Markovian Gaussian Process: A Universal State-Space Representation for Stationary Temporal Gaussian Process

Gaussian Processes (GPs) and Linear Dynamical Systems (LDSs) are essential time series and dynamic system modeling tools. GPs can handle complex, nonlinear dynamics but are computationally demanding, while LDSs offer efficient computation but lack the expressive power of GPs. To combine their benefits, we introduce a universal method that allows an LDS to mirror stationary temporal GPs. This state-space representation, known as the Markovian Gaussian Process (Markovian GP), leverages the flexibility of kernel functions while maintaining efficient linear computation. Unlike existing GP-LDS conversion methods, which require separability for most multi-output kernels, our approach works universally for single- and multi-output stationary temporal kernels. We evaluate our method by computing covariance, performing regression tasks, and applying it to a neuroscience application, demonstrating that our method provides an accurate state-space representation for stationary temporal GPs.

NAP^2: A Benchmark for Naturalness and Privacy-Preserving Text Rewriting by Learning from Human

Increasing concerns about privacy leakage issues in academia and industry arise when employing NLP models from third-party providers to process sensitive texts. To protect privacy before sending sensitive data to those models, we suggest sanitizing sensitive text using two common strategies used by humans: i) deleting sensitive expressions, and ii) obscuring sensitive details by abstracting them. To explore the issues and develop a tool for text rewriting, we curate the first corpus, coined NAP^2, through both crowdsourcing and the use of large language models (LLMs). Compared to the prior works based on differential privacy, which lead to a sharp drop in information utility and unnatural texts, the human-inspired approaches result in more natural rewrites and offer an improved balance between privacy protection and data utility, as demonstrated by our extensive experiments.

Learn to Teach: Improve Sample Efficiency in Teacher-student Learning for Sim-to-Real Transfer

Simulation-to-reality (sim-to-real) transfer is a fundamental problem for robot learning. Domain Randomization, which adds randomization during training, is a powerful technique that effectively addresses the sim-to-real gap. However, the noise in observations makes learning significantly harder. Recently, studies have shown that employing a teacher-student learning paradigm can accelerate training in randomized environments. Learned with privileged information, a teacher agent can instruct the student agent to operate in noisy environments. However, this approach is often not sample efficient as the experience collected by the teacher is discarded completely when training the student, wasting information revealed by the environment. In this work, we extend the teacher-student learning paradigm by proposing a sample efficient learning framework termed Learn to Teach (L2T) that recycles experience collected by the teacher agent. We observe that the dynamics of the environments for both agents remain unchanged, and the state space of the teacher is coupled with the observation space of the student. We show that a single-loop algorithm can train both the teacher and student agents under both Reinforcement Learning and Inverse Reinforcement Learning contexts. We implement variants of our methods, conduct experiments on the MuJoCo benchmark, and apply our methods to the Cassie robot locomotion problem. Extensive experiments show that our method achieves competitive performance while only requiring environmental interaction with the teacher.

A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing

The partially observable generalized linear model (POGLM) is a powerful tool for understanding neural connectivity under the assumption of existing hidden neurons. With spike trains only recorded from visible neurons, existing works use variational inference to learn POGLM meanwhile presenting the difficulty of learning this latent variable model. There are two main issues: (1) the sampled Poisson hidden spike count hinders the use of the pathwise gradient estimator in VI; and (2) the existing design of the variational model is neither expressive nor time-efficient, which further affects the performance. For (1), we propose a new differentiable POGLM, which enables the pathwise gradient estimator, better than the score function gradient estimator used in existing works. For (2), we propose the forward-backward message-passing sampling scheme for the variational model. Comprehensive experiments show that our differentiable POGLMs with our forward-backward message passing produce a better performance on one synthetic and two real-world datasets. Furthermore, our new method yields more interpretable parameters, underscoring its significance in neuroscience.

Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions

Studying the complex interactions between different brain regions is crucial in neuroscience. Various statistical methods have explored the latent communication across multiple brain regions. Two main categories are the Gaussian Process (GP) and Linear Dynamical System (LDS), each with unique strengths. The GP-based approach effectively discovers latent variables such as frequency bands and communication directions. Conversely, the LDS-based approach is computationally efficient but lacks powerful expressiveness in latent representation. In this study, we merge both methodologies by creating an LDS mirroring a multi-output GP, termed Multi-Region Markovian Gaussian Process (MRM-GP). Our work is the first to establish a connection between an LDS and a multi-output GP that explicitly models frequencies and phase delays within the latent space of neural recordings. Consequently, the model achieves a linear inference cost over time points and provides an interpretable low-dimensional representation, revealing communication directions across brain regions and separating oscillatory communications into different frequency bands.

Forward $χ^2$ Divergence Based Variational Importance Sampling

Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

One-hot Generalized Linear Model for Switching Brain State Discovery

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

Infer and Adapt: Bipedal Locomotion Reward Learning from Demonstrations via Inverse Reinforcement Learning

Enabling bipedal walking robots to learn how to maneuver over highly uneven, dynamically changing terrains is challenging due to the complexity of robot dynamics and interacted environments. Recent advancements in learning from demonstrations have shown promising results for robot learning in complex environments. While imitation learning of expert policies has been well-explored, the study of learning expert reward functions is largely under-explored in legged locomotion. This paper brings state-of-the-art Inverse Reinforcement Learning (IRL) techniques to solving bipedal locomotion problems over complex terrains. We propose algorithms for learning expert reward functions, and we subsequently analyze the learned functions. Through nonlinear function approximation, we uncover meaningful insights into the expert's locomotion strategies. Furthermore, we empirically demonstrate that training a bipedal locomotion policy with the inferred reward functions enhances its walking performance on unseen terrains, highlighting the adaptability offered by reward learning.

Extraction and Recovery of Spatio-Temporal Structure in Latent Dynamics Alignment with Diffusion Model

In the field of behavior-related brain computation, it is necessary to meaningfully align raw neural population activities against the drastic shift between them. However, the alignment is non-trivial since most neural population activities are in a multivariate time-series manner. An instrumental framework within neuroscience research posits that trial-based neural population activities rely on low-dimensional latent dynamics. Focusing on such latent dynamics greatly facilitates the alignment procedure. Despite the considerable progress we have reached, existing methods usually ignore the intrinsic spatio-temporal structures within latent dynamics. Thus, those solutions lead to poor quality in dynamics structures and overall performance after alignment. To tackle this problem, we propose a method leveraging the expressiveness of diffusion model to relieve such issues. Specifically, the latent dynamics structures of the source domain are first extracted by the diffusion model. Then, such structures are well-recovered through a maximum likelihood alignment procedure on the target domain. We first demonstrate the effectiveness of our proposed method on a synthetic dataset. Then, when applied to neural recordings from primate motor cortex, under both cross-day and inter-subject settings, our method consistently manifests its capability of preserving the spatio-temporal structure of latent dynamics and outperforms existing approaches in alignment quality.

JGAT: a joint spatio-temporal graph attention model for brain decoding

The decoding of brain neural networks has been an intriguing topic in neuroscience for a well-rounded understanding of different types of brain disorders and cognitive stimuli. Integrating different types of connectivity, e.g., Functional Connectivity (FC) and Structural Connectivity (SC), from multi-modal imaging techniques can take their complementary information into account and therefore have the potential to get better decoding capability. However, traditional approaches for integrating FC and SC overlook the dynamical variations, which stand a great chance to over-generalize the brain neural network. In this paper, we propose a Joint kernel Graph Attention Network (JGAT), which is a new multi-modal temporal graph attention network framework. It integrates the data from functional Magnetic Resonance Images (fMRI) and Diffusion Weighted Imaging (DWI) while preserving the dynamic information at the same time. We conduct brain-decoding tasks with our JGAT on four independent datasets: three of 7T fMRI datasets from the Human Connectome Project (HCP) and one from animal neural recordings. Furthermore, with Attention Scores (AS) and Frame Scores (FS) computed and learned from the model, we can locate several informative temporal segments and build meaningful dynamical pathways along the temporal domain for the HCP datasets. The URL to the code of JGAT model: https://github.com/BRAINML-GT/JGAT.