan Jiang, Sahil Garg, Anderson Schneider, Yuriy Nevmyvaka, Dongjin Song

Recently, there has been a growing interest in leveraging pre-trained large language models (LLMs) for various time series applications. However, the semantic space of LLMs, established through the pre-training, is still underexplored and may help yield more distinctive and informative representations to facilitate time series forecasting. To this end, we propose Semantic Space Informed Prompt learning with LLM ($S^2$IP-LLM) to align the pre-trained semantic space with time series embedding space and perform time series forecasting based on learned prompts from the joint space. We first design a tokenization module tailored for cross-modality alignment, which explicitly concatenates patches of decomposed time series components to create embeddings that effectively encode the temporal dynamics. Next, we leverage the pre-trained word token embeddings to derive semantic anchors and align selected anchors with time series embeddings by maximizing the cosine similarity in the joint space. This way, $S^2$IP-LLM can retrieve relevant semantic anchors as prompts to provide strong indicators (context) for time series that exhibit different temporal dynamics. With thorough empirical studies on multiple benchmark datasets, we demonstrate that the proposed $S^2$IP-LLM can achieve superior forecasting performance over state-of-the-art baselines. Furthermore, our ablation studies and visualizations verify the necessity of prompt learning informed by semantic space.

Applications · Neuroscience, Cognitive Science

Noga Mudrik, Gal Mishne, Adam Charles

Time series data across scientific domains are often collected under distinct states (e.g., tasks), wherein latent processes (e.g., biological factors) create complex inter- and intra-state variability. A key approach to capture this complexity is to uncover fundamental interpretable units within the data, Building Blocks (BBs), which modulate their activity and adjust their structure across observations. Existing methods for identifying BBs in multi-way data often overlook inter- vs. intra-state variability, produce uninterpretable components, or do not align with properties of real-world data, such as missing samples and sessions of different duration. Here, we present a framework for Similarity-driven Building Block Inference using Graphs across States (SiBBlInGS). SiBBlInGS offers a graph-based dictionary learning approach for discovering sparse BBs along with their temporal traces, based on co-activity patterns and inter- vs. intra-state relationships. Moreover, SiBBlInGS captures per-trial temporal variability and controlled cross-state structural BB adaptations, identifies state-specific vs. state-invariant components, and accommodates variability in the number and duration of observed sessions across states. We demonstrate SiBBlInGS's ability to reveal insights into complex phenomena as well as its robustness to noise and missing samples through several synthetic and real-world examples, including web search and neural data.

Deep Learning · Sequential Models, Time series

William Merrill, Jackson Petty, Ashish Sabharwal

State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill & Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). *But do SSMs truly have an advantage (over transformers) in expressive power for state tracking?* Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class $\mathsf{TC}^0$. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state'' in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems.

Deep Learning · Sequential Models, Time series

Ivan Marisca, Cesare Alippi, Filippo Maria Bianchi

Given a set of synchronous time series, each associated with a sensor-point in space and characterized by inter-series relationships, the problem of spatiotemporal forecasting consists of predicting future observations for each point. Spatiotemporal graph neural networks achieve striking results by representing the relationships across time series as a graph. Nonetheless, most existing methods rely on the often unrealistic assumption that inputs are always available and fail to capture hidden spatiotemporal dynamics when part of the data is missing. In this work, we tackle this problem through hierarchical spatiotemporal downsampling. The input time series are progressively coarsened over time and space, obtaining a pool of representations that capture heterogeneous temporal and spatial dynamics. Conditioned on observations and missing data patterns, such representations are combined by an interpretable attention mechanism to generate the forecasts. Our approach outperforms state-of-the-art methods on synthetic and real-world benchmarks under different missing data distributions, particularly in the presence of contiguous blocks of missing values.

Applications · Neuroscience, Cognitive Science

Changze Lv, Yansen Wang, Dongqi Han, Xiaoqing Zheng, Xuanjing Huang, Dongsheng Li

Spiking neural networks (SNNs), inspired by the spiking behavior of biological neurons, provide a unique pathway for capturing the intricacies of temporal data. However, applying SNNs to time-series forecasting is challenging due to difficulties in effective temporal alignment, complexities in encoding processes, and the absence of standardized guidelines for model selection. In this paper, we propose a framework for SNNs in time-series forecasting tasks, leveraging the efficiency of spiking neurons in processing temporal information. Through a series of experiments, we demonstrate that our proposed SNN-based approaches achieve comparable or superior results to traditional time-series forecasting methods on diverse benchmarks with much less energy consumption. Furthermore, we conduct detailed analysis experiments to assess the SNN's capacity to capture temporal dependencies within time-series data, offering valuable insights into its nuanced strengths and effectiveness in modeling the intricate dynamics of temporal data. Our study contributes to the expanding field of SNNs and offers a promising alternative for time-series forecasting tasks, presenting a pathway for the development of more biologically inspired and temporally aware forecasting models. Our code is available at https://github.com/microsoft/SeqSNN.

Applications · Time Series

Bin Lu, Ze Zhao, Luyu Han, Xiaoying Gan, Yuntao Zhou, Lei Zhou, Luoyi Fu, Xinbing Wang, Chenghu Zhou, Jing Zhang

Accurately reconstructing the global ocean deoxygenation over a century is crucial for assessing and protecting marine ecosystem. Existing expert-dominated numerical simulations fail to catch up with the dynamic variation caused by global warming and human activities. Besides, due to the high-cost data collection, the historical observations are severely sparse, leading to big challenge for precise reconstruction. In this work, we propose OxyGenerator, the first deep learning based model, to reconstruct the global ocean deoxygenation from 1920 to 2023. Specifically, to address the heterogeneity across large temporal and spatial scales, we propose zoning-varying graph message-passing to capture the complex oceanographic correlations between missing values and sparse observations. Additionally, to further calibrate the uncertainty, we incorporate inductive bias from dissolved oxygen (DO) variations and chemical effects. Compared with in-situ DO observations, OxyGenerator significantly outperforms CMIP6 numerical simulations, reducing MAPE by 38.77%, demonstrating a promising potential to understand the “breathless ocean” in data-driven manner.

Applications · Time Series

Junxin Lu, Shiliang Sun

Unsupervised domain adaptation of multivariate time series aims to train a model to adapt its classification ability from a labeled source domain to an unlabeled target domain, where there are differences in the distribution between domains. Existing methods extract domain-invariant features directly via a shared feature extractor, neglecting the exploration of the underlying causal patterns, which undermines their reliability, especially in complex multivariate dynamic systems. To address this problem, we propose CauDiTS, an innovative framework for unsupervised domain adaptation of multivariate time series. CauDiTS adopts an adaptive rationale disentangler to disentangle domain-common causal rationales and domain-specific correlations from variable interrelationships. The stability of causal rationales across domains is vital for filtering domainspecific perturbations and facilitating the extraction of domain-invariant representations. Moreover, we promote the cross-domain consistency of intra-class causal rationales employing the learning strategies of causal prototype consistency and domain-intervention causality invariance. CauDiTS is evaluated on four benchmark datasets, demonstrating its effectiveness and outperforming state-of-the-art methods.

Applications · Time Series

Jiecheng Lu, Xu Han, Sun, Shihao Yang

For Multivariate Time Series Forecasting (MTSF), recent deep learning applications show that univariate models frequently outperform multivariate ones. To address the deficiency in multivariate models, we introduce a method to Construct Auxiliary Time Series (CATS) that functions like a 2D temporal-contextual attention mechanism, which generates Auxiliary Time Series (ATS) from Original Time Series (OTS) to effectively represent and incorporate inter-series relationships for forecasting. Key principles of ATS—continuity, sparsity, and variability—are identified and implemented through different modules. Even with a basic 2-layer MLP as the core predictor, CATS achieves state-of-the-art, significantly reducing complexity and parameters compared to previous multivariate models, marking it as an efficient and transferable MTSF solution.

Deep Learning · Sequential Models, Time series

Maude Lizaire, Michael Rizvi-Martel, Marawan Gamal, Guillaume Rabusseau

Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied models from formal language theory. However, their large parameter tensor makes computations intractable. To circumvent this issue, one approach known as MIRNN consists in limiting the type of interactions used by the model. Another is to leverage tensor decomposition to diminish the parameter count. In this work, we study the model resulting from parameterizing 2RNNs using the CP decomposition, which we call CPRNN. Intuitively, the rank of the decomposition should reduce expressivity. We analyze how rank and hidden size affect model capacity and show the relationships between RNNs, 2RNNs, MIRNNs, and CPRNNs based on these parameters. We support these results empirically with experiments on the Penn Treebank dataset which demonstrate that, with a fixed parameter budget, CPRNNs outperforms RNNs, 2RNNs, and MIRNNs with the right choice of rank and hidden size.

Deep Learning · Sequential Models, Time series

Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progress has been achieved with the emergence of large language models, exhibiting unprecedented abilities such as few-shot generalization, scalability, and task generality, which are however absent in small deep models. To change the status quo of training scenario-specific small models from scratch, this paper aims at the early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), which is generative pre-trained by next token prediction and adapted to various downstream tasks with promising capabilities as an LTSM. Code and datasets are available at: https://github.com/thuml/Large-Time-Series-Model.

Deep Learning · Sequential Models, Time series

Yongtuo Liu, Sara Magliacane, Miltiadis (Miltos) Kofinas, Efstratios Gavves

Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage paradigm, i.e. they first group time series into small cluster fragments and then discover equations in each fragment separately through methods in non-hybrid systems. Although effective, performance is then limited because these methods ignore the commonalities in the shared dynamics of fragments that are driven by the same equations. Besides, the two-stage paradigm breaks the interdependence between categorizing and representing dynamics that jointly form hybrid systems. In this paper, we reformulate the problem and propose an end-to-end learning framework, i.e. Amortized Equation Discovery (AMORE), to jointly categorize modes and discover equations characterizing motion dynamics of each mode by all segments of the mode. Experiments on four hybrid and six non-hybrid systems demonstrate the superior performance of our method against previous methods on equation discovery, segmentation, and forecasting.

Deep Learning · Sequential Models, Time series

Fusheng Liu, Qianxiao Li

A State Space Model (SSM) is a foundation model in time series analysis, which has recently been shown as an alternative to transformers in sequence modeling. In this paper, we theoretically study the generalization of SSMs and propose improvements to training algorithms based on the generalization results. Specifically, we give a *data-dependent* generalization bound for SSMs, showing an interplay between the SSM parameters and the temporal dependencies of the training sequences. Leveraging the generalization bound, we (1) set up a scaling rule for model initialization based on the proposed generalization measure, which significantly improves the robustness of the output value scales on SSMs to different temporal patterns in the sequence data; (2) introduce a new regularization method for training SSMs to enhance the generalization performance. Numerical results are conducted to validate our results.

Applications · Time Series

Shengsheng Lin, Weiwei Lin, Wentai Wu, Haojun Chen, Junjie Yang

This paper introduces SparseTSF, a novel, extremely lightweight model for Long-term Time Series Forecasting (LTSF), designed to address the challenges of modeling complex temporal dependencies over extended horizons with minimal computational resources. At the heart of SparseTSF lies the Cross-Period Sparse Forecasting technique, which simplifies the forecasting task by decoupling the periodicity and trend in time series data. This technique involves downsampling the original sequences to focus on cross-period trend prediction, effectively extracting periodic features while minimizing the model's complexity and parameter count. Based on this technique, the SparseTSF model uses fewer than *1k* parameters to achieve competitive or superior performance compared to state-of-the-art models. Furthermore, SparseTSF showcases remarkable generalization capabilities, making it well-suited for scenarios with limited computational resources, small samples, or low-quality data. The code is publicly available at this repository: https://github.com/lss-1138/SparseTSF.

Applications · Time Series

Xin Li, Jingdong Zhang, Qunxi Zhu, Chengli Zhao, Xue Zhang, Xiaojun Duan, Wei Lin

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a simulation-free framework, called Fourier NODEs (FNODEs), that effectively trains NODEs by directly matching the target vector field based on Fourier analysis. Specifically, we employ the Fourier analysis to estimate temporal and potential high-order spatial gradients from noisy observational data. We then incorporate the estimated spatial gradients as additional inputs to a neural network. Furthermore, we utilize the estimated temporal gradient as the optimization objective for the output of the neural network. Later, the trained neural network generates more data points through an ODE solver without participating in the computational graph, facilitating more accurate estimations of gradients based on Fourier analysis. These two steps form a positive feedback loop, enabling accurate dynamics modeling in our framework. Consequently, our approach outperforms state-of-the-art methods in terms of training time, dynamics prediction, and robustness. Finally, we demonstrate the superior performance of our framework using a number of representative complex systems.

Deep Learning · Sequential Models, Time series

Zichong Li, Qunzhi Xu, Zhenghao Xu, Yajun Mei, Tuo Zhao, Hongyuan Zha

Spatio-temporal point processes (STPPs) are potent mathematical tools for modeling and predicting events with both temporal and spatial features. Despite their versatility, most existing methods for learning STPPs either assume a restricted form of the spatio-temporal distribution, or suffer from inaccurate approximations of the intractable integral in the likelihood training objective. These issues typically arise from the normalization term of the probability density function. Moreover, existing works only provide point prediction for events without quantifying their uncertainty, such as confidence intervals for the event's arrival time and confidence regions for the event's location, which is crucial given the considerable randomness of the data. To tackle these challenges, we introduce SMASH: a Score MAtching-based pSeudolikeliHood estimator for learning marked STPPs. Specifically, our framework adopts a normalization-free objective by estimating the pseudolikelihood of marked STPPs through score-matching and predicts confidence intervals/regions for event time and location by generating samples through a score-based sampling algorithm. The superior performance of our proposed framework is demonstrated through extensive experiments on both point and confidence interval/region prediction of events.

Applications · Time Series

Zhonghang Li, Lianghao Xia, Yong Xu, Chao Huang

The objective of traffic prediction is to accurately forecast and analyze the dynamics of transportation patterns, considering both space and time. However, the presence of distribution shift poses a significant challenge in this field, as existing models struggle to generalize well when faced with test data that significantly differs from the training distribution. To tackle this issue, this paper introduces a simple and universal spatio-temporal prompt-tuning framework-FlashST, which adapts pre-trained models to the specific characteristics of diverse downstream datasets, improving generalization in diverse traffic prediction scenarios. Specifically, the FlashST framework employs a lightweight spatio-temporal prompt network for in-context learning, capturing spatio-temporal invariant knowledge and facilitating effective adaptation to diverse scenarios. Additionally, we incorporate a distribution mapping mechanism to align the data distributions of pre-training and downstream data, facilitating effective knowledge transfer in spatio-temporal forecasting. Empirical evaluations demonstrate the effectiveness of our FlashST across different spatio-temporal prediction tasks using diverse urban datasets. Code is available at [https://github.com/HKUDS/FlashST](https://github.com/HKUDS/FlashST).