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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.

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.

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.

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 with 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 establishes 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.

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.

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.

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.

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.

In the field of behavior-related brain computation, it is necessary to align raw neural signals against the drastic domain shift among them. A foundational framework within neuroscience research posits that trial-based neural population activities rely on low-dimensional latent dynamics, thus focusing on the latter greatly facilitates the alignment procedure. Despite this field's progress, existing methods ignore the intrinsic spatio-temporal structure during the alignment phase. Hence, their solutions usually lead to poor quality in latent dynamics structures and overall performance. To tackle this problem, we propose an alignment method ERDiff, which leverages the expressivity of the diffusion model to preserve the spatio-temporal structure of latent dynamics. Specifically, the latent dynamics structures of the source domain are first extracted by a diffusion model. Then, under the guidance of this diffusion model, such structures are well-recovered through a maximum likelihood alignment procedure in the target domain. We first demonstrate the effectiveness of our proposed method on a synthetic dataset. Then, when applied to neural recordings from the non-human primate motor cortex, under both cross-day and inter-subject settings, our method consistently manifests its capability of preserving the spatiotemporal structure of latent dynamics and outperforms existing approaches in alignment goodness-of-fit and neural decoding performance.

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.

We study the problem of Inverse Reinforcement Learning (IRL) with an average-reward criterion. The goal is to recover an unknown policy and a reward function when the agent only has samples of states and actions from an experienced agent. Previous IRL methods assume that the expert is trained in a discounted environment, and the discount factor is known. This work alleviates this assumption by proposing an average-reward framework with efficient learning algorithms. We develop novel stochastic first-order methods to solve the IRL problem under the average-reward setting, which requires solving an Average-reward Markov Decision Process (AMDP) as a subproblem. To solve the subproblem, we develop a Stochastic Policy Mirror Descent (SPMD) method under general state and action spaces that needs $\mathcal{{O}}(1/\varepsilon)$ steps of gradient computation. Equipped with SPMD, we propose the Inverse Policy Mirror Descent (IPMD) method for solving the IRL problem with a $\mathcal{O}(1/\varepsilon^2)$ complexity. To the best of our knowledge, the aforementioned complexity results are new in IRL. Finally, we corroborate our analysis with numerical experiments using the MuJoCo benchmark and additional control tasks.

The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity. In this paper, we propose a novel nonlinear dimensionality reduction method -- Inverse Kernel Decomposition (IKD) -- based on an eigen-decomposition of the sample covariance matrix of data. The method is inspired by Gaussian process latent variable models (GPLVMs) and has comparable performance with GPLVMs. To deal with very noisy data with weak correlations, we propose two solutions -- blockwise and geodesic -- to make use of locally correlated data points and provide better and numerically more stable latent estimations. We use synthetic datasets and four real-world datasets to show that IKD is a better dimensionality reduction method than other eigen-decomposition-based methods, and achieves comparable performance against optimization-based methods with faster running speeds. Open-source IKD implementation in Python can be accessed at this \url{https://github.com/JerrySoybean/ikd}.

Multi-animal pose estimation is essential for studying animals' social behaviors in neuroscience and neuroethology. Advanced approaches have been proposed to support multi-animal estimation and achieve state-of-the-art performance. However, these models rarely exploit unlabeled data during training even though real world applications have exponentially more unlabeled frames than labeled frames. Manually adding dense annotations for a large number of images or videos is costly and labor-intensive, especially for multiple instances. Given these deficiencies, we propose a novel semi-supervised architecture for multi-animal pose estimation, leveraging the abundant structures pervasive in unlabeled frames in behavior videos to enhance training, which is critical for sparsely-labeled problems. The resulting algorithm will provide superior multi-animal pose estimation results on three animal experiments compared to the state-of-the-art baseline and exhibits more predictive power in sparsely-labeled data regimes., Comment: 10 pages, 7 figures, preprint

Researchers have been facing a difficult problem that data generation mechanisms could be influenced by internal or external factors leading to the training and test data with quite different distributions, consequently traditional classification or regression from the training set is unable to achieve satisfying results on test data. In this paper, we address this nontrivial domain generalization problem by finding a central subspace in which domain-based covariance is minimized while the functional relationship is simultaneously maximally preserved. We propose a novel variance measurement for multiple domains so as to minimize the difference between conditional distributions across domains with solid theoretical demonstration and supports, meanwhile, the algorithm preserves the functional relationship via maximizing the variance of conditional expectations given output. Furthermore, we also provide a fast implementation that requires much less computation and smaller memory for large-scale matrix operations, suitable for not only domain generalization but also other kernel-based eigenvalue decompositions. To show the practicality of the proposed method, we compare our methods against some well-known dimension reduction and domain generalization techniques on both synthetic data and real-world applications. We show that for small-scale datasets, we are able to achieve better quantitative results indicating better generalization performance over unseen test datasets. For large-scale problems, the proposed fast implementation maintains the quantitative performance but at a substantially lower computational cost.

Advances in neural recording present increasing opportunities to study neural activity in unprecedented detail. Latent variable models (LVMs) are promising tools for analyzing this rich activity across diverse neural systems and behaviors, as LVMs do not depend on known relationships between the activity and external experimental variables. However, progress with LVMs for neuronal population activity is currently impeded by a lack of standardization, resulting in methods being developed and compared in an ad hoc manner. To coordinate these modeling efforts, we introduce a benchmark suite for latent variable modeling of neural population activity. We curate four datasets of neural spiking activity from cognitive, sensory, and motor areas to promote models that apply to the wide variety of activity seen across these areas. We identify unsupervised evaluation as a common framework for evaluating models across datasets, and apply several baselines that demonstrate benchmark diversity. We release this benchmark through EvalAI. http://neurallatents.github.io

With the wide adoption of functional magnetic resonance imaging (fMRI) by cognitive neuroscience researchers, large volumes of brain imaging data have been accumulated in recent years. Aggregating these data to derive scientific insights often faces the challenge that fMRI data are high-dimensional, heterogeneous across people, and noisy. These challenges demand the development of computational tools that are tailored both for the neuroscience questions and for the properties of the data. We review a few recently developed algorithms in various domains of fMRI research: fMRI in naturalistic tasks, analyzing full-brain functional connectivity, pattern classification, inferring representational similarity and modeling structured residuals. These algorithms all tackle the challenges in fMRI similarly: they start by making clear statements of assumptions about neural data and existing domain knowledge, incorporating those assumptions and domain knowledge into probabilistic graphical models, and using those models to estimate properties of interest or latent structures in the data. Such approaches can avoid erroneous findings, reduce the impact of noise, better utilize known properties of the data, and better aggregate data across groups of subjects. With these successful cases, we advocate wider adoption of explicit model construction in cognitive neuroscience. Although we focus on fMRI, the principle illustrated here is generally applicable to brain data of other modalities., Comment: update with the version accepted by Neuropsychologia

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent trajectories. However, simple state transition structures, linear embedding assumptions, or inflexible inference networks impede the accurate recovery of dynamic portraits. In this paper, we propose a novel latent dynamic model that is capable of capturing nonlinear, non-Markovian, long short-term time-dependent dynamics via recurrent neural networks and tackling complex nonlinear embedding via non-parametric Gaussian process. Due to the complexity and intractability of the model and its inference, we also provide a powerful inference network with bi-directional long short-term memory networks that encode both past and future information into posterior distributions. In the experiment, we show that our model outperforms other state-of-the-art methods in reconstructing insightful latent dynamics from both simulated and experimental neural datasets with either Gaussian or Poisson observations, especially in the low-sample scenario. Our codes and additional materials are available at https://github.com/sheqi/GP-RNN_UAI2019., Comment: 11 pages, 3 figures, 7 Tables, accepted to The Conference on Uncertainty in Artificial Intelligence (UAI), 2019

Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We provide two innovations that aim to turn VB into a robust inference tool for Bayesian neural networks: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel Empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate good predictive performance over alternative approaches.

In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), which model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop Laplace approximation and Monte Carlo Markov Chain (MCMC) sampling to provide efficient inference for the posterior. Furthermore, a two-stage convex relaxation of the Laplace approximation approach is also provided to relax the inevitable non-convexity during the optimization. We finally show substantial improvements over comparable methods for both simulated and real datasets from brain imaging., Comment: 42 pages, 15 figures, submitted to JMLR