Marked Temporal Bayesian Flow Point Processes

Marked event data captures events by recording their continuous-valued occurrence timestamps along with their corresponding discrete-valued types. They have appeared in various real-world scenarios such as social media, financial transactions, and healthcare records, and have been effectively modeled through Marked Temporal Point Process (MTPP) models. Recently, developing generative models for these MTPP models have seen rapid development due to their powerful generative capability and less restrictive functional forms. However, existing generative MTPP models are usually challenged in jointly modeling events' timestamps and types since: (1) mainstream methods design the generative mechanisms for timestamps only and do not include event types; (2) the complex interdependence between the timestamps and event types are overlooked. In this paper, we propose a novel generative MTPP model called BMTPP. Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach. Additionally, by adding joint noise to the marked temporal data space, BMTPP effectively captures and explicitly reveals the interdependence between timestamps and event types. Extensive experiments validate the superiority of our approach over other state-of-the-art models and its ability to effectively capture marked-temporal interdependence.

Learning Coupled Subspaces for Multi-Condition Spike Data

In neuroscience, researchers typically conduct experiments under multiple conditions to acquire neural responses in the form of high-dimensional spike train datasets. Analysing high-dimensional spike data is a challenging statistical problem. To this end, Gaussian process factor analysis (GPFA), a popular class of latent variable models has been proposed. GPFA extracts smooth, low-dimensional latent trajectories underlying high-dimensional spike train datasets. However, such analyses are often done separately for each experimental condition, contrary to the nature of neural datasets, which contain recordings under multiple experimental conditions. Exploiting the parametric nature of these conditions, we propose a multi-condition GPFA model and inference procedure to learn the underlying latent structure in the corresponding datasets in sample-efficient manner. In particular, we propose a non-parametric Bayesian approach to learn a smooth tuning function over the experiment condition space. Our approach not only boosts model accuracy and is faster, but also improves model interpretability compared to approaches that separately fit models for each experimental condition.

Federated Neural Nonparametric Point Processes

Temporal point processes (TPPs) are effective for modeling event occurrences over time, but they struggle with sparse and uncertain events in federated systems, where privacy is a major concern. To address this, we propose \textit{FedPP}, a Federated neural nonparametric Point Process model. FedPP integrates neural embeddings into Sigmoidal Gaussian Cox Processes (SGCPs) on the client side, which is a flexible and expressive class of TPPs, allowing it to generate highly flexible intensity functions that capture client-specific event dynamics and uncertainties while efficiently summarizing historical records. For global aggregation, FedPP introduces a divergence-based mechanism that communicates the distributions of SGCPs' kernel hyperparameters between the server and clients, while keeping client-specific parameters local to ensure privacy and personalization. FedPP effectively captures event uncertainty and sparsity, and extensive experiments demonstrate its superior performance in federated settings, particularly with KL divergence and Wasserstein distance-based global aggregation.

Nonstationary Sparse Spectral Permanental Process

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling while reducing computational complexity to the linear level. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance.

TransFeat-TPP: An Interpretable Deep Covariate Temporal Point Processes

The classical temporal point process (TPP) constructs an intensity function by taking the occurrence times into account. Nevertheless, occurrence time may not be the only relevant factor, other contextual data, termed covariates, may also impact the event evolution. Incorporating such covariates into the model is beneficial, while distinguishing their relevance to the event dynamics is of great practical significance. In this work, we propose a Transformer-based covariate temporal point process (TransFeat-TPP) model to improve the interpretability of deep covariate-TPPs while maintaining powerful expressiveness. TransFeat-TPP can effectively model complex relationships between events and covariates, and provide enhanced interpretability by discerning the importance of various covariates. Experimental results on synthetic and real datasets demonstrate improved prediction accuracy and consistently interpretable feature importance when compared to existing deep covariate-TPPs.

ParamReL: Learning Parameter Space Representation via Progressively Encoding Bayesian Flow Networks

The recently proposed Bayesian Flow Networks~(BFNs) show great potential in modeling parameter spaces, offering a unified strategy for handling continuous, discretized, and discrete data. However, BFNs cannot learn high-level semantic representation from the parameter space since {common encoders, which encode data into one static representation, cannot capture semantic changes in parameters.} This motivates a new direction: learning semantic representations hidden in the parameter spaces to characterize mixed-typed noisy data. {Accordingly, we propose a representation learning framework named ParamReL, which operates in the parameter space to obtain parameter-wise latent semantics that exhibit progressive structures. Specifically, ParamReL proposes a \emph{self-}encoder to learn latent semantics directly from parameters, rather than from observations. The encoder is then integrated into BFNs, enabling representation learning with various formats of observations. Mutual information terms further promote the disentanglement of latent semantics and capture meaningful semantics simultaneously.} We illustrate {conditional generation and reconstruction} in ParamReL via expanding BFNs, and extensive {quantitative} experimental results demonstrate the {superior effectiveness} of ParamReL in learning parameter representation.

Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation

Gaussian process factor analysis (GPFA) is a latent variable modeling technique commonly used to identify smooth, low-dimensional latent trajectories underlying high-dimensional neural recordings. Specifically, researchers model spiking rates as Gaussian observations, resulting in tractable inference. Recently, GPFA has been extended to model spike count data. However, due to the non-conjugacy of the likelihood, the inference becomes intractable. Prior works rely on either black-box inference techniques, numerical integration or polynomial approximations of the likelihood to handle intractability. To overcome this challenge, we propose a conditionally-conjugate Gaussian process factor analysis (ccGPFA) resulting in both analytically and computationally tractable inference for modeling neural activity from spike count data. In particular, we develop a novel data augmentation based method that renders the model conditionally conjugate. Consequently, our model enjoys the advantage of simple closed-form updates using a variational EM algorithm. Furthermore, due to its conditional conjugacy, we show our model can be readily scaled using sparse Gaussian Processes and accelerated inference via natural gradients. To validate our method, we empirically demonstrate its efficacy through experiments.

FedSI: Federated Subnetwork Inference for Efficient Uncertainty Quantification

While deep neural networks (DNNs) based personalized federated learning (PFL) is demanding for addressing data heterogeneity and shows promising performance, existing methods for federated learning (FL) suffer from efficient systematic uncertainty quantification. The Bayesian DNNs-based PFL is usually questioned of either over-simplified model structures or high computational and memory costs. In this paper, we introduce FedSI, a novel Bayesian DNNs-based subnetwork inference PFL framework. FedSI is simple and scalable by leveraging Bayesian methods to incorporate systematic uncertainties effectively. It implements a client-specific subnetwork inference mechanism, selects network parameters with large variance to be inferred through posterior distributions, and fixes the rest as deterministic ones. FedSI achieves fast and scalable inference while preserving the systematic uncertainties to the fullest extent. Extensive experiments on three different benchmark datasets demonstrate that FedSI outperforms existing Bayesian and non-Bayesian FL baselines in heterogeneous FL scenarios.

Bayesian Federated Learning: A Survey

Federated learning (FL) demonstrates its advantages in integrating distributed infrastructure, communication, computing and learning in a privacy-preserving manner. However, the robustness and capabilities of existing FL methods are challenged by limited and dynamic data and conditions, complexities including heterogeneities and uncertainties, and analytical explainability. Bayesian federated learning (BFL) has emerged as a promising approach to address these issues. This survey presents a critical overview of BFL, including its basic concepts, its relations to Bayesian learning in the context of FL, and a taxonomy of BFL from both Bayesian and federated perspectives. We categorize and discuss client- and server-side and FL-based BFL methods and their pros and cons. The limitations of the existing BFL methods and the future directions of BFL research further address the intricate requirements of real-life FL applications.

Free-Form Variational Inference for Gaussian Process State-Space Models

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.